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toggleContents.style.height = \"0px\";\n\n tocShowing = false;\n\n }\n\n };\n\n\n\n \/\/ Get rid of any expanded toggle if the user scrolls\n\n window.document.addEventListener(\n\n \"scroll\",\n\n throttle(() => {\n\n closeToggle();\n\n }, 50)\n\n );\n\n\n\n \/\/ Handle positioning of the toggle\n\n window.addEventListener(\n\n \"resize\",\n\n throttle(() => {\n\n elRect = undefined;\n\n positionToggle();\n\n }, 50)\n\n );\n\n\n\n window.addEventListener(\"quarto-hrChanged\", () => {\n\n elRect = undefined;\n\n });\n\n\n\n \/\/ Process the click\n\n clickEl.onclick = () => {\n\n if (!tocShowing) {\n\n toggleContainer.classList.add(\"expanded\");\n\n toggleContents.style.height = null;\n\n tocShowing = true;\n\n } else {\n\n closeToggle();\n\n }\n\n };\n\n });\n\n };\n\n\n\n \/\/ Converts a sidebar from a menu back to a sidebar\n\n const convertToSidebar = () => {\n\n for (const child of el.children) {\n\n child.style.opacity = 1;\n\n child.style.overflow = null;\n\n }\n\n\n\n const placeholderEl = window.document.getElementById(\n\n placeholderDescriptor.id\n\n );\n\n if (placeholderEl) {\n\n placeholderEl.remove();\n\n }\n\n\n\n el.classList.remove(\"rollup\");\n\n };\n\n\n\n if (isReaderMode()) {\n\n convertToMenu();\n\n isVisible = false;\n\n } else {\n\n \/\/ Find the top and bottom o the element that is being managed\n\n const elTop = el.offsetTop;\n\n const elBottom =\n\n elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight;\n\n\n\n if (!isVisible) {\n\n \/\/ If the element is current not visible reveal if there are\n\n \/\/ no conflicts with overlay regions\n\n if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) {\n\n convertToSidebar();\n\n isVisible = true;\n\n }\n\n } else {\n\n \/\/ If the element is visible, hide it if it conflicts with overlay regions\n\n \/\/ and insert a placeholder toggle (or if we're in reader mode)\n\n if (inHiddenRegion(elTop, elBottom, hiddenRegions)) {\n\n convertToMenu();\n\n isVisible = false;\n\n }\n\n }\n\n }\n\n }\n\n };\n\n };\n\n\n\n const tabEls = document.querySelectorAll('a[data-bs-toggle=\"tab\"]');\n\n for (const tabEl of tabEls) {\n\n const id = tabEl.getAttribute(\"data-bs-target\");\n\n if (id) {\n\n const columnEl = document.querySelector(\n\n `${id} .column-margin, .tabset-margin-content`\n\n );\n\n if (columnEl)\n\n tabEl.addEventListener(\"shown.bs.tab\", function (event) {\n\n const el = event.srcElement;\n\n if (el) {\n\n const visibleCls = `${el.id}-margin-content`;\n\n \/\/ walk up until we find a parent tabset\n\n let panelTabsetEl = el.parentElement;\n\n while (panelTabsetEl) {\n\n if (panelTabsetEl.classList.contains(\"panel-tabset\")) {\n\n break;\n\n }\n\n panelTabsetEl = panelTabsetEl.parentElement;\n\n }\n\n\n\n if (panelTabsetEl) {\n\n const prevSib = panelTabsetEl.previousElementSibling;\n\n if (\n\n prevSib &&\n\n prevSib.classList.contains(\"tabset-margin-container\")\n\n ) {\n\n const childNodes = prevSib.querySelectorAll(\n\n \".tabset-margin-content\"\n\n );\n\n for (const childEl of childNodes) {\n\n if (childEl.classList.contains(visibleCls)) {\n\n childEl.classList.remove(\"collapse\");\n\n } else {\n\n childEl.classList.add(\"collapse\");\n\n }\n\n }\n\n }\n\n }\n\n }\n\n\n\n layoutMarginEls();\n\n });\n\n }\n\n }\n\n\n\n \/\/ Manage the visibility of the toc and the sidebar\n\n const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, {\n\n id: \"quarto-toc-toggle\",\n\n titleSelector: \"#toc-title\",\n\n dismissOnClick: true,\n\n });\n\n const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, {\n\n id: \"quarto-sidebarnav-toggle\",\n\n titleSelector: \".title\",\n\n dismissOnClick: false,\n\n });\n\n let tocLeftScrollVisibility;\n\n if (leftTocEl) {\n\n tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, {\n\n id: \"quarto-lefttoc-toggle\",\n\n titleSelector: \"#toc-title\",\n\n dismissOnClick: true,\n\n });\n\n }\n\n\n\n \/\/ Find the first element that uses formatting in special columns\n\n const conflictingEls = window.document.body.querySelectorAll(\n\n '[class^=\"column-\"], [class*=\" column-\"], aside, [class*=\"margin-caption\"], [class*=\" margin-caption\"], [class*=\"margin-ref\"], [class*=\" margin-ref\"]'\n\n );\n\n\n\n \/\/ Filter all the possibly conflicting elements into ones\n\n \/\/ the do conflict on the left or ride side\n\n const arrConflictingEls = Array.from(conflictingEls);\n\n const leftSideConflictEls = arrConflictingEls.filter((el) => {\n\n if (el.tagName === \"ASIDE\") {\n\n return false;\n\n }\n\n return Array.from(el.classList).find((className) => {\n\n return (\n\n className !== \"column-body\" &&\n\n className.startsWith(\"column-\") &&\n\n !className.endsWith(\"right\") &&\n\n !className.endsWith(\"container\") &&\n\n className !== \"column-margin\"\n\n );\n\n });\n\n });\n\n const rightSideConflictEls = arrConflictingEls.filter((el) => {\n\n if (el.tagName === \"ASIDE\") {\n\n return true;\n\n }\n\n\n\n const hasMarginCaption = Array.from(el.classList).find((className) => {\n\n return className == \"margin-caption\";\n\n });\n\n if (hasMarginCaption) {\n\n return true;\n\n }\n\n\n\n return Array.from(el.classList).find((className) => {\n\n return (\n\n className !== \"column-body\" &&\n\n !className.endsWith(\"container\") &&\n\n className.startsWith(\"column-\") &&\n\n !className.endsWith(\"left\")\n\n );\n\n });\n\n });\n\n\n\n const kOverlapPaddingSize = 10;\n\n function toRegions(els) {\n\n return els.map((el) => {\n\n const boundRect = el.getBoundingClientRect();\n\n const top =\n\n boundRect.top +\n\n document.documentElement.scrollTop -\n\n kOverlapPaddingSize;\n\n return {\n\n top,\n\n bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize,\n\n };\n\n });\n\n }\n\n\n\n let hasObserved = false;\n\n const visibleItemObserver = (els) => {\n\n let visibleElements = [...els];\n\n const intersectionObserver = new IntersectionObserver(\n\n (entries, _observer) => {\n\n entries.forEach((entry) => {\n\n if (entry.isIntersecting) {\n\n if (visibleElements.indexOf(entry.target) === -1) {\n\n visibleElements.push(entry.target);\n\n }\n\n } else {\n\n visibleElements = visibleElements.filter((visibleEntry) => {\n\n return visibleEntry !== entry;\n\n });\n\n }\n\n });\n\n\n\n if (!hasObserved) {\n\n hideOverlappedSidebars();\n\n }\n\n hasObserved = true;\n\n },\n\n {}\n\n );\n\n els.forEach((el) => {\n\n intersectionObserver.observe(el);\n\n });\n\n\n\n return {\n\n getVisibleEntries: () => {\n\n return visibleElements;\n\n },\n\n };\n\n };\n\n\n\n const rightElementObserver = visibleItemObserver(rightSideConflictEls);\n\n const leftElementObserver = visibleItemObserver(leftSideConflictEls);\n\n\n\n const hideOverlappedSidebars = () => {\n\n marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries()));\n\n sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries()));\n\n if (tocLeftScrollVisibility) {\n\n tocLeftScrollVisibility(\n\n toRegions(leftElementObserver.getVisibleEntries())\n\n );\n\n }\n\n };\n\n\n\n window.quartoToggleReader = () => {\n\n \/\/ Applies a slow class (or removes it)\n\n \/\/ to update the transition speed\n\n const slowTransition = (slow) => {\n\n const manageTransition = (id, slow) => {\n\n const el = document.getElementById(id);\n\n if (el) {\n\n if (slow) {\n\n el.classList.add(\"slow\");\n\n } else {\n\n el.classList.remove(\"slow\");\n\n }\n\n }\n\n };\n\n\n\n manageTransition(\"TOC\", slow);\n\n manageTransition(\"quarto-sidebar\", slow);\n\n };\n\n const readerMode = !isReaderMode();\n\n setReaderModeValue(readerMode);\n\n\n\n \/\/ If we're entering reader mode, slow the transition\n\n if (readerMode) {\n\n slowTransition(readerMode);\n\n }\n\n highlightReaderToggle(readerMode);\n\n hideOverlappedSidebars();\n\n\n\n \/\/ If we're exiting reader mode, restore the non-slow transition\n\n if (!readerMode) {\n\n slowTransition(!readerMode);\n\n }\n\n };\n\n\n\n const highlightReaderToggle = (readerMode) => {\n\n const els = document.querySelectorAll(\".quarto-reader-toggle\");\n\n if (els) {\n\n els.forEach((el) => {\n\n if (readerMode) {\n\n el.classList.add(\"reader\");\n\n } else {\n\n el.classList.remove(\"reader\");\n\n }\n\n });\n\n }\n\n };\n\n\n\n const setReaderModeValue = (val) => {\n\n if (window.location.protocol !== \"file:\") {\n\n window.localStorage.setItem(\"quarto-reader-mode\", val);\n\n } else {\n\n localReaderMode = val;\n\n }\n\n };\n\n\n\n const isReaderMode = () => {\n\n if (window.location.protocol !== \"file:\") {\n\n return window.localStorage.getItem(\"quarto-reader-mode\") === \"true\";\n\n } else {\n\n return localReaderMode;\n\n }\n\n };\n\n let localReaderMode = null;\n\n\n\n const tocOpenDepthStr = tocEl?.getAttribute(\"data-toc-expanded\");\n\n const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1;\n\n\n\n \/\/ Walk the TOC and collapse\/expand nodes\n\n \/\/ Nodes are expanded if:\n\n \/\/ - they are top level\n\n \/\/ - they have children that are 'active' links\n\n \/\/ - they are directly below an link that is 'active'\n\n const walk = (el, depth) => {\n\n \/\/ Tick depth when we enter a UL\n\n if (el.tagName === \"UL\") {\n\n depth = depth + 1;\n\n }\n\n\n\n \/\/ It this is active link\n\n let isActiveNode = false;\n\n if (el.tagName === \"A\" && el.classList.contains(\"active\")) {\n\n isActiveNode = true;\n\n }\n\n\n\n \/\/ See if there is an active child to this element\n\n let hasActiveChild = false;\n\n for (child of el.children) {\n\n hasActiveChild = walk(child, depth) || hasActiveChild;\n\n }\n\n\n\n \/\/ Process the collapse state if this is an UL\n\n if (el.tagName === \"UL\") {\n\n if (tocOpenDepth === -1 && depth > 1) {\n\n el.classList.add(\"collapse\");\n\n } else if (\n\n depth <= tocOpenDepth ||\n\n hasActiveChild ||\n\n prevSiblingIsActiveLink(el)\n\n ) {\n\n el.classList.remove(\"collapse\");\n\n } else {\n\n el.classList.add(\"collapse\");\n\n }\n\n\n\n \/\/ untick depth when we leave a UL\n\n depth = depth - 1;\n\n }\n\n return hasActiveChild || isActiveNode;\n\n };\n\n\n\n \/\/ walk the TOC and expand \/ collapse any items that should be shown\n\n\n\n if (tocEl) {\n\n walk(tocEl, 0);\n\n updateActiveLink();\n\n }\n\n\n\n \/\/ Throttle the scroll event and walk peridiocally\n\n window.document.addEventListener(\n\n \"scroll\",\n\n throttle(() => {\n\n if (tocEl) {\n\n updateActiveLink();\n\n walk(tocEl, 0);\n\n }\n\n if (!isReaderMode()) {\n\n hideOverlappedSidebars();\n\n }\n\n }, 5)\n\n );\n\n window.addEventListener(\n\n \"resize\",\n\n throttle(() => {\n\n if (!isReaderMode()) {\n\n hideOverlappedSidebars();\n\n }\n\n }, 10)\n\n );\n\n hideOverlappedSidebars();\n\n highlightReaderToggle(isReaderMode());\n\n});\n\n\n\n\/\/ grouped tabsets\n\nwindow.addEventListener(\"pageshow\", (_event) => {\n\n function getTabSettings() {\n\n const data = localStorage.getItem(\"quarto-persistent-tabsets-data\");\n\n if (!data) {\n\n localStorage.setItem(\"quarto-persistent-tabsets-data\", \"{}\");\n\n return {};\n\n }\n\n if (data) {\n\n return JSON.parse(data);\n\n }\n\n }\n\n\n\n function setTabSettings(data) {\n\n localStorage.setItem(\n\n \"quarto-persistent-tabsets-data\",\n\n JSON.stringify(data)\n\n );\n\n }\n\n\n\n function setTabState(groupName, groupValue) {\n\n const data = getTabSettings();\n\n data[groupName] = groupValue;\n\n setTabSettings(data);\n\n }\n\n\n\n function toggleTab(tab, active) {\n\n const tabPanelId = tab.getAttribute(\"aria-controls\");\n\n const tabPanel = document.getElementById(tabPanelId);\n\n if (active) {\n\n tab.classList.add(\"active\");\n\n tabPanel.classList.add(\"active\");\n\n } else {\n\n tab.classList.remove(\"active\");\n\n tabPanel.classList.remove(\"active\");\n\n }\n\n }\n\n\n\n function toggleAll(selectedGroup, selectorsToSync) {\n\n for 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Object.keys(f).sort((function(t,e){return f[t]-f[e]}))}const si={name:\"flip\",enabled:!0,phase:\"main\",fn:function(t){var e=t.state,i=t.options,n=t.name;if(!e.modifiersData[n]._skip){for(var s=i.mainAxis,o=void 0===s||s,r=i.altAxis,a=void 0===r||r,l=i.fallbackPlacements,c=i.padding,h=i.boundary,d=i.rootBoundary,u=i.altBoundary,f=i.flipVariations,p=void 0===f||f,m=i.allowedAutoPlacements,g=e.options.placement,_=be(g),b=l||(_!==g&&p?function(t){if(be(t)===Kt)return[];var e=Ve(t);return[Qe(t),e,Qe(e)]}(g):[Ve(g)]),v=[g].concat(b).reduce((function(t,i){return t.concat(be(i)===Kt?ni(e,{placement:i,boundary:h,rootBoundary:d,padding:c,flipVariations:p,allowedAutoPlacements:m}):i)}),[]),y=e.rects.reference,w=e.rects.popper,A=new Map,E=!0,T=v[0],C=0;C<v.length;C++){var O=v[C],x=be(O),k=Fe(O)===Xt,L=[zt,Rt].indexOf(x)>=0,S=L?\"width\":\"height\",D=ii(e,{placement:O,boundary:h,rootBoundary:d,altBoundary:u,padding:c}),$=L?k?qt:Vt:k?Rt:zt;y[S]>w[S]&&($=Ve($));var 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e=t.state,i=t.name,n=e.rects.reference,s=e.rects.popper,o=e.modifiersData.preventOverflow,r=ii(e,{elementContext:\"reference\"}),a=ii(e,{altBoundary:!0}),l=oi(r,n),c=oi(a,s,o),h=ri(l),d=ri(c);e.modifiersData[i]={referenceClippingOffsets:l,popperEscapeOffsets:c,isReferenceHidden:h,hasPopperEscaped:d},e.attributes.popper=Object.assign({},e.attributes.popper,{\"data-popper-reference-hidden\":h,\"data-popper-escaped\":d})}},li={name:\"offset\",enabled:!0,phase:\"main\",requires:[\"popperOffsets\"],fn:function(t){var e=t.state,i=t.options,n=t.name,s=i.offset,o=void 0===s?[0,0]:s,r=ee.reduce((function(t,i){return t[i]=function(t,e,i){var n=be(t),s=[Vt,zt].indexOf(n)>=0?-1:1,o=\"function\"==typeof i?i(Object.assign({},e,{placement:t})):i,r=o[0],a=o[1];return 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vi=Object.freeze(Object.defineProperty({__proto__:null,afterMain:ae,afterRead:se,afterWrite:he,applyStyles:_e,arrow:je,auto:Kt,basePlacements:Qt,beforeMain:oe,beforeRead:ie,beforeWrite:le,bottom:Rt,clippingParents:Ut,computeStyles:Be,createPopper:bi,createPopperBase:gi,createPopperLite:_i,detectOverflow:ii,end:Yt,eventListeners:Re,flip:si,hide:ai,left:Vt,main:re,modifierPhases:de,offset:li,placements:ee,popper:Jt,popperGenerator:mi,popperOffsets:ci,preventOverflow:hi,read:ne,reference:Zt,right:qt,start:Xt,top:zt,variationPlacements:te,viewport:Gt,write:ce},Symbol.toStringTag,{value:\"Module\"})),yi=\"dropdown\",wi=\".bs.dropdown\",Ai=\".data-api\",Ei=\"ArrowUp\",Ti=\"ArrowDown\",Ci=`hide${wi}`,Oi=`hidden${wi}`,xi=`show${wi}`,ki=`shown${wi}`,Li=`click${wi}${Ai}`,Si=`keydown${wi}${Ai}`,Di=`keyup${wi}${Ai}`,$i=\"show\",Ii='[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)',Ni=`${Ii}.${$i}`,Pi=\".dropdown-menu\",Mi=p()?\"top-end\":\"top-start\",ji=p()?\"top-start\":\"top-end\",Fi=p()?\"bottom-end\":\"bottom-start\",Hi=p()?\"bottom-start\":\"bottom-end\",Wi=p()?\"left-start\":\"right-start\",Bi=p()?\"right-start\":\"left-start\",zi={autoClose:!0,boundary:\"clippingParents\",display:\"dynamic\",offset:[0,2],popperConfig:null,reference:\"toggle\"},Ri={autoClose:\"(boolean|string)\",boundary:\"(string|element)\",display:\"string\",offset:\"(array|string|function)\",popperConfig:\"(null|object|function)\",reference:\"(string|element|object)\"};class qi extends W{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=z.next(this._element,Pi)[0]||z.prev(this._element,Pi)[0]||z.findOne(Pi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return zi}static get DefaultType(){return Ri}static get NAME(){return yi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(l(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!N.trigger(this._element,xi,t).defaultPrevented){if(this._createPopper(),\"ontouchstart\"in document.documentElement&&!this._parent.closest(\".navbar-nav\"))for(const t of[].concat(...document.body.children))N.on(t,\"mouseover\",h);this._element.focus(),this._element.setAttribute(\"aria-expanded\",!0),this._menu.classList.add($i),this._element.classList.add($i),N.trigger(this._element,ki,t)}}hide(){if(l(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!N.trigger(this._element,Ci,t).defaultPrevented){if(\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,\"mouseover\",h);this._popper&&this._popper.destroy(),this._menu.classList.remove($i),this._element.classList.remove($i),this._element.setAttribute(\"aria-expanded\",\"false\"),F.removeDataAttribute(this._menu,\"popper\"),N.trigger(this._element,Oi,t)}}_getConfig(t){if(\"object\"==typeof(t=super._getConfig(t)).reference&&!o(t.reference)&&\"function\"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${yi.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`);return t}_createPopper(){if(void 0===vi)throw new TypeError(\"Bootstrap's dropdowns require Popper (https:\/\/popper.js.org)\");let t=this._element;\"parent\"===this._config.reference?t=this._parent:o(this._config.reference)?t=r(this._config.reference):\"object\"==typeof this._config.reference&&(t=this._config.reference);const e=this._getPopperConfig();this._popper=bi(t,this._menu,e)}_isShown(){return this._menu.classList.contains($i)}_getPlacement(){const t=this._parent;if(t.classList.contains(\"dropend\"))return Wi;if(t.classList.contains(\"dropstart\"))return Bi;if(t.classList.contains(\"dropup-center\"))return\"top\";if(t.classList.contains(\"dropdown-center\"))return\"bottom\";const e=\"end\"===getComputedStyle(this._menu).getPropertyValue(\"--bs-position\").trim();return t.classList.contains(\"dropup\")?e?ji:Mi:e?Hi:Fi}_detectNavbar(){return null!==this._element.closest(\".navbar\")}_getOffset(){const{offset:t}=this._config;return\"string\"==typeof t?t.split(\",\").map((t=>Number.parseInt(t,10))):\"function\"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:\"preventOverflow\",options:{boundary:this._config.boundary}},{name:\"offset\",options:{offset:this._getOffset()}}]};return(this._inNavbar||\"static\"===this._config.display)&&(F.setDataAttribute(this._menu,\"popper\",\"static\"),t.modifiers=[{name:\"applyStyles\",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(\".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)\",this._menu).filter((t=>a(t)));i.length&&b(i,e,t===Ti,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=qi.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===e[t])throw new TypeError(`No method named \"${t}\"`);e[t]()}}))}static clearMenus(t){if(2===t.button||\"keyup\"===t.type&&\"Tab\"!==t.key)return;const e=z.find(Ni);for(const i of e){const e=qi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||\"inside\"===e._config.autoClose&&!s||\"outside\"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&(\"keyup\"===t.type&&\"Tab\"===t.key||\/input|select|option|textarea|form\/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};\"click\"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=\/input|textarea\/i.test(t.target.tagName),i=\"Escape\"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi=\"backdrop\",Ki=\"show\",Qi=`mousedown.bs.${Vi}`,Xi={className:\"modal-backdrop\",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:\"body\"},Yi={className:\"string\",clickCallback:\"(function|null)\",isAnimated:\"boolean\",isVisible:\"boolean\",rootElement:\"(element|string)\"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement(\"div\");t.className=this._config.className,this._config.isAnimated&&t.classList.add(\"fade\"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=\".bs.focustrap\",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn=\"backward\",en={autofocus:!0,trapElement:null},nn={autofocus:\"boolean\",trapElement:\"element\"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return\"focustrap\"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){\"Tab\"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:\"forward\")}}const on=\".fixed-top, .fixed-bottom, .is-fixed, .sticky-top\",rn=\".sticky-top\",an=\"padding-right\",ln=\"margin-right\";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,\"overflow\"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,\"overflow\"),this._element.style.overflow=\"hidden\"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=\".bs.modal\",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn=\"modal-open\",An=\"show\",En=\"modal-static\",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:\"(boolean|string)\",focus:\"boolean\",keyboard:\"boolean\"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(\".modal-dialog\",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return\"modal\"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display=\"block\",this._element.removeAttribute(\"aria-hidden\"),this._element.setAttribute(\"aria-modal\",!0),this._element.setAttribute(\"role\",\"dialog\"),this._element.scrollTop=0;const e=z.findOne(\".modal-body\",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{\"Escape\"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&(\"static\"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display=\"none\",this._element.setAttribute(\"aria-hidden\",!0),this._element.removeAttribute(\"aria-modal\"),this._element.removeAttribute(\"role\"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains(\"fade\")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;\"hidden\"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY=\"hidden\"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?