2d:null 2e:["$","title",null,{"children":"ANOVA Calculator | Eli Holder | Observable"}] 33:Ta69,criticalQ = ((alpha, dfb, dfw) => { //view-source:http://www.vassarstats.net/tabs.html#q // Looking for # of treatments, not degrees of freedom dfb= dfb+1 if (alpha != 0.05 && alpha != 0.01 ) return null var pi=Math.PI; var pj2=pi/2; var pj4=pi/4; var pi2=2*pi; var e = Math.E; var exx = 1.10517091807564; var dgr=180/pi; function buzz(t,n) { t=Math.abs(t); var rt=t/Math.sqrt(n); var fk=Math.atan(rt); if(n==1) { return 1-fk/pj2 } var ek=Math.sin(fk); var dk=Math.cos(fk) if((n%2)==1) { return 1-(fk+ek*dk*zip(dk*dk,2,n-3,-1))/pj2 } else { return 1-ek*zip(dk*dk,1,n-3,-1) } } function zip(q,i,j,b) { var zz=1; var z=zz; var k=i; while(k<=j) { zz=zz*q*k/(k-b); z=z+zz; k=k+2 } return z } function rnd2(x){return Math.round(x*100)/100} function Tcall(x) { var zk if(x>=0) { zk=''+(x+0.0000005) } else { zk=''+(x-0.0000005) } return zk.substring(0,zk.indexOf('.')+7) } function qcalc() { var t = 1*1.6; var crit0 = 1*0; var t05 = 1*0; var t01 = 1*0; var q05 = 1*0; var q01 = 1*0; var k = Math.floor(dfb*1); var df = Math.floor(dfw*1); for (var j=0; j<10000; j++) { t+=.005; crit0 = Tcall(buzz(eval(t),eval(df))); if(crit0<=.05){t05=t;break;} } for (var j=0; j<10000; j++) { t+=.005; crit0 = Tcall(buzz(eval(t),eval(df))); if(crit0<=.01){t01=t;break;} } if(k==3) { q05 = 2.106973*t05-0.817944; q01 = 1.946821*t01-0.8996111; } if(k==4) { q05 = 2.59017*t05-1.443969; q01 = 2.303537*t01-1.534593; } if(k==5) { q05 = 2.972018*t05-1.96814; q01 = 2.587002*t01-2.064423; } if(k==6) { q05 = 3.27313260295899*t05-2.38279010928828; q01 = 2.85765551110653*t01-2.61819815698612; } if(k==7) { q05 = 3.53785626144803*t05-2.76274478043922; q01 = 3.04988915773087*t01-2.98527857882349; } if(k==8) { q05 = 3.75342544999978*t05-3.06529742825939; q01 = 3.21818903063174*t01-3.31378857989615; } if(k==9) { q05 = 3.94085173471745*t05-3.32653946392437; q01 = 3.37614586515416*t01-3.64658532621697; } if(k==10) { q05 = 4.1063693875735*t05-3.559775633569; q01 = 3.4911129101093*t01-3.8429755454712; } if(k<3||k>10){ return null } return {[.05]: rnd2(q05), [.01]: rnd2(q01)}[alpha] } return qcalc() })34:[] 31:{"id":"369ecbbacc039099","slug":"anova-calculator","title":"ANOVA Calculator","thumbnail":"cea165b8e782c6bcd2602a05655b9e7d16e46025225c6fd2df5c1703efacb39c","access_level":"public","create_time":"$D2020-06-04T22:43:20.597Z","update_time":"$D2021-06-08T00:08:50.455Z","view_time":null,"first_public_time":"$D2020-09-16T20:49:40.988Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"58eacf8e202aa99c","login":"elibryan","name":"Eli Holder","avatar_url":"https://avatars-next.observableusercontent.com/f42ede38e59d5fab5318c3a05de38dc47c2f88ee4bd796d32ced88733e2b8d50","tier":"starter_2024"},"version":216,"publish_version":216,"role":null,"authored":false,"authors":[{"type":"individual","id":"d17a47a44abf3446","login":"elibryan","name":"Eli Holder","avatar_url":"https://avatars-next.observableusercontent.com/f42ede38e59d5fab5318c3a05de38dc47c2f88ee4bd796d32ced88733e2b8d50","tier":null}],"members":[{"type":"individual","id":"d17a47a44abf3446","login":"elibryan","name":"Eli Holder","avatar_url":"https://avatars-next.observableusercontent.com/f42ede38e59d5fab5318c3a05de38dc47c2f88ee4bd796d32ced88733e2b8d50","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"ANOVA