\"paddingLeft\":\"paddingRight\";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?\"paddingRight\":\"paddingLeft\";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft=\"\",this._element.style.paddingRight=\"\"}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===i[t])throw new TypeError(`No method named \"${t}\"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle=\"modal\"]',(function(t){const e=z.getElementFromSelector(this);[\"A\",\"AREA\"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(\".modal.show\");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=\".bs.offcanvas\",kn=\".data-api\",Ln=`load${xn}${kn}`,Sn=\"show\",Dn=\"showing\",$n=\"hiding\",In=\".offcanvas.show\",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:\"(boolean|string)\",keyboard:\"boolean\",scroll:\"boolean\"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return\"offcanvas\"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute(\"aria-modal\",!0),this._element.setAttribute(\"role\",\"dialog\"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute(\"aria-modal\"),this._element.removeAttribute(\"role\"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:\"offcanvas-backdrop\",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{\"static\"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{\"Escape\"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===e[t]||t.startsWith(\"_\")||\"constructor\"===t)throw new TypeError(`No method named \"${t}\"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle=\"offcanvas\"]',(function(t){const e=z.getElementFromSelector(this);if([\"A\",\"AREA\"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find(\"[aria-modal][class*=show][class*=offcanvas-]\"))\"fixed\"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={\"*\":[\"class\",\"dir\",\"id\",\"lang\",\"role\",\/^aria-[\\w-]*$\/i],a:[\"target\",\"href\",\"title\",\"rel\"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:[\"src\",\"srcset\",\"alt\",\"title\",\"width\",\"height\"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set([\"background\",\"cite\",\"href\",\"itemtype\",\"longdesc\",\"poster\",\"src\",\"xlink:href\"]),Qn=\/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:\/?#]*(?:[\/?#]|$))\/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:\"\",html:!1,sanitize:!0,sanitizeFn:null,template:\"<div><\/div>\"},Un={allowList:\"object\",content:\"object\",extraClass:\"(string|function)\",html:\"boolean\",sanitize:\"boolean\",sanitizeFn:\"(null|function)\",template:\"string\"},Gn={entry:\"(string|element|function|null)\",selector:\"(string|element)\"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return\"TemplateFactory\"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement(\"div\");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(\" \")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&\"function\"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,\"text\/html\"),s=[].concat(...n.body.querySelectorAll(\"*\"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e[\"*\"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML=\"\",void e.append(t);e.textContent=t.textContent}}const Zn=new Set([\"sanitize\",\"allowList\",\"sanitizeFn\"]),ts=\"fade\",es=\"show\",is=\".modal\",ns=\"hide.bs.modal\",ss=\"hover\",os=\"focus\",rs={AUTO:\"auto\",TOP:\"top\",RIGHT:p()?\"left\":\"right\",BOTTOM:\"bottom\",LEFT:p()?\"right\":\"left\"},as={allowList:Vn,animation:!0,boundary:\"clippingParents\",container:!1,customClass:\"\",delay:0,fallbackPlacements:[\"top\",\"right\",\"bottom\",\"left\"],html:!1,offset:[0,6],placement:\"top\",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'<div class=\"tooltip\" role=\"tooltip\"><div class=\"tooltip-arrow\"><\/div><div class=\"tooltip-inner\"><\/div><\/div>',title:\"\",trigger:\"hover focus\"},ls={allowList:\"object\",animation:\"boolean\",boundary:\"(string|element)\",container:\"(string|element|boolean)\",customClass:\"(string|function)\",delay:\"(number|object)\",fallbackPlacements:\"array\",html:\"boolean\",offset:\"(array|string|function)\",placement:\"(string|function)\",popperConfig:\"(null|object|function)\",sanitize:\"boolean\",sanitizeFn:\"(null|function)\",selector:\"(string|boolean)\",template:\"string\",title:\"(string|element|function)\",trigger:\"string\"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError(\"Bootstrap's tooltips require Popper (https:\/\/popper.js.org)\");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return\"tooltip\"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute(\"data-bs-original-title\")&&this._element.setAttribute(\"title\",this._element.getAttribute(\"data-bs-original-title\")),this._disposePopper(),super.dispose()}show(){if(\"none\"===this._element.style.display)throw new Error(\"Please use show on visible elements\");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName(\"show\")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute(\"aria-describedby\",i.getAttribute(\"id\"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName(\"inserted\"))),this._popper=this._createPopper(i),i.classList.add(es),\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,\"mouseover\",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName(\"shown\")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName(\"hide\")).defaultPrevented){if(this._getTipElement().classList.remove(es),\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,\"mouseover\",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute(\"aria-describedby\"),N.trigger(this._element,this.constructor.eventName(\"hidden\")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return 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id=\"quarto-bootstrap\" rel=\"stylesheet\"\/>\n<script>$(document).ready(function(){\n\n if (typeof $('[data-toggle=\"tooltip\"]').tooltip === 'function') {\n\n $('[data-toggle=\"tooltip\"]').tooltip();\n\n }\n\n if ($('[data-toggle=\"popover\"]').popover === 'function') {\n\n $('[data-toggle=\"popover\"]').popover();\n\n }\n\n});\n\n<\/script>\n\n<\/head>\n<body class=\"fullcontent\">\n<div class=\"page-layout-custom\">\n<header class=\"quarto-title-block default\" id=\"title-block-header\">\n<div class=\"quarto-title\">\n\n<\/div>\n<div class=\"quarto-title-meta\">\n<\/div>\n<\/header>\nAh, the beautiful concept of p-value. The probability of observing the result as extreme or more extreme than the data at hand, assuming the null hypothesis is true. Not a single person ever simplified it to something else. Like.. I don\u2019t know.. the probability that the null hypothesis is true? Or, in an A\/B test, the probability that treatment is greater\/smaller than zero? \ud83d\udc40<\/p>\nDoing that is equivalent to committing an original data science sin. You\u2019d be banished to the ungodly world full of local optima, spaghetti SQL, Excel downloads and out-of-date dashboards. Or simply wouldn\u2019t pass an screening round in a hiring process.<\/p>\nBUT.<\/p>\nP-value can be equal to the probability that the treatment effect is greater\/smaller than zero. In the context of A\/B testing, where we are in a straightforward univariate hypothesis testing setting, it is as simple as employing a Bayesian approach with an uninformative prior.<\/p>\nThis post, I admit, is partly for kicks. But it has some practical implications, too:<\/p>\n<ul>\n<li>Most articles on using Bayesian A\/B testing will tell you that using uninformative priors is not a very good idea. While I agree, the fact that using them yields results equivalent to a most popular frequentist procedure means that they aren\u2019t a terrible choice. There are <a href=\"https:\/\/www.optimizely.com\/insights\/blog\/why-you-should-choose-sequential-testing-and-not-bayesian\/\">some vendors out there that scaremonger<\/a> into shying away from using Bayesian approaches. This post shows that if you choose to go with uninformative priors, you\u2019ll be shooting yourself into the foot as much as you would with a simple t-test.<\/p><\/li>\n<li>The bad thing, however, is that p-values have such an interpretation under very unrealistic assumptions of prior distributions. In practice, thus, interpreting p-value as a direct measure of evidence or using uninformative priors is a bad idea.<\/p><\/li>\n<\/ul>\n<section class=\"level3\" id=\"the-gaussian-case\">\n<h3 data-anchor-id=\"the-gaussian-case\">The Gaussian case<\/h3>\nLet\u2019s consider the following setup:<\/p>\n<ul>\n<li>We\u2019re interested in measuring the impact of a simple A\/B test.<\/p><\/li>\n<li>Our outcome metric happens to be normally distributed: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_A \\sim N(\\mu_A, \\sigma_A)<\/annotation><\/semantics><\/math> and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>B<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_B \\sim N(\\mu_B, \\sigma_B)<\/annotation><\/semantics><\/math>. For simplicity, we will set <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bc<\/mi><mi>A<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><msub><mi>\u03bc<\/mi><mi>B<\/mi><\/msub><mo>=<\/mo><mn>0.05<\/mn><mo>,<\/mo><mrow><mspace width=\"0.333em\"><\/mspace><mtext mathvariant=\"normal\"> and <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><msub><mi>\u03c3<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>B<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\mu_A = 0, \\mu_B = 0.05, \\text{ and } \\sigma_A, \\sigma_B = 1<\/annotation><\/semantics><\/math>. In other words, equal variance, and a treatment effect of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.05<\/mn><annotation encoding=\"application\/x-tex\">0.05<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<\/ul>\nSuppose we ran an experiment and collected 6,000 samples in each experiment arm (that\u2019s 78% power, assuming we set MDE equal to the true unobservable population effect).<\/p>\n<section class=\"level4\" id=\"a-quick-t-test-refresher\">\n<h4 data-anchor-id=\"a-quick-t-test-refresher\">A quick t-test refresher<\/h4>\nIf we were to evaluate our results using a t-test, we would:<\/p>\n<ul>\n<li>Compute sample means: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mtext mathvariant=\"normal\">mean<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Y_A} = \\text{mean}(Y_A)<\/annotation><\/semantics><\/math>, <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mtext mathvariant=\"normal\">mean<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Y_B} = \\text{mean}(Y_B)<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>Compute sample variances: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>s<\/mi><mi>A<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.222em\"><\/mspace><mo>=<\/mo><mtext mathvariant=\"normal\">var<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">s_A^2\\ =\\text{var}(Y_A)<\/annotation><\/semantics><\/math>, <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>s<\/mi><mi>B<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.222em\"><\/mspace><mo>=<\/mo><mtext mathvariant=\"normal\">var<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">s_B^2\\ =\\text{var}(Y_B)<\/annotation><\/semantics><\/math><\/p><\/li>\n<\/ul>\nThen, enabled by CLT, we can claim that the difference of the means between the two groups is normally distributed (that distribution is referred to as the \u201csampling distribution\u201d), with the following parameters:<\/p>\n<ul>\n<li>Mean: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><mi>Z<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mover><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Z} = \\bar{Y_A} - \\bar{Y_B}<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>Standard error: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>s<\/mi><mi>Z<\/mi><\/msub><mo>=<\/mo><msqrt><mrow><mfrac><msubsup><mi>s<\/mi><mi>A<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>A<\/mi><\/msub><\/mfrac><mo>+<\/mo><mfrac><msubsup><mi>s<\/mi><mi>B<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>B<\/mi><\/msub><\/mfrac><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">s_Z = \\sqrt{\\frac{s_A^2}{n_A} + \\frac{s_B^2}{n_B}}<\/annotation><\/semantics><\/math><\/p><\/li>\n<\/ul>\nFinally, we calculate the test statistic <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><mo>=<\/mo><mover><mi>Z<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>\/<\/mi><msub><mi>s<\/mi><mi>Z<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">t = \\bar{Z} \/ s_Z<\/annotation><\/semantics><\/math>, and look up the associated CDF of the sampling distribution at that point (a.k.a p-value).<\/p>\nThis is how it may look numerically.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb1\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb1-1\" tabindex=\"-1\"><\/a>set.seed<\/span>(42<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-2\" tabindex=\"-1\"><\/a>n =<\/span> 6000<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-3\" tabindex=\"-1\"><\/a>effect_size =<\/span> 0.05<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-4\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-5\" tabindex=\"-1\"><\/a>A =<\/span> rnorm<\/span>(n, 0<\/span>, 1<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-6\" tabindex=\"-1\"><\/a>B =<\/span> rnorm<\/span>(n, effect_size, 1<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-7\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-8\" tabindex=\"-1\"><\/a>sampling_distribution =<\/span> function<\/span>(X, Y) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-9\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-10\" tabindex=\"-1\"><\/a> mean =<\/span> mean<\/span>(X) -<\/span> mean<\/span>(Y),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-11\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>(var<\/span>(X) \/<\/span> n +<\/span> var<\/span>(Y) \/<\/span> n)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-12\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-13\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-14\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-15\" tabindex=\"-1\"><\/a>sdist =<\/span> sampling_distribution<\/span>(B, A)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-16\" tabindex=\"-1\"><\/a>t =<\/span> sdist$<\/span>mean \/<\/span> sdist$<\/span>sd<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-17\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-18\" tabindex=\"-1\"><\/a>as_tibble<\/span>(sdist) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-19\" tabindex=\"-1\"><\/a> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> \"statistic\"<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-20\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Summary statistics of the sampling distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-21\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Summary statistics of the sampling distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.0419394<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.0183665<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb2\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb2-1\" tabindex=\"-1\"><\/a>tibble<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-2\" tabindex=\"-1\"><\/a> statistic =<\/span> c<\/span>('Test statistic'<\/span>, 'P-value'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-3\" tabindex=\"-1\"><\/a> value =<\/span> c<\/span>(t, (1<\/span> -<\/span> pnorm<\/span>(t)) *<\/span> 2<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-4\" tabindex=\"-1\"><\/a>) |><\/span> kbl<\/span>(caption=<\/span>'Hypothesis test outcomes'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-5\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Hypothesis test outcomes<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">Test statistic<\/td>\n<td style=\"text-align: right;\">2.2834717<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">P-value<\/td>\n<td style=\"text-align: right;\">0.0224026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nAs a visual reminder - the p-value is twice the CDF of the sampling distribution in the range <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo form=\"prefix\" stretchy=\"true\">[<\/mo><mo>\u2212<\/mo><mi>\u221e<\/mi><mo>,<\/mo><mn>0<\/mn><mo form=\"postfix\" stretchy=\"true\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">[-\\infty, 0]<\/annotation><\/semantics><\/math> (twice, because we\u2019re testing for a two-sided alternative hypothesis).<\/p>\n<div class=\"cell\">\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nMathematically, we don\u2019t need to calculate the test statistic. We can get the CDF directly using the parameters of our sampling distribution.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb3\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb3-1\" tabindex=\"-1\"><\/a>#this is also a p-value!<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb3-2\" tabindex=\"-1\"><\/a>format<\/span>(pnorm<\/span>(0<\/span>, mean =<\/span> sdist$<\/span>mean, sd =<\/span> sdist$<\/span>sd, lower.tail=<\/span>T) *<\/span> 2<\/span>, digits=<\/span>4<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>[1] \"0.0224\"<\/code><\/pre>\n<\/div>\n<\/div>\nWe can double-check using the built-in R functions.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb5\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb5-1\" tabindex=\"-1\"><\/a>t.test<\/span>(B, A)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>\n\n Welch Two Sample t-test\n\n\n\ndata: B and A\n\nt = 2.2835, df = 11997, p-value = 0.02242\n\nalternative hypothesis: true difference in means is not equal to 0\n\n95 percent confidence interval:\n\n 0.00593807 0.07794067\n\nsample estimates:\n\n mean of x mean of y \n\n 0.033779917 -0.008159451 <\/code><\/pre>\n<\/div>\n<\/div>\nGreat, we can conclude that, if our hypothesis of treatment having no effect were true, we would be observing a difference between two groups at least as large as we did (we observed a difference of <code>0.041<\/code>) roughly 2% of the time.<\/p>\nSounds rare enough that we could reject our null hypothesis and conclude that there indeed is a difference.<\/p>\nWe also conclude that the true effect should be somewhere between <code>0.005<\/code> and <code>0.078<\/code> 95% of the time if we were to repeat this experiment an infinite number of times. As for this particular run - well, it\u2019s either inside that range or not. T-tests (or frequentist approaches, more generally) don\u2019t tell you anything about this particular experiment. Just long-term probabilities.<\/p>\nA mouthful. But hey, this isn\u2019t a post about issues with null hypothesis testing. I wrote that <a href=\"https:\/\/aurimas.eu\/blog\/2023\/02\/getting-faster-to-decisions-in-a-b-tests-part-2-misinterpretations-and-practical-challenges-of-classical-hypothesis-testing\/\">one already<\/a>.<\/p>\n<\/section>\n<section class=\"level4\" id=\"a-bayesian-approach\">\n<h4 data-anchor-id=\"a-bayesian-approach\">A Bayesian approach<\/h4>\nGenerally, saying \u201cI\u2019m using a Bayesian approach\u201d is like saying \u201cI\u2019m using linear algebra\u201d. It\u2019s not a statistical method. We need an estimand! We will use the simplest one: the probability that the treatment is larger than 0.<\/p>\nNext, we will need uninformative priors. We can achieve that by choosing normal distribution priors with variance approaching infinity (making any number in the real domain roughly equally likely), i.e.:<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mn>0<\/mn><mo>,<\/mo><mn>1<\/mn><mi>\/<\/mi><mi>\u03c4<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_A, Y_B \\sim N(0, 1\/\\tau)<\/annotation><\/semantics><\/math>, where <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>\u03c4<\/mi><annotation encoding=\"application\/x-tex\">\\tau<\/annotation><\/semantics><\/math> is some tiny number, e.g.\u00a00.001.<\/p>\nNote that we did not choose a prior for the treatment effect itself. Instead, we\u2019re effectively saying that both experiment arms have the same mean and can take almost any value with the same likelihood.<\/p>\nHowever, we can see what kind of treatment effect prior distribution our choice implies by leveraging the fact that a difference between two independent normal distributions is just another normal distribution:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mtext mathvariant=\"normal\">if <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><mi>X<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>,<\/mo><mi>Y<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mspace width=\"0.167em\"><\/mspace><mrow><mspace width=\"0.333em\"><\/mspace><mtext mathvariant=\"normal\"> then <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>X<\/mi><mo>\u2212<\/mo><mi>Y<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\n\\text{if } X \\sim N(\\mu_x, s_x^2), Y \\sim N(\\mu_y, s_y^2)\\, \\text{ then } (X - Y) \\sim N(\\mu_x - \\mu_y, s_x^2 + s_y^2)\n\n<\/annotation><\/semantics><\/math><\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb7\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb7-1\" tabindex=\"-1\"><\/a>difference_of_two_normals =<\/span> function<\/span>(X, Y) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-2\" tabindex=\"-1\"><\/a> list<\/span> (<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-3\" tabindex=\"-1\"><\/a> mean =<\/span> X$<\/span>mean -<\/span> Y$<\/span>mean,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-4\" tabindex=\"-1\"><\/a> tau =<\/span> 1<\/span> \/<\/span> ((1<\/span> \/<\/span> X$<\/span>tau) +<\/span> (1<\/span> \/<\/span> Y$<\/span>tau)),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-5\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>((1<\/span> \/<\/span> X$<\/span>tau) +<\/span> (1<\/span> \/<\/span> Y$<\/span>tau))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-6\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-7\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-8\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-9\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-10\" tabindex=\"-1\"><\/a>difference_of_two_normals<\/span>(list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>), list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>)) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-11\" tabindex=\"-1\"><\/a> as_tibble<\/span>() |><\/span> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> 'statistic'<\/span>) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-12\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Implied treatment effect prior distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-13\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Implied treatment effect prior distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.00000<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">tau<\/td>\n<td style=\"text-align: right;\">0.00050<\/td>\n<\/tr>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">44.72136<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nWe can see that choosing a prior for experiment results of zero mean and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c4<\/mi><mo>=<\/mo><mn>0.001<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\tau=0.001<\/annotation><\/semantics><\/math> (or, equivalently, the standard deviation of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mi>(<\/mi><\/msqrt><mfrac><mn>1<\/mn><mn>0.001<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>31.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt(\\frac{1}{0.001})=31.6<\/annotation><\/semantics><\/math>) yields a prior on the treatment effect that also has a zero mean but has even more uncertainty, with a standard deviation of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>44.7<\/mn><annotation encoding=\"application\/x-tex\">44.7<\/annotation><\/semantics><\/math>.<\/p>\nNext, we need to get to posterior distributions. Luckily, a normal prior and a normal likelihood form a conjugate pair that yields a normal posterior distribution, so we can do this algebraically.<\/p>\nSpecifically, suppose the prior distribution is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mn>0<\/mn><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>,<\/mo><msubsup><mi>\u03c4<\/mi><mn>0<\/mn><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P_0 \\sim N(\\mu_0, \\tau_0^{-1})<\/annotation><\/semantics><\/math>, the observed mean is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> and observed precision is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mfrac><mn>1<\/mn><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{\\tau} = \\frac{1}{s^2_x}<\/annotation><\/semantics><\/math>. Then the posterior is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>n<\/mi><\/mrow><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><\/mfrac><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P \\sim N \\left(\\frac{\\tau_0 \\mu_0+\\bar{\\tau} \\bar{X} n}{\\tau_0+ n \\bar{\\tau}},\\left(\\tau_0+n \\bar{\\tau}\\right)^{-1}\\right)<\/annotation><\/semantics><\/math>. Let\u2019s calculate the posteriors for our samples.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb8\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb8-1\" tabindex=\"-1\"><\/a>calculate_normal_posterior =<\/span> function<\/span>(X, prior) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-2\" tabindex=\"-1\"><\/a> n =<\/span> length<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-3\" tabindex=\"-1\"><\/a> observed_mu =<\/span> mean<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-4\" tabindex=\"-1\"><\/a> observed_tau =<\/span> 1<\/span> \/<\/span> var<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-5\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-6\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-7\" tabindex=\"-1\"><\/a> mean =<\/span> (prior$<\/span>tau *<\/span> prior$<\/span>mean +<\/span> observed_tau *<\/span> observed_mu *<\/span> n) \/<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-8\" tabindex=\"-1\"><\/a> tau =<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-9\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>(1<\/span> \/<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-10\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-11\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-12\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-13\" tabindex=\"-1\"><\/a>A_posterior =<\/span> calculate_normal_posterior<\/span>(A, list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-14\" tabindex=\"-1\"><\/a>B_posterior =<\/span> calculate_normal_posterior<\/span>(B, list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-15\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-16\" tabindex=\"-1\"><\/a>bind_rows<\/span>(A_posterior, B_posterior, .id =<\/span> 'ID'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-17\" tabindex=\"-1\"><\/a> mutate<\/span>(ID =<\/span> str_replace_all<\/span>(ID, c<\/span>('1'<\/span>=<\/span>'A'<\/span>, '2'<\/span>=<\/span>'B'<\/span>))) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-18\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Posterior distributions of experiment arms'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-19\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Posterior distributions of experiment arms<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">ID<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">mean<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">tau<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">sd<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">A<\/td>\n<td style=\"text-align: right;\">-0.0081594<\/td>\n<td style=\"text-align: right;\">5873.761<\/td>\n<td style=\"text-align: right;\">0.0130479<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">B<\/td>\n<td style=\"text-align: right;\">0.0337799<\/td>\n<td style=\"text-align: right;\">5985.180<\/td>\n<td style=\"text-align: right;\">0.0129259<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nWe have posterior distributions for the data of the two samples, but we are after the treatment effect - i.e., the difference between the two samples. We can use the same approach as we did previously when estimating the implied treatment effect prior previously and calculate it, as the two posteriors can be assumed to be independent, too.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb9\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb9-1\" tabindex=\"-1\"><\/a>treatment_posterior =<\/span> difference_of_two_normals<\/span>(B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-2\" tabindex=\"-1\"><\/a>treatment_posterior |><\/span> as_tibble<\/span>() |><\/span> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> 'statistic'<\/span>) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-3\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Posterior distribution of the treatment effect'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-4\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Posterior distribution of the treatment effect<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.0419394<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">tau<\/td>\n<td style=\"text-align: right;\">2964.4734513<\/td>\n<\/tr>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.0183665<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nLet\u2019s visualize it.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb10\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb10-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-2\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-3\" tabindex=\"-1\"><\/a> args =<\/span> within<\/span>(treatment_posterior, rm<\/span>(\"tau\"<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-4\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.1<\/span>, 0.1<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-5\" tabindex=\"-1\"><\/a> geom_vline<\/span>(xintercept=<\/span>0<\/span>, color=<\/span>'red'<\/span>, linetype=<\/span>'dashed'<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-6\" tabindex=\"-1\"><\/a> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"PDF the treatment effect\"<\/span>) +<\/span> ylab<\/span>(\"Density\"<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-7\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>())<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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\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7bff\/usLihQpsnr16ldffVWv13\/55Zc5ff\/ff\/\/92rVrrq6unp6e2srSv9q3b5+I1KxZs0CBAsaLPj4+FSpUMBgMBw4cyOlDAQAAYNP279+vHUhUrVq1oKAg1XEAO+fp6dm6dWsRefTo0Zo1a1THAfB0phZAWvnSq1evsmXLPus1Li4uPXv2FJFffvklp+\/fvXv3Zf\/fk\/3Ok7RNpqtXr\/6n69oVc21BDQAAAFvB9s9ALmMVGGD9TC2ALl68KCI1atT4+5eVK1dORM6ePWvi457q2rVrIqIt\/nqSduXq1auWeCgAAACsU3p6+sqVK0XEyckpLCxMdRwgT2jQoEGpUqVEZM+ePXwHD1gnUwsgFxcXEbl3797fv+zy5csi8qw1XCZKS0sTkb\/OD\/Lw8BCRhw8fWuKhAAAAsE7x8fHaLiTvvvuuj4+P6jhAnuDg4BAZGSkiBoNhyZIlquMAeApTD0QIDAz86aefdu7c2aNHj795mbYRz98sEzNFZmamiOTPn\/9P17V9yDIyMv56S0pKytGjR\/963WAwWCAgAAAAcg\/rvwAlOnfuHB0dbTAYFi9ePHr0aAcHMxw5DcCMTP2dDAkJEZHY2NgNGzY86zU\/\/PDDihUrRCQ4ONjExz2VNvdHO4f+Sdrcn6fuHOTs7FzkaSw0RwkAAAC5IykpKSEhQUS8vb2bNm2qOg6Qh5QrV+5f\/\/qXiFy6dGn37t2q4wD4M1MLoL59+5YsWVJEQkJCPv744z9tuGMwGOLj49u0aZOZmVmyZMnBgweb+Lin8vb2FpHU1NQ\/XdeuFCpU6K+3uLu7Bz2NJeIBAAAg1yxdujQrK0tEOnTo4OrqqjoOkLewFTRgzUwtgNzd3Tds2FCoUKGsrKwvvviiZMmSpUuX1n5Uu3ZtX1\/fVq1aJScn63S6RYsWPbWLMZ2Xl5eIJCcn\/+n63bt3RaRw4cKWeCgAAMALmTFDevWSXr0kKUl1lDxh6dKl2oD1X0Du69Chg7Y1x6pVq\/76DT0AtcywLLNatWqnT5\/u37+\/tiH0H3\/8oV3fv39\/UlKSiLz22mv79u1r0KCB6c96Kq1yOnbs2J+uHz9+XET8\/Pws9FwAAIDn27ZN5syROXPkeYdmwHRHjx795ZdfRKRixYq1atVSHQfIcwoWLNi8eXMRSUtLW7t2reo4AP6HqZtAa4oVK\/b1119\/+OGHW7ZsOXfuXGJiYlJSkp+fX\/ny5WvUqNGiRQuL7q3z2muvrV+\/\/vDhwxkZGcaJvvfv3\/\/1119dXFzq1atnuUcDAADAerD9M6Bcp06d4uLiRGTx4sXvvfee6jgA\/o95CiCNn59fnz59zPiGL6hy5crly5c\/c+bM119\/HRUV5ejomJGRER0dnZmZ2bBhQ3d399yPBAAAgFyWlZW1cuVKEXFwcAgPD1cdB8ijGjdu7Ovre\/369V27dl28eJEFGYD1sJOT+aKiogoWLPjjjz9GREQMHjw4IiLixIkTJUqU6NKli+poAAAAyA2bNm3S9h9o1KiRdkoJgNzn5OQUEREhIgaDISYmRnUcAP\/H1BlA2dnZJ0+e\/Pnnn2\/dupWSkiIihQoVKlq0aLVq1SpUqODo6GiOkM\/n6+s7derU5cuXHzlyJDEx0dvbu3bt2mFhYW5ubrkTAAAAAGqx\/guwEp07d\/7iiy9EZPHixSNGjLDofiAAXtzLF0BHjhyZNWvWypUrHzx48NQXeHp6hoWFvf\/++9WqVXvppzxp2bJlf\/NTb2\/vfv36meVBAAAAsC3JycmbN28WEU9Pz5YtW6qOA+RplSpVql69+tGjRxMTE\/ft21enTh3ViQCIvNwSsNTU1N69e9eqVWvevHnPan9E5P79+3PmzKlRo0bfvn3T0tJMCAkAAAD8neXLl2dkZIhIu3btmAMOKGeciGecmgdAuRzPAEpNTQ0ODt6zZ4\/2HwMCAlq0aFG1atXSpUsXKFBAp9Pdv3\/\/8uXLx44d27hxY2JiosFgmDFjxokTJzZv3sx+zAAAALAE1n8BVkXbmzUjI2PlypVTpkyhlgWsQY4LoD59+mjtzz\/+8Y+pU6e+++67T33Ze++9N3ny5K1bt37wwQfnzp3bvXt3\/\/79FyxYYGpeAAAA4H+dPHny8OHDIuLn58diE8AaFC5cODg4eP369ffv34+Pj+\/QoYPqRAByuATs4MGDS5cuFZEqVaocOHDgWe2P0TvvvHPgwIGqVauKyKJFi7R\/mAEAAAAzMk7\/6dy5M9vNAlaCVWCAtclZAaRtw+zo6Lh06dLChQu\/yC3e3t5Lly51cnIyGAx\/v4szAACAHQoIkBo1pEYNyZdPdRT7pNfrly9fLiI6nS4yMlJ1HAD\/1bRp06JFi4pIQkLClStXVMcBkMMCaOfOnSLy5ptv\/vOf\/3zxuypXrlyvXj0R+e6773L0OAAAAJs3ebIcPiyHD0vp0qqj2Kft27drf1u++eab\/v7+quMA+C9nZ2dt5Zder4+JiVEdB0AOC6CrV6+KSN26dXP6GO0W7XYAAADAXNj+GbBaxt9KdoMFrEHOCqB79+6JSLFixXL6mOLFi4vI3bt3c3ojAAAA8Cz379\/fsGGDiLi5ubVt21Z1HAD\/o3r16kFBQSJy9uzZQ4cOqY4D5HU5K4A0zs7OuXALAAAA8Pfi4uIePnwoIm3atClQoIDqOAD+7L333tMGixYtUhoEwEsVQAAAAIA1mD9\/vjZg\/RdgnSIiIpycnEQkNjY2IyNDdRwgT6MAAgAAgE369ddfDxw4ICJly5atX7++6jgAnqJ48eJNmjQRkeTk5I0bN6qOA+RpFEAAAACwSfPmzdMGXbt2dXDgYy1gpYwT9IxT9gAo4fQS9xw9enTNmjU5uuXw4cMv8SAAAADgqdLT05ctWyYijo6OnTt3Vh0HwDO1bNmyaNGit27d2r59+6VLl8qUKaM6EZBHvUwBNGfOnDlz5pg9CgAAAPCC1qxZk5ycLCLvvvtuqVKlVMcB8EwuLi4dO3acPHmyXq9fsGDB2LFjVScC8ijmygIAAMD2zJ07Vxt0795dbRIAz9WzZ0+dTici8+fPz87OVh0HyKNyNgPIuNAaAAAAUOX8+fO7d+8WkeLFiwcHB6uOA+A5ypcvX6dOnT179ly9enXLli3NmjVTnQjIi3JWAHXr1s1COQAAAOxTz57y3XciIjt2iJ+f6jR2Ys6cOQaDQUS6devm7OysOg6A5+vRo8eePXtEZO7cuRRAgBIsAQMAALCkpCS5cEEuXJDMTNVR7ERWVtbSpUtFRKfTdenSRXUcAC8kNDS0UKFCIrJ58+arV6+qjgPkRRRAAAAAsCXx8fHXr18XkQYNGgQEBKiOA+CF5M+fPzw8XESysrIWLVqkOg6QF1EAAQAAwJYYt3\/u0aOH2iQAcqRnz57aYP78+Xq9Xm0YIA+iAAIAAIDN+OOPP3bs2CEihQsXbtmypeo4AHIgKCjotddeE5GLFy9qv8gAchMFEADj4v8+AAAgAElEQVQAAGzGvHnztDOkO3fu7OrqqjoOgJwxTtwzTuUDkGsogAAAAGAb9Hq9ceuQrl27Ks0C4GWEhYV5enqKSHx8\/I0bN1THAfIWCiAAAADYhi1btly+fFlE6tatW7FiRdVxAOSYh4dH+\/btRSQzM1M7zg9ArqEAAgAAgG2YN2+eNmD7Z8B2GX9\/Z8+ebTAY1IYB8hQKIAAAANiAGzdubNq0SUQKFizYtm1b1XEAvKRatWpVq1ZNRM6fP\/\/DDz+ojgPkIRRAAAAAsAELFy7MzMwUkYiICDc3N9VxALy87t27awO2ggZyEwUQAACAJbVpI0OGyJAh4u2tOooNMxgMCxYs0MbGPx0B2ChjjbtmzZrbt2+rjgPkFRRAAAAAltSpk0RHS3S0FCmiOooN27lzZ2JioojUrFlTWzwCwHYVLFgwNDRURDIyMmJiYlTHAfIKCiAAAABYO+P2z0z\/AezDk1tBq00C5B0UQAAAALBqd+7cWb9+vYi4u7t36NBBdRwAZlCnTp1KlSqJyKlTp\/bv3686DpAnUAABAADAqi1ZsiQ9PV1E2rdv7+npqToOAPNgK2ggl1EAAQAAwKrNnz9fGxjXjACwAx07dsyXL5+IxMbGpqSkqI4D2D8KIAAAAFivffv2\/fbbbyJSoUKF119\/XXUcAGZTuHDh1q1bi8ijR49WrFihOg5g\/yiAAAAAYL2Ma0N69eqlNgkAszNO65s1a5baJEBeQAEEAAAAK3Xv3r1Vq1aJiKura0REhOo4AMzsrbfeCgwMFJFffvnlyJEjquMAdo4CCAAAAFZq+fLlaWlpIhISElKkSBHVcQCYmU6n69atmzZmK2jA0iiAAAAAYKXmzZunDYynBQGwM507d3Z2dhaRmJiYBw8eqI4D2DMKIAAAAEtKTZW7d+XuXcnOVh3Fxhw\/fvzo0aMi4u\/v\/9Zbb6mOA8AifHx8WrRoISKpqalxcXGq4wD2jAIIAADAkiIixNtbvL3l\/HnVUWzM7NmztUHPnj11Op3aMAAsx7gVNKvAAIuiAAIAAIDVMR4L7eTk9N5776mOA8CCGjVqVLZsWRE5ePDgsWPHVMcB7BYFEAAAAKzOypUrU1JSRKR58+a+vr6q4wCwIAcHB+NW0PPnz1cbBrBjFEAAAACwOjNnztQGxrUhAOxYly5dnJycRCQmJubRo0eq4wD2iQIIAAAA1uXgwYM\/\/fSTiPj7+zdp0kR1HAAW98orrwQHB4vI3bt3V69erToOYJ8ogAAAAGBdpk2bpg369u3r4MDnVSBPME73mz59utokgL3iH1QAAABYkZs3b65atUpE3NzcOnfurDoOgFzStGlTf39\/eWIOIADzogACAACAFZk1a1ZGRoaIdOzY0dvbW3UcALnEwcGhd+\/e2vibb75RGwawSxRAAAAAsBZZWVlz5szRxn369FEbBkAu6969u7u7u4jExcXduHFDdRzA3lAAAQAAwFqsWbPm6tWrIvL2228HBQWpjgMgV3l5eUVERIjI48ePjV0wAHOhAAIAAIC1MK776Nevn9okAJT44IMPdDqdiMyaNevx48eq4wB2hQIIAADAkgYPlrg4iYsTX1\/VUazdsWPH9u7dKyKlS5du0aKF6jgAFKhUqVK9evVE5Pr162vXrlUdB7ArFEAAAACWVKeOhIZKaKgUKKA6irUzTv\/p3bu3k5OT2jAAVOnfv782YCtowLwogAAAAKDe3bt3Y2NjRcTV1bVr166q4wBQpmXLln5+fiKyb9++Q4cOqY4D2A8KIAAAAKg3Z86chw8fikh4eHixYsVUxwGgjKOjY69evbTx9OnT1YYB7AkFEAAAABTLzs6ePXu2Nub0dwA9e\/Z0c3MTkdjY2KSkJNVxADtBAQQAAADFNmzYcPHiRRGpXbt2zZo1VccBoFihQoU6dOggIhkZGfPmzVMdB7ATFEAAAABQbNq0adrAuPkrgDxu4MCB2mDGjBmZmZlqwwD2gQIIAAAAKp08eXLXrl0i4uvr26ZNG9VxAFiFypUr\/\/vf\/xaRa9eurVu3TnUcwB5QAAEAAEClb775xmAwiEivXr1cXFxUxwFgLTgPHjAvCiAAAAAok5KSsmzZMhFxdnbu3r276jgArEjr1q1LlSolInv27Dly5IjqOIDNowACAACAMgsXLkxNTRWR0NDQV155RXUcAFbEycnp\/fff18YzZsxQGwawAxRAAAAAlrR3r6xaJatWyYMHqqNYHYPBMGvWLG3cr18\/tWEAWKGePXvmy5dPRGJiYm7evKk6DmDbKIAAAAAs6T\/\/kXbtpF07uX5ddRSrs2XLlrNnz4pItWrV3njjDdVxAFidIkWKhIWFiUhGRsaCBQtUxwFsGwUQAAAA1DBu7DpgwAC1SQBYrQ8++EAbzJw5MysrS20YwKZRAAEAAECBxMTE7du3i0iRIkXat2+vOg4AK1WtWrU6deqIyOXLl+Pj41XHAWwYBRAAAAAUmDZtml6vlyf2+ACAp+I8eMAsKIAAAACQ21JTUxctWiQijo6OPXv2VB0HgFULCQkpWbKkiPzwww\/Hjx9XHQewVRRAAAAAyG1Lliy5d++eiLRq1apMmTKq4wCwak5OTsameNq0aWrDALaLAggAAAC5bebMmdrAuLIDAP7G+++\/bzwP\/s6dO6rjADaJAggAAAC5aseOHSdOnBCRSpUqvfnmm6rjALABRYsWDQ0NFZFHjx5xHjzwciiAAAAAkKuMKzg++OADnU6nNgwAWzFw4EBtMH369OzsbLVhAFtEAQQAAIDcc+nSpW+\/\/VZEvLy8IiIiVMcBYDOqV6\/++uuvi8ilS5c2btyoOg5geyiAAAAAkHumTZumfXXftWtXd3d31XEA2BLOgwdMQQEEAABgSTExkpwsyckSEKA6inopKSlz5swREUdHxz59+qiOA8DGtG3b1tfXV0R27dqlbSUG4MVRAAEAAFiSh4cUKiSFComjo+oo6s2cOfP+\/fsiEhISEkAjBiCHXFxcevXqJSIGg2HKlCmq4wA2hgIIAAAAuSE9PX3q1KnaePDgwWrDALBRvXr10s6DX7p06dWrV1XHAWwJBRAAAAByw8KFC5OSkkSkcePGNWrUUB0HgE0qXrx4p06dROTx48dfffWV6jiALaEAAgAAgMVlZ2dPnjxZGw8ZMkRtGAA2bfDgwU5OTiIya9asO3fuqI4D2AwKIAAAAFjcqlWrEhMTRaRWrVr169dXHQeADfP39w8JCRGRtLS0GTNmqI4D2AwKIAAAAFjcpEmTtAHTfwCYbtiwYTqdTkSmTp2alpamOg5gGyiAAAAAYFnbtm07evSoiAQEBLRq1Up1HAA2r0qVKk2aNBGRO3fuLFiwQHUcwDZQAAEAAMCyJk6cqA2GDh3q6OioNgwA+2CcTjhp0qTHjx+rDQPYBAogAAAAWNChQ4d27dolIj4+PpGRkarjALATb731Vu3atUXkjz\/+iI2NVR0HsAEUQAAAALCg6OhobRAVFZUvXz61YQDYk8GDB2uD6OhovV6vNgxg\/SiAAAAALGnxYhk6VIYOldu3VUdR4MyZM+vXrxcRT0\/PXr16qY4DwK60aNGicuXKInLq1Klvv\/1WdRzA2lEAAQAAWNLatTJxokycKMnJqqMoMGnSJO1r+b59+xYsWFB1HAB2RafTDRo0SBtPmDBBbRjA+lEAAQAAwCJu3LgRExMjIq6urv3791cdB4AdCg8PL1OmjIgcPHjwhx9+UB0HsGoUQAAAALCIL7\/8Mj09XUS6dOni6+urOg4AO+Ts7BwVFaWNjQcOAngqCiAAAACY37179+bOnSsijo6Oxj\/PAMDsunfvXrRoURHZsmXL0aNHVccBrBcFEAAAAMxv+vTp9+7dE5G2bdsGBgaqjgPAbrm5ufXr108bT5o0SW0YwJpRAAEAAMDM0tPTp02bpo0\/\/vhjtWEA2L1+\/foVKFBARFatWnXu3DnVcQArRQEEAAAAM1u4cOH169dFpHHjxjVq1FAdB4Cd8\/b27tGjh4hkZ2dPnjxZdRzASlEAAQAAwJye\/ANsyJAhasMAyCOioqJcXFzkiQIawJ9QAAEAAMCcVq1alZiYKCK1atWqX7++6jgA8oRXXnmlY8eOIpKRkfH111+rjgNYIwogAAAAmJNxE1am\/wDITR9\/\/LGDg4OIzJgxIyUlRXUcwOpQAAEAAFhSQIDUqCE1aki+fKqj5IZt27ZpxzAHBAS0atVKdRwAeUj58uVbt24tIvfv3585c6bqOIDVoQACAACwpMmT5fBhOXxYSpdWHSU3TJw4URsMGTLE0dFRbRgAec2IESN0Op2ITJky5dGjR6rjANaFAggAAADmcejQoV27domIj4+PthkHAOSmatWqNWjQQERu3ry5aNEi1XEA60IBBAAAAPOIjo7WBlFRUfnyxpI3ANbGuPvYpEmTsrKy1IYBrAoFEAAAAMzgzJkz69evFxFPT89evXqpjgMgj2rYsOHrr78uIhcvXoyLi1MdB7AiFEAAAAAwg+joaL1eLyJ9+vQpWLCg6jgA8q5BgwZpg\/\/85z8Gg0FtGMB6UAABAADAVKdPn166dKmIuLm5DRgwQHUcAHla69aty5cvLyLHjx\/fvHmz6jiAtaAAAgAAgKlGjRqVnZ0tIn379i1evLjqOADyNAcHh48\/\/lgbjx07lklAgIYCCAAAACb5+eefV69eLSKenp7G7VcBQKGOHTv6+\/uLyKFDh9atW6c6DmAVKIAAAABgkpEjR2pfsEdFRRUuXFh1HAAQFxeXMWPGaOPhw4dzHBggFEAAAAAwxd69e7UtNgoXLvzhhx+qjgMA\/xUREVGlShUROXPmzPLly1XHAdSjAAIAAMDL++STT7TB0KFDPT091YYBACMHB4fRo0dr49GjR2dkZKjNAyhHAQQAAGBJUVFSs6bUrCmXL6uOYn7bt2\/ftWuXiPj6+vbp00d1HAD4H61bt3799ddF5Pfff583b57qOIBiFEAAAACWdP68HDkiR45IerrqKOY3atQobfDJJ5+4ubmpDQMAfzVu3Dht8Nlnn6WlpakNA6hFAQQAAICXsW7duoMHD4pI2bJlu3XrpjoOADxFw4YN69evLyLXr1\/\/5ptvVMcBVKIAAgAAQI7p9fqxY8dq47Fjx7q4uKjNAwDPEh0drdPpRGTixIl3795VHQdQhgIIAAAAObZ8+fLjx4+LSLly5cLDw1XHAYBnqlWrVosWLUQkJSXlyy+\/VB0HUMZJdQDzWLlyZUxMzFN\/NHPmzFdeeSWX8wAAANixrKys8ePHa+PPPvvMyclOPlICsFfjx4\/fuHGjXq+fMmVK\/\/79fXx8VCcCFLCTGUA3btxQHQEAACCvWLBgwZkzZ0SkevXqISEhquMAwHNUrlxZm6uYlpb2+eefq44DqGEnX9doBdCXX35ZqlSpP\/3I1dVVRSIAAAD7lJ6ebpz+M378eG1nDQCwcuPGjYuLi3v8+PHMmTMHDBjg5+enOhGQ2+xqBlCpUqXy\/QUfSgAAAMxo5syZf\/zxh4jUqVMnODhYdRwAeCFly5bt2rWriDx+\/NjYYgN5ij0UQI8fP05OTvby8sqXL5\/qLAAAAPYsNTV14sSJ2pi\/oADYllGjRrm5uYnI4sWLT506pToOkNvsoQBKSkoyGAzFixdXHQQAAMDOTZkyJSkpSUSaNGny1ltvqY4DADng6+vbt29fEcnOzh49erTqOEBus4c9gLT1X15eXmvWrPn++++TkpKKFCni5+cXEhLi7++vOh0AAMjbmjQR7WuqggVVRzFVSkrK5MmTtfHYsWPVhgGAlzBs2LB58+bdvXt39erVP\/3002uvvaY6EZB77KcAOnDgwIEDB5ycnDw9Pa9cuXLlypV9+\/Z16dKlRYsWf70lIyND+\/IKAADAsvr0UZ3AbCZOnHj37l0RadOmzb\/+9S\/VcQAgxwoVKjRw4MDRo0cbDIbRo0dv2bJFdSIg99hPAeTh4fHBBx\/UrFnTyckpLS0tNjY2Pj5+wYIFFStW\/Mc\/\/vGnW9LS0n755Ze\/vpWzs3NuJAYAALA1t27dmj59uog4ODiwdAKA7YqKipoxY0ZSUtLWrVu\/\/\/57VrMi77CHAqhhw4Y1atQoXbp0kSJFtCvu7u7dunW7e\/fu7t274+Lihg8f\/qdbChUq1KRJk7++1c6dOy0eFwAAwAaNHz\/+wYMHIhIREREUFKQ6DgC8JA8PjyFDhkRFRYnIyJEj9+zZozoRkEvsYRNoPz+\/6tWrG9sfI63iuXDhwl9v0el0zk+TG3EBAABszeXLl2fPni0izs7OTP8BYOt69+5dqlQpEdm7d+\/mzZtVxwFyiT0UQM\/i4+MjIsnJyQaDQXUWAAAAG\/bpp59mZGSISLdu3QICAlTHAQCT5MuXb9SoUdp46NCher1ebR4gd9h8AfTw4cONGzdu2rTpry3P7du3RaR06dI6nU5FNAAAAHtw7ty5xYsXi0i+fPlGjBihOg4AmEGXLl1effVVEfn1119XrVqlOg6QG2y+AMqfP39cXNzs2bOPHj36px\/t2rVLRMqXL68iFwAAgJ0YOnRoVlaWiPTp06dkyZKq4wCAGTg6Oo4ZM0Ybjxo1Svt\/OcC+2XwBpNPpmjZtKiJTpkw5fvy4djE9PT0mJmb79u0FChTo0KGD0oAAAAA2LCEhYe3atSLi5eU1bNgw1XEAwGxCQ0OrVq0qImfPnp0\/f77qOIDF2cMpYKGhoY8ePVq3bt0nn3xSoECB\/Pnz37p1y2AwFChQICoqysvLS3VAAAAAm5SZmTlgwABtPHr06L+euQEAtsvBwWHChAnvvvuuiIwcOTI0NNTb21t1KMCCbH4GkIg4Ojp26dLlk08+qVatmojcv38\/MDCwWbNmM2bMqFGjhup0AAAAturrr78+deqUiFSqVKlfv36q4wCAmQUHBzdu3FhEbt++PXLkSNVxAMvScULWk7Zt2+bn51euXDnVQQAAABRLSkoqX778vXv3ROS7776rX7++6kQAYH7nzp375z\/\/mZGR4eDgcODAgVq1aqlOBLwQvV6\/efPmoKCg0qVLv+At9jADCAAAwHq1bCk6neh0cvas6ig5M2jQIK39adeuHe0PAHsVGBiorXXV6\/UDBgxghgTsGAUQAAAA\/mzfvn0xMTEi4ubm9p\/\/\/Ed1HACwoNGjR2tzKPbv37948WLVcQBLoQACAADA\/9Dr9QMHDtS+Bh8xYkSZMmVUJwIAC3Jzc5s4caI2HjJkSEpKito8gIVQAAEAAOB\/zJ49+9ChQyISEBAQFRWlOg4AWFxYWJi21vXmzZujR49WHQewCAogAAAA\/J\/k5ORRo0Zp4ylTpuTLl09tHgDIHd98842zs7OITJ8+\/fjx46rjAOZHAQQAAID\/M3z48Nu3b4tI48aNmzVrpjoOAOSSihUr9uvXT0Sys7P79evHbtCwPxRAAAAA+K+ff\/553rx5IuLi4vLNN9+ojgMAuWrs2LElSpQQkT179ixfvlx1HMDMKIAAAAAgImIwGAYOHJidnS0igwYNKleunOpEAJCrChQoEB0drY0\/+uije\/fuqc0DmBcFEAAAAEREli5dunv3bhEpWbLksGHDVMcBAAUiIyPr1asnIklJSePGjVMdBzAnCiAAAADIgwcPjKXPF1984eHhoTYPACih0+mmTZvm5OQkIlOnTv31119VJwLMhgIIAAAAMmbMmGvXrolI3bp127VrpzoOAChTuXLl3r17i0hWVlbfvn3ZDRp2gwIIAADAkgYPlrg4iYsTX1\/VUZ7p1KlT2pbPTk5O06dP1+l0qhMBgErjx4\/39fUVkR9\/\/HHVqlWq4wDmQQEEAABgSXXqSGiohIZKgQKqozxTVFRUZmamiPTt2zcoKEh1HABQzNPT87PPPtPGH330UWpqqto8gFlQAAEAAORpa9as2bp1q4gUK1ZszJgxquMAgFXo3LnzG2+8ISJXrlwxlkGATaMAAgAAyLsePXo0aNAgbfz55597eXmpzQMAVkLbDdrR0VFEJk+efPr0adWJAFNRAAEAAORdn3\/++e+\/\/y4iNWrU6Ny5s+I0AGBNqlev3qNHDxF5\/Phx\/\/79VccBTEUBBAAAkEdduHBh0qRJIuLg4DB9+nQHBz4ZAsD\/mDBhQpEiRURkx44da9euVR0HMAn\/zAMAAORFBoPh\/fffT09PF5EuXbr861\/\/Up0IAKxOoUKFJkyYoI2joqIePnyoNg9gCgogAACAvGjmzJkJCQki4u3t\/fnnn6uOAwBWqlu3brVq1RKRS5cujR07VnUc4OVRAAEAAOQ5iYmJgwcP1sbTp08vWrSo2jwAYLUcHBymTZumLZL98ssv9+7dqzoR8JIogAAAAPIWvV7frVu3tLQ0EWndunVYWJjqRABg1V577bWPPvpIRLKzszt27PjgwQPViYCXQQEEAACQt0yaNGn37t0iUqxYsVmzZqmOAwA2YNy4cUFBQSJy8eLFjz\/+WHUc4GVQAAEAAFjS8eOyY4fs2CHWsXXoyZMnx4wZo41nzZpVrFgxpXEAwDa4urouXrzYxcVFRGbPnr1p0ybViYAcowACAACwpFGjpFEjadRIrlxRHUWysrI6deqknfzVtWvX1q1bq04EADajatWqo0eP1sY9evS4c+eO2jxATlEAAQAA5BWffvrp4cOHRaRkyZJffvml6jgAYGOGDh3673\/\/W0SuX7\/eo0cP1XGAnKEAAgAAyBOOHj0aHR0tIjqdbt68eV5eXqoTAYCNcXBwWLRokYeHh4isW7duxYoVqhMBOUABBAAAYP8yMjI6deqUmZkpIv3792\/SpInqRABgk\/z9\/SdOnKiN+\/Tp88cff6jNA7w4CiAAAAD7N3z48BMnTohIQEDAZ599pjoOANiw3r17BwcHi0hKSkq3bt0MBoPqRMALoQACAACwc3v37p06dar87+IFAMDL0RbSent7i0hCQsKsWbNUJwJeCAUQAACAPUtLS+vcuXN2draIDBkypG7duqoTAYDNK1GixDfffKONBw0adPbsWbV5gBdBAQQAAGDPoqKiEhMTRaRixYqjRo1SHQcA7ER4eHj79u1F5OHDh8aeHbBmFEAAAAB2KyEhYe7cuSLi7Oy8ZMmSfPnyqU4EAPZj1qxZJUuWFJH9+\/cbd4YGrBYFEAAAgH16cnfSMWPG1KhRQ3UiALArXl5e8+fP1+l0IjJmzJjDhw+rTgT8HQogAAAA+9S3b1\/tfOIaNWp8\/PHHquMAgB1q3Lhxz549RSQzM7NTp07p6emqEwHPRAEEAABgSbNny\/nzcv68+Pnl5mPj4+OXL18uIvny5Vu8eLGzs3NuPh0A8o4vv\/wyMDBQRE6ePDl69GjVcYBnogACAACwpOLFxd9f\/P0lFyuYW7du9erVSxtHR0dXqlQp1x4NAHmNu7v7okWLHB0dReSLL7744YcfVCcCno4CCAAAwK5kZ2dHREQkJSWJyFtvvdW\/f3\/ViQDAztWuXXvQoEEiotfru3btmpqaqjoR8BQUQAAAAHZl+PDhCQkJIuLp6blw4UIHBz7vAYDFjR07NigoSEQuXLjQs2dPbQN+wKrwgQAAAMB+xMXFTZo0SUR0Ot2SJUvKli2rOhEA5Amurq5LlixxdXUVkRUrVnzxxReqEwF\/RgEEAABgJ3799deuXbtqXzuPGjWqZcuWqhMBQB5SpUqV2bNna+OhQ4du3rxZbR7gTyiAAAAA7MHdu3fbtGmTlpYmIk2aNPnkk09UJwKAPKdTp069e\/cWEb1eHxkZmZiYqDoR8H8ogAAAAGyeXq+PiIjQ\/tIoV65cbGysdh4NACCXTZ06tV69eiJy9+7d5s2b379\/X3Ui4L8ogAAAAGzeiBEjtmzZIiIeHh5r16718vJSnQgA8ihnZ+eVK1eWKlVKRE6fPv3ee++xITSsBAUQAACAbVu\/fv3EiRNFRKfTLViwoFKlSqoTAUCe5uPjEx8f7+bmJiLx8fHjx49XnQgQoQACAACwaadPn+7UqZP29fKIESNCQ0NVJwIASLVq1YwbQo8ePXrNmjVq8wBCAQQAAGBZa9bIxIkycaIkJ5v9vZ\/cYKJx48Zjxowx+yMAAC8nMjLyww8\/FBGDwdClS5fffvtNdSLkdRRAAAAAlrRkiQwdKkOHyu3b5n1jvV7fsWNHbeNnPz+\/5cuXs\/EzAFiVSZMmvfPOOyLy4MGDNm3apKSkqE6EPI0CCAAAwCaNGjVq06ZNIuLh4bFhw4bChQurTgQA+B+Ojo4xMTEBAQEicvbs2fbt22dnZ6sOhbyLAggAAMD2xMfHT5gwQUR0Ot38+fMrV66sOhEA4Cm8vb3Xrl3r7u4uItu3bx89erTqRMi7KIAAAABszJkzZ4znCg8dOrRdu3aqEwEAnikoKGjJkiU6nU5EJkyYsHLlStWJkEdRAAEAANiSBw8etG7dWtv4uVGjRuPGjVOdCADwHG3atBkyZIiIGAyGbt26\/frrr6oTIS+iAAIAALAZer0+PDz81KlTIlK2bFk2fgYAW\/HZZ581bdpURNLS0lq0aHHb3CcDAM9FAQQAAGAzhgwZ8u2334qIu7t7fHx8kSJFVCcCALwQBweHZcuWBQYGisjvv\/8eHh7OhtDIZRRAAAAAtmH8+PFffPGF\/P+Nn4OCglQnAgDkgJeX1\/r16wsUKCAiCQkJffv21XZzA3IHBRAAAIANmDp16ieffKKNx40b1759e7V5AAAvoWLFikuXLtU2hJ49e\/ZHH32kOhHyEAogAAAAazd\/\/vwPP\/xQGw8ePHjEiBFq8wAAXlrLli2nTp2qjb\/66itjuQ9YmpPqAAAAAHbNx0f8\/UVEnJ1f7g3Wrl37\/vvva8sEunbtGh0dbcZ0AIDc179\/\/6ysrKioKBEZP368m5vbsGHDVIeC\/aMAAgAAsKQ5c0y5e\/v27eHh4VlZWSISGRk5d+5cbeEAAMCmffjhh8nJyePHjxeR4cOHOzs7Dxo0SHUo2CU9WYsAACAASURBVDmWgAEAAFipnTt3tmzZMiMjQ0RatWq1cOFCBwc+vAGAnRg3btzgwYO18eDBg2fPnq02D+wenyEAAACs0cGDB1u1apWeni4iDRs2jI2NdXJi7jYA2JXo6OjevXuLiMFg6NOnT0xMjOpEsGcUQAAAAFbnl19+effddx88eCAib7zxxvr1611dXVWHAgCYmU6nmz59evfu3UVEr9d36tQpLi5OdSjYLQogAAAA63Lu3LkmTZokJyeLSNWqVTdt2uTu7q46FADAInQ63axZs8LCwkQkOzu7Y8eOmzZtUh0K9okCCAAAwIr88ccfjRo1unHjhohUrlx5x44dhQoVUh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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nThat looks familiar! Let\u2019s overlay the sampling distribution from the t-test:<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb11\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb11-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-2\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-3\" tabindex=\"-1\"><\/a> args =<\/span> within<\/span>(treatment_posterior, rm<\/span>(\"tau\"<\/span>)),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-4\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Posterior of a treatment effect'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-5\" tabindex=\"-1\"><\/a> linetype=<\/span>'dashed'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-6\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.1<\/span>, 0.1<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-7\" tabindex=\"-1\"><\/a> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-8\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-9\" tabindex=\"-1\"><\/a> args =<\/span> sdist,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-10\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Sampling distribution'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-11\" tabindex=\"-1\"><\/a> linetype=<\/span>'twodash'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-12\" tabindex=\"-1\"><\/a>) +<\/span> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"Treatment effect posterior distribution vs. Sampling distribution\"<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-13\" tabindex=\"-1\"><\/a> ylab<\/span>(\"Density\"<\/span>) +<\/span> labs<\/span>(color=<\/span>''<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-14\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>(), legend.position=<\/span>'bottom'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nThey are identical! This means that the probability of the treatment effect being smaller than zero is\u2014you guessed it\u2014equal to 1\/2 of a two-sided p-value\u2014or, in other words, identical to the one-sided p-value.<\/p>\n<div class=\"quarto-figure quarto-figure-center\">\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid quarto-figure quarto-figure-center figure-img\" 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\"\/><\/p>\n<\/figure>\n<\/div>\nThis is no coincidence. We can prove that mathematically. Here\u2019s the posterior formula again:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>n<\/mi><\/mrow><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><\/mfrac><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\nP \\sim N \\left(\\frac{\\tau_0 \\mu_0+\\bar{\\tau}\\bar{X}n}{\\tau_0+ n \\bar\\tau},\\left(\\tau_0+n \\bar\\tau\\right)^{-1}\\right)\n\n<\/annotation><\/semantics><\/math><\/p>\nNow, if we let the prior variance go to infinity, the <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\tau_0<\/annotation><\/semantics><\/math> term goes to zero. In that case, the posterior simplifies to:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\nP \\sim N \\left(\\bar{X},\\left(n \\bar\\tau\\right)^{-1}\\right)\n\n<\/annotation><\/semantics><\/math><\/p>\nWe can plug it into the formula for calculating the difference between two normal distributions:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>X<\/mi><mo>\u2212<\/mo><mi>Y<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><mi>Y<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>n<\/mi><mi>X<\/mi><\/msub><msub><mi>\u03c4<\/mi><mi>X<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>n<\/mi><mi>Y<\/mi><\/msub><msub><mi>\u03c4<\/mi><mi>Y<\/mi><\/msub><\/mrow><\/mfrac><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><mi>Y<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><mfrac><msubsup><mi>s<\/mi><mi>X<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>X<\/mi><\/msub><\/mfrac><mo>+<\/mo><mfrac><msubsup><mi>s<\/mi><mi>Y<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>Y<\/mi><\/msub><\/mfrac><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\n(X - Y) \\sim N(\\mu_x - \\mu_y, s_x^2 + s_y^2) = N(\\bar{X} - \\bar{Y}, \\frac{1}{n_X \\tau_X} + \\frac{1}{n_Y \\tau_Y}) = N(\\bar{X} - \\bar{Y}, \\frac{s_X^2}{n_X} + \\frac{s^2_Y}{n_Y})\n\n<\/annotation><\/semantics><\/math><\/p>\nWhat we get is precisely the sampling distribution used in the frequentist t-test.<\/p>\nSo, no, it\u2019s not true that using uninformative priors will yield rubbish results in an A\/B test<\/strong>. In fact, you\u2019ll get precisely the same results as a one-sided p-value, which also means you have the same statistical guarantees. If your decision criterion is to look at experiment results once and adopt the treatment when the probability that it is above zero is 95% or more (and thus the probability it\u2019s below zero is 5% or less), you will be right 95% of the time, just like you would if you were to rely on p-values and statistical significance.<\/p>\nIt also shows that Bayesian methods are not immune to peeking (as the results are equivalent to a t-test which isn\u2019t either). Peeking is either addressed by informative priors or by <a href=\"http:\/\/varianceexplained.org\/r\/bayesian-ab-testing\/\">reframing the errors you care about altogether<\/a>.<\/p>\n<\/section>\n<\/section>\n<section class=\"level3\" id=\"one-sided-vs.-two-sided-p-values\">\n<h3 data-anchor-id=\"one-sided-vs.-two-sided-p-values\">One-sided vs.\u00a0two-sided p-values<\/h3>\nAt first, the fact that the Bayesian approach leads to a one-sided p-value confused me a bit. I always found one-sided tests weird. What do you mean you are testing only in one direction?<\/em> I understand that there may be situations where only a single direction matters, but in an A\/B testing context, where the outcome metric is a business KPI, surely you want to know if it\u2019s positive or negative? And how stupid<\/em> it would be when you upfront choose to test only in a positive direction but the observed effect is negative and then you don\u2019t report whether it\u2019s statistically significant from zero?<\/p>\nFor a minute, I thought perhaps all those people arguing for one-sided tests were right. 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To be able to claim that it is larger\/smaller than zero, you need two one-sided t-tests instead. Of course, because you are now doing two tests instead of one, you need to adjust for multiple comparisons, so to achieve a 5% Type I error rate, you need to use <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mn>0.025<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=0.025<\/annotation><\/semantics><\/math>.<\/p>\nThis is all horribly confusing if you ask me. Let\u2019s move on.<\/p>\n<\/section>\n<section class=\"level3\" id=\"a-non-gaussian-case\">\n<h3 data-anchor-id=\"a-non-gaussian-case\">A non-Gaussian case<\/h3>\nYou may rightfully wonder if the above result extends to non-Gaussian situations. I can\u2019t prove it mathematically, but numerical simulations tell me the answer is yes. Let\u2019s consider the most popular A\/B testing situation involving binary outcomes (e.g., conversion rates).<\/p>\n<ul>\n<li>Our outcome metric follows the Bernoulli distribution: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><mo>\u223c<\/mo><mtext mathvariant=\"normal\">Bernoulli<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>p<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">X \\sim \\text{Bernoulli}(p)<\/annotation><\/semantics><\/math>. Because the individual user observations are independent, we can interpret the entire sample with <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math> observations and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>k<\/mi><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math> successes as a binomial distribution with rate <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>p<\/mi><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<li>We will use uninformative beta distribution priors <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mn>0<\/mn><\/msub><mo>\u223c<\/mo><mtext mathvariant=\"normal\">Beta<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03b1<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P_0 \\sim \\text{Beta}(\\alpha_0=1,\\beta_0=1)<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>The posterior of a beta prior and binomial likelihood is another conjugate pair, resulting in a beta distribution with parameters <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><msub><mi>\u03b1<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>k<\/mi><mo>,<\/mo><mi>\u03b2<\/mi><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>k<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=\\alpha_0 + k, \\beta = \\beta_0 + (n - k)<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<\/ul>\nWe will also need to be able to calculate a difference between two random variables following Beta distributions. A <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/03610929308831114\">closed-form solution<\/a> exists to calculate this difference, but it involves Appell F1 hypergeometric functions that I couldn\u2019t get to work with large <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math>. So instead, we will rely on the fact that a <a href=\"https:\/\/www.countbayesie.com\/blog\/2022\/11\/30\/understanding-convolutions-in-probability-a-mad-science-perspective\">sum\/difference of two independent PDFs can be calculated using convolutions<\/a>.<\/p>\nLet\u2019s generate some data. We\u2019ll use a baseline of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.17<\/mn><annotation encoding=\"application\/x-tex\">0.17<\/annotation><\/semantics><\/math>, an effect size of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.02<\/mn><annotation encoding=\"application\/x-tex\">0.02<\/annotation><\/semantics><\/math>, and a group size of 6,000, which should yield us ~80% power.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb12\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb12-1\" tabindex=\"-1\"><\/a>eff =<\/span> 0.02<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-2\" tabindex=\"-1\"><\/a>baseline =<\/span> 0.17<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-3\" tabindex=\"-1\"><\/a>n_group =<\/span> 6000<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-4\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-5\" tabindex=\"-1\"><\/a>power.prop.test<\/span>(n=<\/span>n_group, p1 =<\/span> baseline, p2 =<\/span> baseline +<\/span> eff, sig.level=<\/span>0.05<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>\n\n Two-sample comparison of proportions power calculation \n\n\n\n n = 6000\n\n p1 = 0.17\n\n p2 = 0.19\n\n sig.level = 0.05\n\n power = 0.8137145\n\n alternative = two.sided\n\n\n\nNOTE: n is number in *each* group<\/code><\/pre>\n<\/div>\n<\/div>\nLet\u2019s define a couple of helper functions.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb14\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb14-1\" tabindex=\"-1\"><\/a>get_samples =<\/span> function<\/span>(n_group, baseline, eff) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-2\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-3\" tabindex=\"-1\"><\/a> A =<\/span> rbinom<\/span>(n_group, 1<\/span>, baseline),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-4\" tabindex=\"-1\"><\/a> B =<\/span> rbinom<\/span>(n_group, 1<\/span>, baseline +<\/span> eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-5\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-6\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-7\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-8\" tabindex=\"-1\"><\/a>calculate_beta_posterior =<\/span> function<\/span>(X, prior){<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-9\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-10\" tabindex=\"-1\"><\/a> alpha =<\/span> prior$<\/span>alpha +<\/span> sum<\/span>(X),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-11\" tabindex=\"-1\"><\/a> beta =<\/span> prior$<\/span>beta +<\/span> (length<\/span>(X) -<\/span> sum<\/span>(X))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-12\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-13\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-14\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-15\" tabindex=\"-1\"><\/a>#calculate density at a given point X for the difference between two beta distributions<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-16\" tabindex=\"-1\"><\/a>pdf_beta_diff =<\/span> function<\/span>(X, d1, d2) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-17\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-18\" tabindex=\"-1\"><\/a> sapply<\/span>(X, function<\/span>(t) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-19\" tabindex=\"-1\"><\/a> integrate<\/span>(function<\/span>(i) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-20\" tabindex=\"-1\"><\/a> (dbeta<\/span>(i, d1$<\/span>alpha, d1$<\/span>beta) *<\/span> dbeta<\/span>(i-<\/span>t, d2$<\/span>alpha, d2$<\/span>beta) +<\/span> dbeta<\/span>(i, d2$<\/span>alpha, d2$<\/span>beta) *<\/span> dbeta<\/span>(i+<\/span>t, d1$<\/span>alpha, d1$<\/span>beta)) \/<\/span> 2<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-21\" tabindex=\"-1\"><\/a> }, lower=<\/span>-<\/span>Inf<\/span>, upper=<\/span>Inf<\/span>, stop.on.error =<\/span> F)$<\/span>value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-22\" tabindex=\"-1\"><\/a> })<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-23\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-24\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-25\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-26\" tabindex=\"-1\"><\/a>#calculate a total CDF between X and Y for two beta distributions<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-27\" tabindex=\"-1\"><\/a>cdf_beta_diff =<\/span> function<\/span>(X, Y, d1, d2) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-28\" tabindex=\"-1\"><\/a> integrate<\/span>(pdf_beta_diff, d1, d2, lower=<\/span>X, upper=<\/span>Y, stop.on.error =<\/span> F)$<\/span>value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-29\" tabindex=\"-1\"><\/a>}<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\nNow, let\u2019s draw one sample and do the calculations.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb15\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb15-1\" tabindex=\"-1\"><\/a>set.seed<\/span>(42<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-2\" tabindex=\"-1\"><\/a>data =<\/span> get_samples<\/span>(n_group, baseline, eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-3\" tabindex=\"-1\"><\/a>sdist =<\/span> sampling_distribution<\/span>(data$<\/span>B, data$<\/span>A)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-4\" tabindex=\"-1\"><\/a>sdist |><\/span>as_tibble<\/span>() |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-5\" tabindex=\"-1\"><\/a> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> \"statistic\"<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-6\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Summary statistics of the sampling distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-7\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Summary statistics of the sampling distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.016500<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.007012<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb16\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb16-1\" tabindex=\"-1\"><\/a>A_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>A, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb16-2\" tabindex=\"-1\"><\/a>B_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>B, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\nLet\u2019s visualize the posterior vs.\u00a0the sampling distribution.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb17\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb17-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-2\" tabindex=\"-1\"><\/a> fun =<\/span> pdf_beta_diff, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-3\" tabindex=\"-1\"><\/a> args =<\/span> list<\/span>(d1=<\/span>B_posterior, d2=<\/span>A_posterior),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-4\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Posterior of treatment effect'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-5\" tabindex=\"-1\"><\/a> linetype=<\/span>'twodash'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-6\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.05<\/span>, 0.05<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-7\" tabindex=\"-1\"><\/a> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-8\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-9\" tabindex=\"-1\"><\/a> args =<\/span> sdist,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-10\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Sampling distribution'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-11\" tabindex=\"-1\"><\/a> linetype=<\/span>'dotted'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-12\" tabindex=\"-1\"><\/a>) +<\/span> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"Treatment effect posterior distribution vs. Sampling distribution\"<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-13\" tabindex=\"-1\"><\/a> ylab<\/span>(\"Density\"<\/span>) +<\/span> labs<\/span>(color=<\/span>''<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-14\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>(), legend.position=<\/span>'bottom'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nAnd compare one-sided p-value vs.\u00a0posterior probability that treatment is below zero.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb18\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb18-1\" tabindex=\"-1\"><\/a>tibble<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-2\" tabindex=\"-1\"><\/a> statistic =<\/span> c<\/span>('One-sided p-value'<\/span>, 'Probabability treatment is < 0'<\/span>), <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-3\" tabindex=\"-1\"><\/a> value =<\/span> c<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-4\" tabindex=\"-1\"><\/a> t.test<\/span>(data$<\/span>B, data$<\/span>A, alternative=<\/span>'g'<\/span>)$<\/span>p.value, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-5\" tabindex=\"-1\"><\/a> cdf_beta_diff<\/span>(-<\/span>Inf<\/span>, 0<\/span>, B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-6\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-7\" tabindex=\"-1\"><\/a>) |><\/span> kbl<\/span>(caption=<\/span>'P-value vs. Bayesian estimate of treatment effect < 0'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-8\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>P-value vs. Bayesian estimate of treatment effect<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">One-sided p-value<\/td>\n<td style=\"text-align: right;\">0.0093164<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">Probabability treatment is < 0<\/td>\n<td style=\"text-align: right;\">0.0093215<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nEverything looks identical. To be sure, we can repeat the procedure 1000 times.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb19\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb19-1\" tabindex=\"-1\"><\/a>sim_results =<\/span> sapply<\/span>(1<\/span>:<\/span>1000<\/span>, function<\/span>(i) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-2\" tabindex=\"-1\"><\/a> data =<\/span> get_samples<\/span>(n_group, baseline, eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-3\" tabindex=\"-1\"><\/a> A_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>A, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-4\" tabindex=\"-1\"><\/a> B_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>B, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-5\" tabindex=\"-1\"><\/a> posterior_prob_above_zero =<\/span> cdf_beta_diff<\/span>(-<\/span>Inf<\/span>, 0<\/span>, B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-6\" tabindex=\"-1\"><\/a> p_value =<\/span> t.test<\/span>(data$<\/span>B, data$<\/span>A, alternative=<\/span>'g'<\/span>)$<\/span>p.value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-7\" tabindex=\"-1\"><\/a> c<\/span>(posterior_prob_above_zero, p_value)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-8\" tabindex=\"-1\"><\/a>})<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\n<div class=\"cell\">\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nI hope that\u2019s convincing.<\/p>\nAll those difficulties with interpreting p-values? A p-value is not a measure for evidence, etc.? Well, I think I have proven to myself (and hopefully, you, too) that if we are willing to assume that we are equally likely to observe data of any value, then under our very simple and restrictive setting of two independent samples with data generating process following Normal distribution (or distribution that converges to Normal, such as Beta)<\/em>:<\/p>\n<ul>\n<li>A one-sided p-value is equal to the probability that the treatment is negative;<\/p><\/li>\n<li>(1 - p-value) is equal to the probability that the treatment is positive (gasp!)<\/p><\/li>\n<\/ul>\nIn other words, we can all run t-tests and report p-values as probabilities of treatment effects. No more worrying about explaining statistical significance!<\/p>\nSure, I am joking. Or am I?<\/strong><\/p>\nOne good reason not to do that is because the assumption of flat priors is a pretty bad one. 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{"id":635,"date":"2024-06-09T20:12:32","date_gmt":"2024-06-09T20:12:32","guid":{"rendered":"https:\/\/aurimas.eu\/blog\/?p=635"},"modified":"2024-06-09T20:12:32","modified_gmt":"2024-06-09T20:12:32","slug":"p-value-is-the-probability-that-the-treatment-effect-is-larger-than-zero-under-certain-conditions","status":"publish","type":"post","link":"https:\/\/aurimas.eu\/blog\/2024\/06\/p-value-is-the-probability-that-the-treatment-effect-is-larger-than-zero-under-certain-conditions\/","title":{"rendered":"P-value is the probability that the treatment effect is larger than zero (under certain conditions)"},"content":{"rendered":"\n

All code behind this blog post is available on GitHub<\/a>.<\/p>\n\n\n\n\n\n\n\nP-value is the probability that treatment effect is larger than zero. 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toggleContents.style.height = \"0px\";\n\n tocShowing = false;\n\n }\n\n };\n\n\n\n \/\/ Get rid of any expanded toggle if the user scrolls\n\n window.document.addEventListener(\n\n \"scroll\",\n\n throttle(() => {\n\n closeToggle();\n\n }, 50)\n\n );\n\n\n\n \/\/ Handle positioning of the toggle\n\n window.addEventListener(\n\n \"resize\",\n\n throttle(() => {\n\n elRect = undefined;\n\n positionToggle();\n\n }, 50)\n\n );\n\n\n\n window.addEventListener(\"quarto-hrChanged\", () => {\n\n elRect = undefined;\n\n });\n\n\n\n \/\/ Process the click\n\n clickEl.onclick = () => {\n\n if (!tocShowing) {\n\n toggleContainer.classList.add(\"expanded\");\n\n toggleContents.style.height = null;\n\n tocShowing = true;\n\n } else {\n\n closeToggle();\n\n }\n\n };\n\n });\n\n };\n\n\n\n \/\/ Converts a sidebar from a menu back to a sidebar\n\n const convertToSidebar = () => {\n\n for (const child of el.children) {\n\n child.style.opacity = 1;\n\n child.style.overflow = null;\n\n }\n\n\n\n const placeholderEl = window.document.getElementById(\n\n placeholderDescriptor.id\n\n );\n\n if (placeholderEl) {\n\n placeholderEl.remove();\n\n }\n\n\n\n el.classList.remove(\"rollup\");\n\n };\n\n\n\n if (isReaderMode()) {\n\n convertToMenu();\n\n isVisible = false;\n\n } else {\n\n \/\/ Find the top and bottom o the element that is being managed\n\n const elTop = el.offsetTop;\n\n const elBottom =\n\n elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight;\n\n\n\n if (!isVisible) {\n\n \/\/ If the element is current not visible reveal if there are\n\n \/\/ no conflicts with overlay regions\n\n if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) {\n\n convertToSidebar();\n\n isVisible = true;\n\n }\n\n } else {\n\n \/\/ If the element is visible, hide it if it conflicts with overlay regions\n\n \/\/ and insert a placeholder toggle (or if we're in reader mode)\n\n if (inHiddenRegion(elTop, elBottom, hiddenRegions)) {\n\n convertToMenu();\n\n isVisible = false;\n\n }\n\n }\n\n }\n\n }\n\n };\n\n };\n\n\n\n const tabEls = document.querySelectorAll('a[data-bs-toggle=\"tab\"]');\n\n for (const tabEl of tabEls) {\n\n const id = tabEl.getAttribute(\"data-bs-target\");\n\n if (id) {\n\n const columnEl = document.querySelector(\n\n `${id} .column-margin, .tabset-margin-content`\n\n );\n\n if (columnEl)\n\n tabEl.addEventListener(\"shown.bs.tab\", function (event) {\n\n const el = event.srcElement;\n\n if (el) {\n\n const visibleCls = `${el.id}-margin-content`;\n\n \/\/ walk up until we find a parent tabset\n\n let panelTabsetEl = el.parentElement;\n\n while (panelTabsetEl) {\n\n if (panelTabsetEl.classList.contains(\"panel-tabset\")) {\n\n break;\n\n }\n\n panelTabsetEl = panelTabsetEl.parentElement;\n\n }\n\n\n\n if (panelTabsetEl) {\n\n const prevSib = panelTabsetEl.previousElementSibling;\n\n if (\n\n prevSib &&\n\n prevSib.classList.contains(\"tabset-margin-container\")\n\n ) {\n\n const childNodes = prevSib.querySelectorAll(\n\n \".tabset-margin-content\"\n\n );\n\n for (const childEl of childNodes) {\n\n if (childEl.classList.contains(visibleCls)) {\n\n childEl.classList.remove(\"collapse\");\n\n } else {\n\n childEl.classList.add(\"collapse\");\n\n }\n\n }\n\n }\n\n }\n\n }\n\n\n\n layoutMarginEls();\n\n });\n\n }\n\n }\n\n\n\n \/\/ Manage the visibility of the toc and the sidebar\n\n const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, {\n\n id: \"quarto-toc-toggle\",\n\n titleSelector: \"#toc-title\",\n\n dismissOnClick: true,\n\n });\n\n const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, {\n\n id: \"quarto-sidebarnav-toggle\",\n\n titleSelector: \".title\",\n\n dismissOnClick: false,\n\n });\n\n let tocLeftScrollVisibility;\n\n if (leftTocEl) {\n\n tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, {\n\n id: \"quarto-lefttoc-toggle\",\n\n titleSelector: \"#toc-title\",\n\n dismissOnClick: true,\n\n });\n\n }\n\n\n\n \/\/ Find the first element that uses formatting in special columns\n\n const conflictingEls = window.document.body.querySelectorAll(\n\n '[class^=\"column-\"], [class*=\" column-\"], aside, [class*=\"margin-caption\"], [class*=\" margin-caption\"], [class*=\"margin-ref\"], [class*=\" margin-ref\"]'\n\n );\n\n\n\n \/\/ Filter all the possibly conflicting elements into ones\n\n \/\/ the do conflict on the left or ride side\n\n const arrConflictingEls = Array.from(conflictingEls);\n\n const leftSideConflictEls = arrConflictingEls.filter((el) => {\n\n if (el.tagName === \"ASIDE\") {\n\n return false;\n\n }\n\n return Array.from(el.classList).find((className) => {\n\n return (\n\n className !== \"column-body\" &&\n\n className.startsWith(\"column-\") &&\n\n !className.endsWith(\"right\") &&\n\n !className.endsWith(\"container\") &&\n\n className !== \"column-margin\"\n\n );\n\n });\n\n });\n\n const rightSideConflictEls = arrConflictingEls.filter((el) => {\n\n if (el.tagName === \"ASIDE\") {\n\n return true;\n\n }\n\n\n\n const hasMarginCaption = Array.from(el.classList).find((className) => {\n\n return className == \"margin-caption\";\n\n });\n\n if (hasMarginCaption) {\n\n return true;\n\n }\n\n\n\n return Array.from(el.classList).find((className) => {\n\n return (\n\n className !== \"column-body\" &&\n\n !className.endsWith(\"container\") &&\n\n className.startsWith(\"column-\") &&\n\n !className.endsWith(\"left\")\n\n );\n\n });\n\n });\n\n\n\n const kOverlapPaddingSize = 10;\n\n function toRegions(els) {\n\n return els.map((el) => {\n\n const boundRect = el.getBoundingClientRect();\n\n const top =\n\n boundRect.top +\n\n document.documentElement.scrollTop -\n\n kOverlapPaddingSize;\n\n return {\n\n top,\n\n bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize,\n\n };\n\n });\n\n }\n\n\n\n let hasObserved = false;\n\n const visibleItemObserver = (els) => {\n\n let visibleElements = [...els];\n\n const intersectionObserver = new IntersectionObserver(\n\n (entries, _observer) => {\n\n entries.forEach((entry) => {\n\n if (entry.isIntersecting) {\n\n if (visibleElements.indexOf(entry.target) === -1) {\n\n visibleElements.push(entry.target);\n\n }\n\n } else {\n\n visibleElements = visibleElements.filter((visibleEntry) => {\n\n return visibleEntry !== entry;\n\n });\n\n }\n\n });\n\n\n\n if (!hasObserved) {\n\n hideOverlappedSidebars();\n\n }\n\n hasObserved = true;\n\n },\n\n {}\n\n );\n\n els.forEach((el) => {\n\n intersectionObserver.observe(el);\n\n });\n\n\n\n return {\n\n getVisibleEntries: () => {\n\n return visibleElements;\n\n },\n\n };\n\n };\n\n\n\n const rightElementObserver = visibleItemObserver(rightSideConflictEls);\n\n const leftElementObserver = visibleItemObserver(leftSideConflictEls);\n\n\n\n const hideOverlappedSidebars = () => {\n\n marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries()));\n\n sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries()));\n\n if (tocLeftScrollVisibility) {\n\n tocLeftScrollVisibility(\n\n toRegions(leftElementObserver.getVisibleEntries())\n\n );\n\n }\n\n };\n\n\n\n window.quartoToggleReader = () => {\n\n \/\/ Applies a slow class (or removes it)\n\n \/\/ to update the transition speed\n\n const slowTransition = (slow) => {\n\n const manageTransition = (id, slow) => {\n\n const el = document.getElementById(id);\n\n if (el) {\n\n if (slow) {\n\n el.classList.add(\"slow\");\n\n } else {\n\n el.classList.remove(\"slow\");\n\n }\n\n }\n\n };\n\n\n\n manageTransition(\"TOC\", slow);\n\n manageTransition(\"quarto-sidebar\", slow);\n\n };\n\n const readerMode = !isReaderMode();\n\n setReaderModeValue(readerMode);\n\n\n\n \/\/ If we're entering reader mode, slow the transition\n\n if (readerMode) {\n\n slowTransition(readerMode);\n\n }\n\n highlightReaderToggle(readerMode);\n\n hideOverlappedSidebars();\n\n\n\n \/\/ If we're exiting reader mode, restore the non-slow transition\n\n if (!readerMode) {\n\n slowTransition(!readerMode);\n\n }\n\n };\n\n\n\n const highlightReaderToggle = (readerMode) => {\n\n const els = document.querySelectorAll(\".quarto-reader-toggle\");\n\n if (els) {\n\n els.forEach((el) => {\n\n if (readerMode) {\n\n el.classList.add(\"reader\");\n\n } else {\n\n el.classList.remove(\"reader\");\n\n }\n\n });\n\n }\n\n };\n\n\n\n const setReaderModeValue = (val) => {\n\n if (window.location.protocol !== \"file:\") {\n\n window.localStorage.setItem(\"quarto-reader-mode\", val);\n\n } else {\n\n localReaderMode = val;\n\n }\n\n };\n\n\n\n const isReaderMode = () => {\n\n if (window.location.protocol !== \"file:\") {\n\n return window.localStorage.getItem(\"quarto-reader-mode\") === \"true\";\n\n } else {\n\n return localReaderMode;\n\n }\n\n };\n\n let localReaderMode = null;\n\n\n\n const tocOpenDepthStr = tocEl?.getAttribute(\"data-toc-expanded\");\n\n const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1;\n\n\n\n \/\/ Walk the TOC and collapse\/expand nodes\n\n \/\/ Nodes are expanded if:\n\n \/\/ - they are top level\n\n \/\/ - they have children that are 'active' links\n\n \/\/ - they are directly below an link that is 'active'\n\n const walk = (el, depth) => {\n\n \/\/ Tick depth when we enter a UL\n\n if (el.tagName === \"UL\") {\n\n depth = depth + 1;\n\n }\n\n\n\n \/\/ It this is active link\n\n let isActiveNode = false;\n\n if (el.tagName === \"A\" && el.classList.contains(\"active\")) {\n\n isActiveNode = true;\n\n }\n\n\n\n \/\/ See if there is an active child to this element\n\n let hasActiveChild = false;\n\n for (child of el.children) {\n\n hasActiveChild = walk(child, depth) || hasActiveChild;\n\n }\n\n\n\n \/\/ Process the collapse state if this is an UL\n\n if (el.tagName === \"UL\") {\n\n if (tocOpenDepth === -1 && depth > 1) {\n\n el.classList.add(\"collapse\");\n\n } else if (\n\n depth <= tocOpenDepth ||\n\n hasActiveChild ||\n\n prevSiblingIsActiveLink(el)\n\n ) {\n\n el.classList.remove(\"collapse\");\n\n } else {\n\n el.classList.add(\"collapse\");\n\n }\n\n\n\n \/\/ untick depth when we leave a UL\n\n depth = depth - 1;\n\n }\n\n return hasActiveChild || isActiveNode;\n\n };\n\n\n\n \/\/ walk the TOC and expand \/ collapse any items that should be shown\n\n\n\n if (tocEl) {\n\n walk(tocEl, 0);\n\n updateActiveLink();\n\n }\n\n\n\n \/\/ Throttle the scroll event and walk peridiocally\n\n window.document.addEventListener(\n\n \"scroll\",\n\n throttle(() => {\n\n if (tocEl) {\n\n updateActiveLink();\n\n walk(tocEl, 0);\n\n }\n\n if (!isReaderMode()) {\n\n hideOverlappedSidebars();\n\n }\n\n }, 5)\n\n );\n\n window.addEventListener(\n\n \"resize\",\n\n throttle(() => {\n\n if (!isReaderMode()) {\n\n hideOverlappedSidebars();\n\n }\n\n }, 10)\n\n );\n\n hideOverlappedSidebars();\n\n highlightReaderToggle(isReaderMode());\n\n});\n\n\n\n\/\/ grouped tabsets\n\nwindow.addEventListener(\"pageshow\", (_event) => {\n\n function getTabSettings() {\n\n const data = localStorage.getItem(\"quarto-persistent-tabsets-data\");\n\n if (!data) {\n\n localStorage.setItem(\"quarto-persistent-tabsets-data\", \"{}\");\n\n return {};\n\n }\n\n if (data) {\n\n return JSON.parse(data);\n\n }\n\n }\n\n\n\n function setTabSettings(data) {\n\n localStorage.setItem(\n\n \"quarto-persistent-tabsets-data\",\n\n JSON.stringify(data)\n\n );\n\n }\n\n\n\n function setTabState(groupName, groupValue) {\n\n const data = getTabSettings();\n\n data[groupName] = groupValue;\n\n setTabSettings(data);\n\n }\n\n\n\n function toggleTab(tab, active) {\n\n const tabPanelId = tab.getAttribute(\"aria-controls\");\n\n const tabPanel = document.getElementById(tabPanelId);\n\n if (active) {\n\n tab.classList.add(\"active\");\n\n tabPanel.classList.add(\"active\");\n\n } else {\n\n tab.classList.remove(\"active\");\n\n tabPanel.classList.remove(\"active\");\n\n }\n\n }\n\n\n\n function toggleAll(selectedGroup, selectorsToSync) {\n\n for 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Object.keys(f).sort((function(t,e){return f[t]-f[e]}))}const si={name:\"flip\",enabled:!0,phase:\"main\",fn:function(t){var e=t.state,i=t.options,n=t.name;if(!e.modifiersData[n]._skip){for(var s=i.mainAxis,o=void 0===s||s,r=i.altAxis,a=void 0===r||r,l=i.fallbackPlacements,c=i.padding,h=i.boundary,d=i.rootBoundary,u=i.altBoundary,f=i.flipVariations,p=void 0===f||f,m=i.allowedAutoPlacements,g=e.options.placement,_=be(g),b=l||(_!==g&&p?function(t){if(be(t)===Kt)return[];var e=Ve(t);return[Qe(t),e,Qe(e)]}(g):[Ve(g)]),v=[g].concat(b).reduce((function(t,i){return t.concat(be(i)===Kt?ni(e,{placement:i,boundary:h,rootBoundary:d,padding:c,flipVariations:p,allowedAutoPlacements:m}):i)}),[]),y=e.rects.reference,w=e.rects.popper,A=new Map,E=!0,T=v[0],C=0;C<v.length;C++){var O=v[C],x=be(O),k=Fe(O)===Xt,L=[zt,Rt].indexOf(x)>=0,S=L?\"width\":\"height\",D=ii(e,{placement:O,boundary:h,rootBoundary:d,altBoundary:u,padding:c}),$=L?k?qt:Vt:k?Rt:zt;y[S]>w[S]&&($=Ve($));var 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e=t.state,i=t.name,n=e.rects.reference,s=e.rects.popper,o=e.modifiersData.preventOverflow,r=ii(e,{elementContext:\"reference\"}),a=ii(e,{altBoundary:!0}),l=oi(r,n),c=oi(a,s,o),h=ri(l),d=ri(c);e.modifiersData[i]={referenceClippingOffsets:l,popperEscapeOffsets:c,isReferenceHidden:h,hasPopperEscaped:d},e.attributes.popper=Object.assign({},e.attributes.popper,{\"data-popper-reference-hidden\":h,\"data-popper-escaped\":d})}},li={name:\"offset\",enabled:!0,phase:\"main\",requires:[\"popperOffsets\"],fn:function(t){var e=t.state,i=t.options,n=t.name,s=i.offset,o=void 0===s?[0,0]:s,r=ee.reduce((function(t,i){return t[i]=function(t,e,i){var n=be(t),s=[Vt,zt].indexOf(n)>=0?-1:1,o=\"function\"==typeof i?i(Object.assign({},e,{placement:t})):i,r=o[0],a=o[1];return 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vi=Object.freeze(Object.defineProperty({__proto__:null,afterMain:ae,afterRead:se,afterWrite:he,applyStyles:_e,arrow:je,auto:Kt,basePlacements:Qt,beforeMain:oe,beforeRead:ie,beforeWrite:le,bottom:Rt,clippingParents:Ut,computeStyles:Be,createPopper:bi,createPopperBase:gi,createPopperLite:_i,detectOverflow:ii,end:Yt,eventListeners:Re,flip:si,hide:ai,left:Vt,main:re,modifierPhases:de,offset:li,placements:ee,popper:Jt,popperGenerator:mi,popperOffsets:ci,preventOverflow:hi,read:ne,reference:Zt,right:qt,start:Xt,top:zt,variationPlacements:te,viewport:Gt,write:ce},Symbol.toStringTag,{value:\"Module\"})),yi=\"dropdown\",wi=\".bs.dropdown\",Ai=\".data-api\",Ei=\"ArrowUp\",Ti=\"ArrowDown\",Ci=`hide${wi}`,Oi=`hidden${wi}`,xi=`show${wi}`,ki=`shown${wi}`,Li=`click${wi}${Ai}`,Si=`keydown${wi}${Ai}`,Di=`keyup${wi}${Ai}`,$i=\"show\",Ii='[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)',Ni=`${Ii}.${$i}`,Pi=\".dropdown-menu\",Mi=p()?\"top-end\":\"top-start\",ji=p()?\"top-start\":\"top-end\",Fi=p()?\"bottom-end\":\"bottom-start\",Hi=p()?\"bottom-start\":\"bottom-end\",Wi=p()?\"left-start\":\"right-start\",Bi=p()?\"right-start\":\"left-start\",zi={autoClose:!0,boundary:\"clippingParents\",display:\"dynamic\",offset:[0,2],popperConfig:null,reference:\"toggle\"},Ri={autoClose:\"(boolean|string)\",boundary:\"(string|element)\",display:\"string\",offset:\"(array|string|function)\",popperConfig:\"(null|object|function)\",reference:\"(string|element|object)\"};class qi extends W{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=z.next(this._element,Pi)[0]||z.prev(this._element,Pi)[0]||z.findOne(Pi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return zi}static get DefaultType(){return Ri}static get NAME(){return yi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(l(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!N.trigger(this._element,xi,t).defaultPrevented){if(this._createPopper(),\"ontouchstart\"in document.documentElement&&!this._parent.closest(\".navbar-nav\"))for(const t of[].concat(...document.body.children))N.on(t,\"mouseover\",h);this._element.focus(),this._element.setAttribute(\"aria-expanded\",!0),this._menu.classList.add($i),this._element.classList.add($i),N.trigger(this._element,ki,t)}}hide(){if(l(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!N.trigger(this._element,Ci,t).defaultPrevented){if(\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,\"mouseover\",h);this._popper&&this._popper.destroy(),this._menu.classList.remove($i),this._element.classList.remove($i),this._element.setAttribute(\"aria-expanded\",\"false\"),F.removeDataAttribute(this._menu,\"popper\"),N.trigger(this._element,Oi,t)}}_getConfig(t){if(\"object\"==typeof(t=super._getConfig(t)).reference&&!o(t.reference)&&\"function\"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${yi.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`);return t}_createPopper(){if(void 0===vi)throw new TypeError(\"Bootstrap's dropdowns require Popper (https:\/\/popper.js.org)\");let t=this._element;\"parent\"===this._config.reference?t=this._parent:o(this._config.reference)?t=r(this._config.reference):\"object\"==typeof this._config.reference&&(t=this._config.reference);const e=this._getPopperConfig();this._popper=bi(t,this._menu,e)}_isShown(){return this._menu.classList.contains($i)}_getPlacement(){const t=this._parent;if(t.classList.contains(\"dropend\"))return Wi;if(t.classList.contains(\"dropstart\"))return Bi;if(t.classList.contains(\"dropup-center\"))return\"top\";if(t.classList.contains(\"dropdown-center\"))return\"bottom\";const e=\"end\"===getComputedStyle(this._menu).getPropertyValue(\"--bs-position\").trim();return t.classList.contains(\"dropup\")?e?ji:Mi:e?Hi:Fi}_detectNavbar(){return null!==this._element.closest(\".navbar\")}_getOffset(){const{offset:t}=this._config;return\"string\"==typeof t?t.split(\",\").map((t=>Number.parseInt(t,10))):\"function\"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:\"preventOverflow\",options:{boundary:this._config.boundary}},{name:\"offset\",options:{offset:this._getOffset()}}]};return(this._inNavbar||\"static\"===this._config.display)&&(F.setDataAttribute(this._menu,\"popper\",\"static\"),t.modifiers=[{name:\"applyStyles\",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(\".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)\",this._menu).filter((t=>a(t)));i.length&&b(i,e,t===Ti,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=qi.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===e[t])throw new TypeError(`No method named \"${t}\"`);e[t]()}}))}static clearMenus(t){if(2===t.button||\"keyup\"===t.type&&\"Tab\"!==t.key)return;const e=z.find(Ni);for(const i of e){const e=qi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||\"inside\"===e._config.autoClose&&!s||\"outside\"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&(\"keyup\"===t.type&&\"Tab\"===t.key||\/input|select|option|textarea|form\/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};\"click\"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=\/input|textarea\/i.test(t.target.tagName),i=\"Escape\"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi=\"backdrop\",Ki=\"show\",Qi=`mousedown.bs.${Vi}`,Xi={className:\"modal-backdrop\",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:\"body\"},Yi={className:\"string\",clickCallback:\"(function|null)\",isAnimated:\"boolean\",isVisible:\"boolean\",rootElement:\"(element|string)\"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement(\"div\");t.className=this._config.className,this._config.isAnimated&&t.classList.add(\"fade\"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=\".bs.focustrap\",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn=\"backward\",en={autofocus:!0,trapElement:null},nn={autofocus:\"boolean\",trapElement:\"element\"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return\"focustrap\"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){\"Tab\"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:\"forward\")}}const on=\".fixed-top, .fixed-bottom, .is-fixed, .sticky-top\",rn=\".sticky-top\",an=\"padding-right\",ln=\"margin-right\";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,\"overflow\"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,\"overflow\"),this._element.style.overflow=\"hidden\"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=\".bs.modal\",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn=\"modal-open\",An=\"show\",En=\"modal-static\",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:\"(boolean|string)\",focus:\"boolean\",keyboard:\"boolean\"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(\".modal-dialog\",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return\"modal\"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display=\"block\",this._element.removeAttribute(\"aria-hidden\"),this._element.setAttribute(\"aria-modal\",!0),this._element.setAttribute(\"role\",\"dialog\"),this._element.scrollTop=0;const e=z.findOne(\".modal-body\",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{\"Escape\"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&(\"static\"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display=\"none\",this._element.setAttribute(\"aria-hidden\",!0),this._element.removeAttribute(\"aria-modal\"),this._element.removeAttribute(\"role\"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains(\"fade\")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;\"hidden\"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY=\"hidden\"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?\"paddingLeft\":\"paddingRight\";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?\"paddingRight\":\"paddingLeft\";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft=\"\",this._element.style.paddingRight=\"\"}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===i[t])throw new TypeError(`No method named \"${t}\"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle=\"modal\"]',(function(t){const e=z.getElementFromSelector(this);[\"A\",\"AREA\"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(\".modal.show\");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=\".bs.offcanvas\",kn=\".data-api\",Ln=`load${xn}${kn}`,Sn=\"show\",Dn=\"showing\",$n=\"hiding\",In=\".offcanvas.show\",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:\"(boolean|string)\",keyboard:\"boolean\",scroll:\"boolean\"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return\"offcanvas\"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute(\"aria-modal\",!0),this._element.setAttribute(\"role\",\"dialog\"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute(\"aria-modal\"),this._element.removeAttribute(\"role\"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:\"offcanvas-backdrop\",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{\"static\"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{\"Escape\"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if(\"string\"==typeof t){if(void 0===e[t]||t.startsWith(\"_\")||\"constructor\"===t)throw new TypeError(`No method named \"${t}\"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle=\"offcanvas\"]',(function(t){const e=z.getElementFromSelector(this);if([\"A\",\"AREA\"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find(\"[aria-modal][class*=show][class*=offcanvas-]\"))\"fixed\"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={\"*\":[\"class\",\"dir\",\"id\",\"lang\",\"role\",\/^aria-[\\w-]*$\/i],a:[\"target\",\"href\",\"title\",\"rel\"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:[\"src\",\"srcset\",\"alt\",\"title\",\"width\",\"height\"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set([\"background\",\"cite\",\"href\",\"itemtype\",\"longdesc\",\"poster\",\"src\",\"xlink:href\"]),Qn=\/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:\/?#]*(?:[\/?#]|$))\/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:\"\",html:!1,sanitize:!0,sanitizeFn:null,template:\"<div><\/div>\"},Un={allowList:\"object\",content:\"object\",extraClass:\"(string|function)\",html:\"boolean\",sanitize:\"boolean\",sanitizeFn:\"(null|function)\",template:\"string\"},Gn={entry:\"(string|element|function|null)\",selector:\"(string|element)\"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return\"TemplateFactory\"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement(\"div\");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(\" \")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&\"function\"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,\"text\/html\"),s=[].concat(...n.body.querySelectorAll(\"*\"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e[\"*\"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML=\"\",void e.append(t);e.textContent=t.textContent}}const Zn=new Set([\"sanitize\",\"allowList\",\"sanitizeFn\"]),ts=\"fade\",es=\"show\",is=\".modal\",ns=\"hide.bs.modal\",ss=\"hover\",os=\"focus\",rs={AUTO:\"auto\",TOP:\"top\",RIGHT:p()?\"left\":\"right\",BOTTOM:\"bottom\",LEFT:p()?\"right\":\"left\"},as={allowList:Vn,animation:!0,boundary:\"clippingParents\",container:!1,customClass:\"\",delay:0,fallbackPlacements:[\"top\",\"right\",\"bottom\",\"left\"],html:!1,offset:[0,6],placement:\"top\",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'<div class=\"tooltip\" role=\"tooltip\"><div class=\"tooltip-arrow\"><\/div><div class=\"tooltip-inner\"><\/div><\/div>',title:\"\",trigger:\"hover focus\"},ls={allowList:\"object\",animation:\"boolean\",boundary:\"(string|element)\",container:\"(string|element|boolean)\",customClass:\"(string|function)\",delay:\"(number|object)\",fallbackPlacements:\"array\",html:\"boolean\",offset:\"(array|string|function)\",placement:\"(string|function)\",popperConfig:\"(null|object|function)\",sanitize:\"boolean\",sanitizeFn:\"(null|function)\",selector:\"(string|boolean)\",template:\"string\",title:\"(string|element|function)\",trigger:\"string\"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError(\"Bootstrap's tooltips require Popper (https:\/\/popper.js.org)\");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return\"tooltip\"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute(\"data-bs-original-title\")&&this._element.setAttribute(\"title\",this._element.getAttribute(\"data-bs-original-title\")),this._disposePopper(),super.dispose()}show(){if(\"none\"===this._element.style.display)throw new Error(\"Please use show on visible elements\");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName(\"show\")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute(\"aria-describedby\",i.getAttribute(\"id\"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName(\"inserted\"))),this._popper=this._createPopper(i),i.classList.add(es),\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,\"mouseover\",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName(\"shown\")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName(\"hide\")).defaultPrevented){if(this._getTipElement().classList.remove(es),\"ontouchstart\"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,\"mouseover\",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute(\"aria-describedby\"),N.trigger(this._element,this.constructor.eventName(\"hidden\")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return 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id=\"quarto-bootstrap\" rel=\"stylesheet\"\/>\n<script>$(document).ready(function(){\n\n if (typeof $('[data-toggle=\"tooltip\"]').tooltip === 'function') {\n\n $('[data-toggle=\"tooltip\"]').tooltip();\n\n }\n\n if ($('[data-toggle=\"popover\"]').popover === 'function') {\n\n $('[data-toggle=\"popover\"]').popover();\n\n }\n\n});\n\n<\/script>\n\n<\/head>\n<body class=\"fullcontent\">\n<div class=\"page-layout-custom\">\n<header class=\"quarto-title-block default\" id=\"title-block-header\">\n<div class=\"quarto-title\">\n\n<\/div>\n<div class=\"quarto-title-meta\">\n<\/div>\n<\/header>\nAh, the beautiful concept of p-value. The probability of observing the result as extreme or more extreme than the data at hand, assuming the null hypothesis is true. Not a single person ever simplified it to something else. Like.. I don\u2019t know.. the probability that the null hypothesis is true? Or, in an A\/B test, the probability that treatment is greater\/smaller than zero? \ud83d\udc40<\/p>\nDoing that is equivalent to committing an original data science sin. You\u2019d be banished to the ungodly world full of local optima, spaghetti SQL, Excel downloads and out-of-date dashboards. Or simply wouldn\u2019t pass an screening round in a hiring process.<\/p>\nBUT.<\/p>\nP-value can be equal to the probability that the treatment effect is greater\/smaller than zero. In the context of A\/B testing, where we are in a straightforward univariate hypothesis testing setting, it is as simple as employing a Bayesian approach with an uninformative prior.<\/p>\nThis post, I admit, is partly for kicks. But it has some practical implications, too:<\/p>\n<ul>\n<li>Most articles on using Bayesian A\/B testing will tell you that using uninformative priors is not a very good idea. While I agree, the fact that using them yields results equivalent to a most popular frequentist procedure means that they aren\u2019t a terrible choice. There are <a href=\"https:\/\/www.optimizely.com\/insights\/blog\/why-you-should-choose-sequential-testing-and-not-bayesian\/\">some vendors out there that scaremonger<\/a> into shying away from using Bayesian approaches. This post shows that if you choose to go with uninformative priors, you\u2019ll be shooting yourself into the foot as much as you would with a simple t-test.<\/p><\/li>\n<li>The bad thing, however, is that p-values have such an interpretation under very unrealistic assumptions of prior distributions. In practice, thus, interpreting p-value as a direct measure of evidence or using uninformative priors is a bad idea.<\/p><\/li>\n<\/ul>\n<section class=\"level3\" id=\"the-gaussian-case\">\n<h3 data-anchor-id=\"the-gaussian-case\">The Gaussian case<\/h3>\nLet\u2019s consider the following setup:<\/p>\n<ul>\n<li>We\u2019re interested in measuring the impact of a simple A\/B test.<\/p><\/li>\n<li>Our outcome metric happens to be normally distributed: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_A \\sim N(\\mu_A, \\sigma_A)<\/annotation><\/semantics><\/math> and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>B<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_B \\sim N(\\mu_B, \\sigma_B)<\/annotation><\/semantics><\/math>. For simplicity, we will set <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03bc<\/mi><mi>A<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><msub><mi>\u03bc<\/mi><mi>B<\/mi><\/msub><mo>=<\/mo><mn>0.05<\/mn><mo>,<\/mo><mrow><mspace width=\"0.333em\"><\/mspace><mtext mathvariant=\"normal\"> and <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><msub><mi>\u03c3<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>\u03c3<\/mi><mi>B<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\mu_A = 0, \\mu_B = 0.05, \\text{ and } \\sigma_A, \\sigma_B = 1<\/annotation><\/semantics><\/math>. In other words, equal variance, and a treatment effect of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.05<\/mn><annotation encoding=\"application\/x-tex\">0.05<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<\/ul>\nSuppose we ran an experiment and collected 6,000 samples in each experiment arm (that\u2019s 78% power, assuming we set MDE equal to the true unobservable population effect).<\/p>\n<section class=\"level4\" id=\"a-quick-t-test-refresher\">\n<h4 data-anchor-id=\"a-quick-t-test-refresher\">A quick t-test refresher<\/h4>\nIf we were to evaluate our results using a t-test, we would:<\/p>\n<ul>\n<li>Compute sample means: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mtext mathvariant=\"normal\">mean<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Y_A} = \\text{mean}(Y_A)<\/annotation><\/semantics><\/math>, <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mtext mathvariant=\"normal\">mean<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Y_B} = \\text{mean}(Y_B)<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>Compute sample variances: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>s<\/mi><mi>A<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.222em\"><\/mspace><mo>=<\/mo><mtext mathvariant=\"normal\">var<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">s_A^2\\ =\\text{var}(Y_A)<\/annotation><\/semantics><\/math>, <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>s<\/mi><mi>B<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.222em\"><\/mspace><mo>=<\/mo><mtext mathvariant=\"normal\">var<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">s_B^2\\ =\\text{var}(Y_B)<\/annotation><\/semantics><\/math><\/p><\/li>\n<\/ul>\nThen, enabled by CLT, we can claim that the difference of the means between the two groups is normally distributed (that distribution is referred to as the \u201csampling distribution\u201d), with the following parameters:<\/p>\n<ul>\n<li>Mean: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><mi>Z<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mover><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{Z} = \\bar{Y_A} - \\bar{Y_B}<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>Standard error: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>s<\/mi><mi>Z<\/mi><\/msub><mo>=<\/mo><msqrt><mrow><mfrac><msubsup><mi>s<\/mi><mi>A<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>A<\/mi><\/msub><\/mfrac><mo>+<\/mo><mfrac><msubsup><mi>s<\/mi><mi>B<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>B<\/mi><\/msub><\/mfrac><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">s_Z = \\sqrt{\\frac{s_A^2}{n_A} + \\frac{s_B^2}{n_B}}<\/annotation><\/semantics><\/math><\/p><\/li>\n<\/ul>\nFinally, we calculate the test statistic <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><mo>=<\/mo><mover><mi>Z<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>\/<\/mi><msub><mi>s<\/mi><mi>Z<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">t = \\bar{Z} \/ s_Z<\/annotation><\/semantics><\/math>, and look up the associated CDF of the sampling distribution at that point (a.k.a p-value).<\/p>\nThis is how it may look numerically.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb1\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb1-1\" tabindex=\"-1\"><\/a>set.seed<\/span>(42<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-2\" tabindex=\"-1\"><\/a>n =<\/span> 6000<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-3\" tabindex=\"-1\"><\/a>effect_size =<\/span> 0.05<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-4\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-5\" tabindex=\"-1\"><\/a>A =<\/span> rnorm<\/span>(n, 0<\/span>, 1<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-6\" tabindex=\"-1\"><\/a>B =<\/span> rnorm<\/span>(n, effect_size, 1<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-7\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-8\" tabindex=\"-1\"><\/a>sampling_distribution =<\/span> function<\/span>(X, Y) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-9\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-10\" tabindex=\"-1\"><\/a> mean =<\/span> mean<\/span>(X) -<\/span> mean<\/span>(Y),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-11\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>(var<\/span>(X) \/<\/span> n +<\/span> var<\/span>(Y) \/<\/span> n)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-12\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-13\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-14\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-15\" tabindex=\"-1\"><\/a>sdist =<\/span> sampling_distribution<\/span>(B, A)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-16\" tabindex=\"-1\"><\/a>t =<\/span> sdist$<\/span>mean \/<\/span> sdist$<\/span>sd<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-17\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-18\" tabindex=\"-1\"><\/a>as_tibble<\/span>(sdist) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-19\" tabindex=\"-1\"><\/a> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> \"statistic\"<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-20\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Summary statistics of the sampling distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb1-21\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Summary statistics of the sampling distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.0419394<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.0183665<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb2\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb2-1\" tabindex=\"-1\"><\/a>tibble<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-2\" tabindex=\"-1\"><\/a> statistic =<\/span> c<\/span>('Test statistic'<\/span>, 'P-value'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-3\" tabindex=\"-1\"><\/a> value =<\/span> c<\/span>(t, (1<\/span> -<\/span> pnorm<\/span>(t)) *<\/span> 2<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-4\" tabindex=\"-1\"><\/a>) |><\/span> kbl<\/span>(caption=<\/span>'Hypothesis test outcomes'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb2-5\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Hypothesis test outcomes<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">Test statistic<\/td>\n<td style=\"text-align: right;\">2.2834717<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">P-value<\/td>\n<td style=\"text-align: right;\">0.0224026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nAs a visual reminder - the p-value is twice the CDF of the sampling distribution in the range <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo form=\"prefix\" stretchy=\"true\">[<\/mo><mo>\u2212<\/mo><mi>\u221e<\/mi><mo>,<\/mo><mn>0<\/mn><mo form=\"postfix\" stretchy=\"true\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">[-\\infty, 0]<\/annotation><\/semantics><\/math> (twice, because we\u2019re testing for a two-sided alternative hypothesis).<\/p>\n<div class=\"cell\">\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nMathematically, we don\u2019t need to calculate the test statistic. We can get the CDF directly using the parameters of our sampling distribution.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb3\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb3-1\" tabindex=\"-1\"><\/a>#this is also a p-value!<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb3-2\" tabindex=\"-1\"><\/a>format<\/span>(pnorm<\/span>(0<\/span>, mean =<\/span> sdist$<\/span>mean, sd =<\/span> sdist$<\/span>sd, lower.tail=<\/span>T) *<\/span> 2<\/span>, digits=<\/span>4<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>[1] \"0.0224\"<\/code><\/pre>\n<\/div>\n<\/div>\nWe can double-check using the built-in R functions.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb5\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb5-1\" tabindex=\"-1\"><\/a>t.test<\/span>(B, A)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>\n\n Welch Two Sample t-test\n\n\n\ndata: B and A\n\nt = 2.2835, df = 11997, p-value = 0.02242\n\nalternative hypothesis: true difference in means is not equal to 0\n\n95 percent confidence interval:\n\n 0.00593807 0.07794067\n\nsample estimates:\n\n mean of x mean of y \n\n 0.033779917 -0.008159451 <\/code><\/pre>\n<\/div>\n<\/div>\nGreat, we can conclude that, if our hypothesis of treatment having no effect were true, we would be observing a difference between two groups at least as large as we did (we observed a difference of <code>0.041<\/code>) roughly 2% of the time.<\/p>\nSounds rare enough that we could reject our null hypothesis and conclude that there indeed is a difference.<\/p>\nWe also conclude that the true effect should be somewhere between <code>0.005<\/code> and <code>0.078<\/code> 95% of the time if we were to repeat this experiment an infinite number of times. As for this particular run - well, it\u2019s either inside that range or not. T-tests (or frequentist approaches, more generally) don\u2019t tell you anything about this particular experiment. Just long-term probabilities.<\/p>\nA mouthful. But hey, this isn\u2019t a post about issues with null hypothesis testing. I wrote that <a href=\"https:\/\/aurimas.eu\/blog\/2023\/02\/getting-faster-to-decisions-in-a-b-tests-part-2-misinterpretations-and-practical-challenges-of-classical-hypothesis-testing\/\">one already<\/a>.<\/p>\n<\/section>\n<section class=\"level4\" id=\"a-bayesian-approach\">\n<h4 data-anchor-id=\"a-bayesian-approach\">A Bayesian approach<\/h4>\nGenerally, saying \u201cI\u2019m using a Bayesian approach\u201d is like saying \u201cI\u2019m using linear algebra\u201d. It\u2019s not a statistical method. We need an estimand! We will use the simplest one: the probability that the treatment is larger than 0.<\/p>\nNext, we will need uninformative priors. We can achieve that by choosing normal distribution priors with variance approaching infinity (making any number in the real domain roughly equally likely), i.e.:<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>Y<\/mi><mi>A<\/mi><\/msub><mo>,<\/mo><msub><mi>Y<\/mi><mi>B<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mn>0<\/mn><mo>,<\/mo><mn>1<\/mn><mi>\/<\/mi><mi>\u03c4<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">Y_A, Y_B \\sim N(0, 1\/\\tau)<\/annotation><\/semantics><\/math>, where <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>\u03c4<\/mi><annotation encoding=\"application\/x-tex\">\\tau<\/annotation><\/semantics><\/math> is some tiny number, e.g.\u00a00.001.<\/p>\nNote that we did not choose a prior for the treatment effect itself. Instead, we\u2019re effectively saying that both experiment arms have the same mean and can take almost any value with the same likelihood.<\/p>\nHowever, we can see what kind of treatment effect prior distribution our choice implies by leveraging the fact that a difference between two independent normal distributions is just another normal distribution:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mtext mathvariant=\"normal\">if <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><mi>X<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>,<\/mo><mi>Y<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mspace width=\"0.167em\"><\/mspace><mrow><mspace width=\"0.333em\"><\/mspace><mtext mathvariant=\"normal\"> then <\/mtext><mspace width=\"0.333em\"><\/mspace><\/mrow><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>X<\/mi><mo>\u2212<\/mo><mi>Y<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\n\\text{if } X \\sim N(\\mu_x, s_x^2), Y \\sim N(\\mu_y, s_y^2)\\, \\text{ then } (X - Y) \\sim N(\\mu_x - \\mu_y, s_x^2 + s_y^2)\n\n<\/annotation><\/semantics><\/math><\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb7\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb7-1\" tabindex=\"-1\"><\/a>difference_of_two_normals =<\/span> function<\/span>(X, Y) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-2\" tabindex=\"-1\"><\/a> list<\/span> (<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-3\" tabindex=\"-1\"><\/a> mean =<\/span> X$<\/span>mean -<\/span> Y$<\/span>mean,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-4\" tabindex=\"-1\"><\/a> tau =<\/span> 1<\/span> \/<\/span> ((1<\/span> \/<\/span> X$<\/span>tau) +<\/span> (1<\/span> \/<\/span> Y$<\/span>tau)),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-5\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>((1<\/span> \/<\/span> X$<\/span>tau) +<\/span> (1<\/span> \/<\/span> Y$<\/span>tau))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-6\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-7\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-8\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-9\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-10\" tabindex=\"-1\"><\/a>difference_of_two_normals<\/span>(list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>), list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>)) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-11\" tabindex=\"-1\"><\/a> as_tibble<\/span>() |><\/span> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> 'statistic'<\/span>) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-12\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Implied treatment effect prior distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb7-13\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Implied treatment effect prior distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.00000<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">tau<\/td>\n<td style=\"text-align: right;\">0.00050<\/td>\n<\/tr>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">44.72136<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nWe can see that choosing a prior for experiment results of zero mean and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c4<\/mi><mo>=<\/mo><mn>0.001<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\tau=0.001<\/annotation><\/semantics><\/math> (or, equivalently, the standard deviation of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mi>(<\/mi><\/msqrt><mfrac><mn>1<\/mn><mn>0.001<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>31.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt(\\frac{1}{0.001})=31.6<\/annotation><\/semantics><\/math>) yields a prior on the treatment effect that also has a zero mean but has even more uncertainty, with a standard deviation of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>44.7<\/mn><annotation encoding=\"application\/x-tex\">44.7<\/annotation><\/semantics><\/math>.<\/p>\nNext, we need to get to posterior distributions. Luckily, a normal prior and a normal likelihood form a conjugate pair that yields a normal posterior distribution, so we can do this algebraically.<\/p>\nSpecifically, suppose the prior distribution is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mn>0<\/mn><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>,<\/mo><msubsup><mi>\u03c4<\/mi><mn>0<\/mn><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P_0 \\sim N(\\mu_0, \\tau_0^{-1})<\/annotation><\/semantics><\/math>, the observed mean is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> and observed precision is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>=<\/mo><mfrac><mn>1<\/mn><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{\\tau} = \\frac{1}{s^2_x}<\/annotation><\/semantics><\/math>. Then the posterior is <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>n<\/mi><\/mrow><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><\/mfrac><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P \\sim N \\left(\\frac{\\tau_0 \\mu_0+\\bar{\\tau} \\bar{X} n}{\\tau_0+ n \\bar{\\tau}},\\left(\\tau_0+n \\bar{\\tau}\\right)^{-1}\\right)<\/annotation><\/semantics><\/math>. Let\u2019s calculate the posteriors for our samples.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb8\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb8-1\" tabindex=\"-1\"><\/a>calculate_normal_posterior =<\/span> function<\/span>(X, prior) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-2\" tabindex=\"-1\"><\/a> n =<\/span> length<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-3\" tabindex=\"-1\"><\/a> observed_mu =<\/span> mean<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-4\" tabindex=\"-1\"><\/a> observed_tau =<\/span> 1<\/span> \/<\/span> var<\/span>(X)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-5\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-6\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-7\" tabindex=\"-1\"><\/a> mean =<\/span> (prior$<\/span>tau *<\/span> prior$<\/span>mean +<\/span> observed_tau *<\/span> observed_mu *<\/span> n) \/<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-8\" tabindex=\"-1\"><\/a> tau =<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-9\" tabindex=\"-1\"><\/a> sd =<\/span> sqrt<\/span>(1<\/span> \/<\/span> (prior$<\/span>tau +<\/span> n *<\/span> observed_tau))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-10\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-11\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-12\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-13\" tabindex=\"-1\"><\/a>A_posterior =<\/span> calculate_normal_posterior<\/span>(A, list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-14\" tabindex=\"-1\"><\/a>B_posterior =<\/span> calculate_normal_posterior<\/span>(B, list<\/span>(mean=<\/span>0<\/span>, tau=<\/span>0.001<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-15\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-16\" tabindex=\"-1\"><\/a>bind_rows<\/span>(A_posterior, B_posterior, .id =<\/span> 'ID'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-17\" tabindex=\"-1\"><\/a> mutate<\/span>(ID =<\/span> str_replace_all<\/span>(ID, c<\/span>('1'<\/span>=<\/span>'A'<\/span>, '2'<\/span>=<\/span>'B'<\/span>))) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-18\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Posterior distributions of experiment arms'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb8-19\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Posterior distributions of experiment arms<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">ID<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">mean<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">tau<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">sd<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">A<\/td>\n<td style=\"text-align: right;\">-0.0081594<\/td>\n<td style=\"text-align: right;\">5873.761<\/td>\n<td style=\"text-align: right;\">0.0130479<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">B<\/td>\n<td style=\"text-align: right;\">0.0337799<\/td>\n<td style=\"text-align: right;\">5985.180<\/td>\n<td style=\"text-align: right;\">0.0129259<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nWe have posterior distributions for the data of the two samples, but we are after the treatment effect - i.e., the difference between the two samples. We can use the same approach as we did previously when estimating the implied treatment effect prior previously and calculate it, as the two posteriors can be assumed to be independent, too.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb9\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb9-1\" tabindex=\"-1\"><\/a>treatment_posterior =<\/span> difference_of_two_normals<\/span>(B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-2\" tabindex=\"-1\"><\/a>treatment_posterior |><\/span> as_tibble<\/span>() |><\/span> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> 'statistic'<\/span>) |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-3\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Posterior distribution of the treatment effect'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb9-4\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Posterior distribution of the treatment effect<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.0419394<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">tau<\/td>\n<td style=\"text-align: right;\">2964.4734513<\/td>\n<\/tr>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.0183665<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nLet\u2019s visualize it.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb10\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb10-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-2\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-3\" tabindex=\"-1\"><\/a> args =<\/span> within<\/span>(treatment_posterior, rm<\/span>(\"tau\"<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-4\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.1<\/span>, 0.1<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-5\" tabindex=\"-1\"><\/a> geom_vline<\/span>(xintercept=<\/span>0<\/span>, color=<\/span>'red'<\/span>, linetype=<\/span>'dashed'<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-6\" tabindex=\"-1\"><\/a> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"PDF the treatment effect\"<\/span>) +<\/span> ylab<\/span>(\"Density\"<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb10-7\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>())<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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\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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nThat looks familiar! Let\u2019s overlay the sampling distribution from the t-test:<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb11\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb11-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-2\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-3\" tabindex=\"-1\"><\/a> args =<\/span> within<\/span>(treatment_posterior, rm<\/span>(\"tau\"<\/span>)),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-4\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Posterior of a treatment effect'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-5\" tabindex=\"-1\"><\/a> linetype=<\/span>'dashed'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-6\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.1<\/span>, 0.1<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-7\" tabindex=\"-1\"><\/a> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-8\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-9\" tabindex=\"-1\"><\/a> args =<\/span> sdist,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-10\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Sampling distribution'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-11\" tabindex=\"-1\"><\/a> linetype=<\/span>'twodash'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-12\" tabindex=\"-1\"><\/a>) +<\/span> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"Treatment effect posterior distribution vs. Sampling distribution\"<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-13\" tabindex=\"-1\"><\/a> ylab<\/span>(\"Density\"<\/span>) +<\/span> labs<\/span>(color=<\/span>''<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb11-14\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>(), legend.position=<\/span>'bottom'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nThey are identical! This means that the probability of the treatment effect being smaller than zero is\u2014you guessed it\u2014equal to 1\/2 of a two-sided p-value\u2014or, in other words, identical to the one-sided p-value.<\/p>\n<div class=\"quarto-figure quarto-figure-center\">\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid quarto-figure quarto-figure-center figure-img\" 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\"\/><\/p>\n<\/figure>\n<\/div>\nThis is no coincidence. We can prove that mathematically. Here\u2019s the posterior formula again:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mfrac><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mi>n<\/mi><\/mrow><mrow><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><\/mrow><\/mfrac><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\nP \\sim N \\left(\\frac{\\tau_0 \\mu_0+\\bar{\\tau}\\bar{X}n}{\\tau_0+ n \\bar\\tau},\\left(\\tau_0+n \\bar\\tau\\right)^{-1}\\right)\n\n<\/annotation><\/semantics><\/math><\/p>\nNow, if we let the prior variance go to infinity, the <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>\u03c4<\/mi><mn>0<\/mn><\/msub><annotation encoding=\"application\/x-tex\">\\tau_0<\/annotation><\/semantics><\/math> term goes to zero. In that case, the posterior simplifies to:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><msup><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>n<\/mi><mover><mi>\u03c4<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\nP \\sim N \\left(\\bar{X},\\left(n \\bar\\tau\\right)^{-1}\\right)\n\n<\/annotation><\/semantics><\/math><\/p>\nWe can plug it into the formula for calculating the difference between two normal distributions:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>X<\/mi><mo>\u2212<\/mo><mi>Y<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>\u223c<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03bc<\/mi><mi>x<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>\u03bc<\/mi><mi>y<\/mi><\/msub><mo>,<\/mo><msubsup><mi>s<\/mi><mi>x<\/mi><mn>2<\/mn><\/msubsup><mo>+<\/mo><msubsup><mi>s<\/mi><mi>y<\/mi><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><mi>Y<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>n<\/mi><mi>X<\/mi><\/msub><msub><mi>\u03c4<\/mi><mi>X<\/mi><\/msub><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mrow><msub><mi>n<\/mi><mi>Y<\/mi><\/msub><msub><mi>\u03c4<\/mi><mi>Y<\/mi><\/msub><\/mrow><\/mfrac><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>N<\/mi><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mover><mi>X<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mover><mi>Y<\/mi><mo accent=\"true\">\u203e<\/mo><\/mover><mo>,<\/mo><mfrac><msubsup><mi>s<\/mi><mi>X<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>X<\/mi><\/msub><\/mfrac><mo>+<\/mo><mfrac><msubsup><mi>s<\/mi><mi>Y<\/mi><mn>2<\/mn><\/msubsup><msub><mi>n<\/mi><mi>Y<\/mi><\/msub><\/mfrac><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\n\n(X - Y) \\sim N(\\mu_x - \\mu_y, s_x^2 + s_y^2) = N(\\bar{X} - \\bar{Y}, \\frac{1}{n_X \\tau_X} + \\frac{1}{n_Y \\tau_Y}) = N(\\bar{X} - \\bar{Y}, \\frac{s_X^2}{n_X} + \\frac{s^2_Y}{n_Y})\n\n<\/annotation><\/semantics><\/math><\/p>\nWhat we get is precisely the sampling distribution used in the frequentist t-test.<\/p>\nSo, no, it\u2019s not true that using uninformative priors will yield rubbish results in an A\/B test<\/strong>. In fact, you\u2019ll get precisely the same results as a one-sided p-value, which also means you have the same statistical guarantees. If your decision criterion is to look at experiment results once and adopt the treatment when the probability that it is above zero is 95% or more (and thus the probability it\u2019s below zero is 5% or less), you will be right 95% of the time, just like you would if you were to rely on p-values and statistical significance.<\/p>\nIt also shows that Bayesian methods are not immune to peeking (as the results are equivalent to a t-test which isn\u2019t either). Peeking is either addressed by informative priors or by <a href=\"http:\/\/varianceexplained.org\/r\/bayesian-ab-testing\/\">reframing the errors you care about altogether<\/a>.<\/p>\n<\/section>\n<\/section>\n<section class=\"level3\" id=\"one-sided-vs.-two-sided-p-values\">\n<h3 data-anchor-id=\"one-sided-vs.-two-sided-p-values\">One-sided vs.\u00a0two-sided p-values<\/h3>\nAt first, the fact that the Bayesian approach leads to a one-sided p-value confused me a bit. I always found one-sided tests weird. What do you mean you are testing only in one direction?<\/em> I understand that there may be situations where only a single direction matters, but in an A\/B testing context, where the outcome metric is a business KPI, surely you want to know if it\u2019s positive or negative? And how stupid<\/em> it would be when you upfront choose to test only in a positive direction but the observed effect is negative and then you don\u2019t report whether it\u2019s statistically significant from zero?<\/p>\nFor a minute, I thought perhaps all those people arguing for one-sided tests were right. 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To be able to claim that it is larger\/smaller than zero, you need two one-sided t-tests instead. Of course, because you are now doing two tests instead of one, you need to adjust for multiple comparisons, so to achieve a 5% Type I error rate, you need to use <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mn>0.025<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=0.025<\/annotation><\/semantics><\/math>.<\/p>\nThis is all horribly confusing if you ask me. Let\u2019s move on.<\/p>\n<\/section>\n<section class=\"level3\" id=\"a-non-gaussian-case\">\n<h3 data-anchor-id=\"a-non-gaussian-case\">A non-Gaussian case<\/h3>\nYou may rightfully wonder if the above result extends to non-Gaussian situations. I can\u2019t prove it mathematically, but numerical simulations tell me the answer is yes. Let\u2019s consider the most popular A\/B testing situation involving binary outcomes (e.g., conversion rates).<\/p>\n<ul>\n<li>Our outcome metric follows the Bernoulli distribution: <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><mo>\u223c<\/mo><mtext mathvariant=\"normal\">Bernoulli<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>p<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">X \\sim \\text{Bernoulli}(p)<\/annotation><\/semantics><\/math>. Because the individual user observations are independent, we can interpret the entire sample with <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math> observations and <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>k<\/mi><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math> successes as a binomial distribution with rate <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>p<\/mi><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<li>We will use uninformative beta distribution priors <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mn>0<\/mn><\/msub><mo>\u223c<\/mo><mtext mathvariant=\"normal\">Beta<\/mtext><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><msub><mi>\u03b1<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>1<\/mn><mo>,<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">P_0 \\sim \\text{Beta}(\\alpha_0=1,\\beta_0=1)<\/annotation><\/semantics><\/math><\/p><\/li>\n<li>The posterior of a beta prior and binomial likelihood is another conjugate pair, resulting in a beta distribution with parameters <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><msub><mi>\u03b1<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mi>k<\/mi><mo>,<\/mo><mi>\u03b2<\/mi><mo>=<\/mo><msub><mi>\u03b2<\/mi><mn>0<\/mn><\/msub><mo>+<\/mo><mrow><mo form=\"prefix\" stretchy=\"true\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>k<\/mi><mo form=\"postfix\" stretchy=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=\\alpha_0 + k, \\beta = \\beta_0 + (n - k)<\/annotation><\/semantics><\/math>.<\/p><\/li>\n<\/ul>\nWe will also need to be able to calculate a difference between two random variables following Beta distributions. A <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/03610929308831114\">closed-form solution<\/a> exists to calculate this difference, but it involves Appell F1 hypergeometric functions that I couldn\u2019t get to work with large <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math>. So instead, we will rely on the fact that a <a href=\"https:\/\/www.countbayesie.com\/blog\/2022\/11\/30\/understanding-convolutions-in-probability-a-mad-science-perspective\">sum\/difference of two independent PDFs can be calculated using convolutions<\/a>.<\/p>\nLet\u2019s generate some data. We\u2019ll use a baseline of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.17<\/mn><annotation encoding=\"application\/x-tex\">0.17<\/annotation><\/semantics><\/math>, an effect size of <math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mn>0.02<\/mn><annotation encoding=\"application\/x-tex\">0.02<\/annotation><\/semantics><\/math>, and a group size of 6,000, which should yield us ~80% power.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb12\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb12-1\" tabindex=\"-1\"><\/a>eff =<\/span> 0.02<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-2\" tabindex=\"-1\"><\/a>baseline =<\/span> 0.17<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-3\" tabindex=\"-1\"><\/a>n_group =<\/span> 6000<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-4\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb12-5\" tabindex=\"-1\"><\/a>power.prop.test<\/span>(n=<\/span>n_group, p1 =<\/span> baseline, p2 =<\/span> baseline +<\/span> eff, sig.level=<\/span>0.05<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output cell-output-stdout\">\n<pre><code>\n\n Two-sample comparison of proportions power calculation \n\n\n\n n = 6000\n\n p1 = 0.17\n\n p2 = 0.19\n\n sig.level = 0.05\n\n power = 0.8137145\n\n alternative = two.sided\n\n\n\nNOTE: n is number in *each* group<\/code><\/pre>\n<\/div>\n<\/div>\nLet\u2019s define a couple of helper functions.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb14\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb14-1\" tabindex=\"-1\"><\/a>get_samples =<\/span> function<\/span>(n_group, baseline, eff) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-2\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-3\" tabindex=\"-1\"><\/a> A =<\/span> rbinom<\/span>(n_group, 1<\/span>, baseline),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-4\" tabindex=\"-1\"><\/a> B =<\/span> rbinom<\/span>(n_group, 1<\/span>, baseline +<\/span> eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-5\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-6\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-7\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-8\" tabindex=\"-1\"><\/a>calculate_beta_posterior =<\/span> function<\/span>(X, prior){<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-9\" tabindex=\"-1\"><\/a> list<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-10\" tabindex=\"-1\"><\/a> alpha =<\/span> prior$<\/span>alpha +<\/span> sum<\/span>(X),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-11\" tabindex=\"-1\"><\/a> beta =<\/span> prior$<\/span>beta +<\/span> (length<\/span>(X) -<\/span> sum<\/span>(X))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-12\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-13\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-14\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-15\" tabindex=\"-1\"><\/a>#calculate density at a given point X for the difference between two beta distributions<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-16\" tabindex=\"-1\"><\/a>pdf_beta_diff =<\/span> function<\/span>(X, d1, d2) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-17\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-18\" tabindex=\"-1\"><\/a> sapply<\/span>(X, function<\/span>(t) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-19\" tabindex=\"-1\"><\/a> integrate<\/span>(function<\/span>(i) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-20\" tabindex=\"-1\"><\/a> (dbeta<\/span>(i, d1$<\/span>alpha, d1$<\/span>beta) *<\/span> dbeta<\/span>(i-<\/span>t, d2$<\/span>alpha, d2$<\/span>beta) +<\/span> dbeta<\/span>(i, d2$<\/span>alpha, d2$<\/span>beta) *<\/span> dbeta<\/span>(i+<\/span>t, d1$<\/span>alpha, d1$<\/span>beta)) \/<\/span> 2<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-21\" tabindex=\"-1\"><\/a> }, lower=<\/span>-<\/span>Inf<\/span>, upper=<\/span>Inf<\/span>, stop.on.error =<\/span> F)$<\/span>value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-22\" tabindex=\"-1\"><\/a> })<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-23\" tabindex=\"-1\"><\/a> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-24\" tabindex=\"-1\"><\/a>}<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-25\" tabindex=\"-1\"><\/a><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-26\" tabindex=\"-1\"><\/a>#calculate a total CDF between X and Y for two beta distributions<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-27\" tabindex=\"-1\"><\/a>cdf_beta_diff =<\/span> function<\/span>(X, Y, d1, d2) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-28\" tabindex=\"-1\"><\/a> integrate<\/span>(pdf_beta_diff, d1, d2, lower=<\/span>X, upper=<\/span>Y, stop.on.error =<\/span> F)$<\/span>value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb14-29\" tabindex=\"-1\"><\/a>}<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\nNow, let\u2019s draw one sample and do the calculations.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb15\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb15-1\" tabindex=\"-1\"><\/a>set.seed<\/span>(42<\/span>)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-2\" tabindex=\"-1\"><\/a>data =<\/span> get_samples<\/span>(n_group, baseline, eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-3\" tabindex=\"-1\"><\/a>sdist =<\/span> sampling_distribution<\/span>(data$<\/span>B, data$<\/span>A)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-4\" tabindex=\"-1\"><\/a>sdist |><\/span>as_tibble<\/span>() |><\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-5\" tabindex=\"-1\"><\/a> pivot_longer<\/span>(everything<\/span>(), names_to =<\/span> \"statistic\"<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-6\" tabindex=\"-1\"><\/a> kbl<\/span>(caption=<\/span>'Summary statistics of the sampling distribution'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb15-7\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>Summary statistics of the sampling distribution<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">mean<\/td>\n<td style=\"text-align: right;\">0.016500<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">sd<\/td>\n<td style=\"text-align: right;\">0.007012<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"cell\">\n<details class=\"code-fold\" open=\"\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb16\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb16-1\" tabindex=\"-1\"><\/a>A_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>A, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb16-2\" tabindex=\"-1\"><\/a>B_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>B, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\nLet\u2019s visualize the posterior vs.\u00a0the sampling distribution.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb17\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb17-1\" tabindex=\"-1\"><\/a>ggplot<\/span>() +<\/span> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-2\" tabindex=\"-1\"><\/a> fun =<\/span> pdf_beta_diff, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-3\" tabindex=\"-1\"><\/a> args =<\/span> list<\/span>(d1=<\/span>B_posterior, d2=<\/span>A_posterior),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-4\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Posterior of treatment effect'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-5\" tabindex=\"-1\"><\/a> linetype=<\/span>'twodash'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-6\" tabindex=\"-1\"><\/a>) +<\/span> xlim<\/span>(-<\/span>0.05<\/span>, 0.05<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-7\" tabindex=\"-1\"><\/a> geom_function<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-8\" tabindex=\"-1\"><\/a> fun =<\/span> dnorm, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-9\" tabindex=\"-1\"><\/a> args =<\/span> sdist,<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-10\" tabindex=\"-1\"><\/a> aes<\/span>(color =<\/span> 'Sampling distribution'<\/span>),<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-11\" tabindex=\"-1\"><\/a> linetype=<\/span>'dotted'<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-12\" tabindex=\"-1\"><\/a>) +<\/span> xlab<\/span>(\"\"<\/span>) +<\/span> ggtitle<\/span>(\"Treatment effect posterior distribution vs. Sampling distribution\"<\/span>) +<\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-13\" tabindex=\"-1\"><\/a> ylab<\/span>(\"Density\"<\/span>) +<\/span> labs<\/span>(color=<\/span>''<\/span>) +<\/span><\/span>\n\n<a aria-hidden=\"true\" href=\"#cb17-14\" tabindex=\"-1\"><\/a> theme_light<\/span>() +<\/span> theme<\/span>(panel.grid=<\/span>element_blank<\/span>(), legend.position=<\/span>'bottom'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nAnd compare one-sided p-value vs.\u00a0posterior probability that treatment is below zero.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb18\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb18-1\" tabindex=\"-1\"><\/a>tibble<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-2\" tabindex=\"-1\"><\/a> statistic =<\/span> c<\/span>('One-sided p-value'<\/span>, 'Probabability treatment is < 0'<\/span>), <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-3\" tabindex=\"-1\"><\/a> value =<\/span> c<\/span>(<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-4\" tabindex=\"-1\"><\/a> t.test<\/span>(data$<\/span>B, data$<\/span>A, alternative=<\/span>'g'<\/span>)$<\/span>p.value, <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-5\" tabindex=\"-1\"><\/a> cdf_beta_diff<\/span>(-<\/span>Inf<\/span>, 0<\/span>, B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-6\" tabindex=\"-1\"><\/a> )<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-7\" tabindex=\"-1\"><\/a>) |><\/span> kbl<\/span>(caption=<\/span>'P-value vs. Bayesian estimate of treatment effect < 0'<\/span>) |><\/span> <\/span>\n\n<a aria-hidden=\"true\" href=\"#cb18-8\" tabindex=\"-1\"><\/a> kable_minimal<\/span>(full_width =<\/span> T, position=<\/span>'left'<\/span>)<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<div class=\"cell-output-display\">\n<table class=\"lightable-minimal table table-sm table-striped small\" data-quarto-postprocess=\"true\">\n<caption>P-value vs. Bayesian estimate of treatment effect<\/caption>\n<thead>\n<tr class=\"header\">\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: left;\">statistic<\/th>\n<th data-quarto-table-cell-role=\"th\" style=\"text-align: right;\">value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"odd\">\n<td style=\"text-align: left;\">One-sided p-value<\/td>\n<td style=\"text-align: right;\">0.0093164<\/td>\n<\/tr>\n<tr class=\"even\">\n<td style=\"text-align: left;\">Probabability treatment is < 0<\/td>\n<td style=\"text-align: right;\">0.0093215<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\nEverything looks identical. To be sure, we can repeat the procedure 1000 times.<\/p>\n<div class=\"cell\">\n<details class=\"code-fold\">\n<summary>Show code<\/summary>\n<div class=\"sourceCode cell-code\" id=\"cb19\"><pre class=\"sourceCode r code-with-copy\"><code class=\"sourceCode r\"><a aria-hidden=\"true\" href=\"#cb19-1\" tabindex=\"-1\"><\/a>sim_results =<\/span> sapply<\/span>(1<\/span>:<\/span>1000<\/span>, function<\/span>(i) {<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-2\" tabindex=\"-1\"><\/a> data =<\/span> get_samples<\/span>(n_group, baseline, eff)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-3\" tabindex=\"-1\"><\/a> A_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>A, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-4\" tabindex=\"-1\"><\/a> B_posterior =<\/span> calculate_beta_posterior<\/span>(data$<\/span>B, list<\/span>(alpha=<\/span>1<\/span>, beta=<\/span>1<\/span>))<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-5\" tabindex=\"-1\"><\/a> posterior_prob_above_zero =<\/span> cdf_beta_diff<\/span>(-<\/span>Inf<\/span>, 0<\/span>, B_posterior, A_posterior)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-6\" tabindex=\"-1\"><\/a> p_value =<\/span> t.test<\/span>(data$<\/span>B, data$<\/span>A, alternative=<\/span>'g'<\/span>)$<\/span>p.value<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-7\" tabindex=\"-1\"><\/a> c<\/span>(posterior_prob_above_zero, p_value)<\/span>\n\n<a aria-hidden=\"true\" href=\"#cb19-8\" tabindex=\"-1\"><\/a>})<\/span><\/code><button class=\"code-copy-button\" title=\"Copy to Clipboard\"><\/i><\/button><\/pre><\/div>\n<\/details>\n<\/div>\n<div class=\"cell\">\n<div class=\"cell-output-display\">\n<div>\n<figure class=\"figure\">\n<img decoding=\"async\" class=\"img-fluid figure-img\" 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width=\"768\"\/><\/p>\n<\/figure>\n<\/div>\n<\/div>\n<\/div>\nI hope that\u2019s convincing.<\/p>\nAll those difficulties with interpreting p-values? A p-value is not a measure for evidence, etc.? Well, I think I have proven to myself (and hopefully, you, too) that if we are willing to assume that we are equally likely to observe data of any value, then under our very simple and restrictive setting of two independent samples with data generating process following Normal distribution (or distribution that converges to Normal, such as Beta)<\/em>:<\/p>\n<ul>\n<li>A one-sided p-value is equal to the probability that the treatment is negative;<\/p><\/li>\n<li>(1 - p-value) is equal to the probability that the treatment is positive (gasp!)<\/p><\/li>\n<\/ul>\nIn other words, we can all run t-tests and report p-values as probabilities of treatment effects. No more worrying about explaining statistical significance!<\/p>\nSure, I am joking. Or am I?<\/strong><\/p>\nOne good reason not to do that is because the assumption of flat priors is a pretty bad one. 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