Calculator","cells":[{"id":0,"value":"md`# ANOVA Calculator\nReproducing this explainer: https://www.brownmath.com/stat/anova1.htm#Indiv`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"md`## Example 1: Donut Fat`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"fatAbsorptionData = ({\n 'fat1': [64, 72, 68, 77, 56, 95],\n 'fat2': [78, 91, 97, 82, 85, 77],\n 'fat3': [75, 93, 78, 71, 63, 76],\n 'fat4': [55, 66, 49, 64, 70, 68],\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"table(\n Object.entries(fatAbsorptionData).map(([k,vs])=>({\n \"\": k,\n \"g Fat Aborbed in Batch\": vs.join(\", \"),\n \"mean\": d3.mean(vs),\n \"SD\": d3.deviation(vs)\n })))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"alpha = 0.05","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"{\n let data = Object.values(fatAbsorptionData)\n\n const hasSimilarSizeSamples = d3.deviation(data.map(vs=>vs.length))==0\n const isNormal = '??'\n const hasSimilarSDs= d3.max(data.map(ds=>d3.deviation(ds))) <= (2 * d3.min(data.map(ds=>d3.deviation(ds))))\n \nreturn md`## ANOVA Requirements:\n\n* Independent Samples, close to the same size: ${hasSimilarSizeSamples}\n* Samples are normally distributed: ??\n* Samples have similar standard deviations: ${hasSimilarSDs }\n`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"md`## ANOVA Results`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":108,"value":"anovaResults= oneWayANOVA(Object.values(fatAbsorptionData))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":90,"value":"{\n return table(\n [{\"\": \"Between\", \"SS\": anovaResults.ssb, \"df\": anovaResults.dfb, \"MS\": anovaResults.msb, \"F\": anovaResults.fScore, \"p\": anovaResults.pValue, \"eta^2\": anovaResults.eta2},\n {\"\": \"Within\", \"SS\": anovaResults.ssw, \"df\": anovaResults.dfw, \"MS\": anovaResults.msw},\n {\"\": \"Total\", \"SS\": anovaResults.ssw+anovaResults.ssb, \"df\": anovaResults.dfw+anovaResults.dfb}]\n )}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"md`${((alpha>=anovaResults.pValue)? \"p <= alpha, therefore significant\": \"p > alpha, therefore not significant\") }`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"md`## Post-Hoc Analysis`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":174,"value":"{\n const postHocResults = tukeyTable(fatAbsorptionData)\n \n return table(Object.keys(postHocResults).map(rowKey=>{\n \n const row = Object.keys(postHocResults).reduce((acc,columnKey)=>{\n if (rowKey == columnKey) return {}\n \n const pairResults = postHocResults[rowKey][columnKey]\n \n return {...acc, ...{[columnKey]: `${pairResults.meanDiff} ± ${pairResults.ci.toFixed(2)} ${(pairResults.significant? \"(significant)\" : \"\")}`}\n \n }},{})\n \n return {\"\": rowKey, ...row}\n \n })\n \n )}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"tukeyTable = ((data)=> {\n \n const anovaResults = oneWayANOVA(Object.values(data))\n return Object.entries(data).reduce((acc,[rowKey,rowValues])=>{\n \n const row = Object.entries(data)\n .reduce((acc,[columnKey,columnValues])=> {\n if (rowKey == columnKey) return acc\n\n const meanDiff= d3.mean(rowValues) - d3.mean(columnValues)\n const critQ = criticalQ(alpha, anovaResults.dfb, anovaResults.dfw)\n const standardizedError = Math.sqrt(anovaResults.msw*0.5*((1/rowValues.length)+(1/columnValues.length)))\n const ci = critQ * standardizedError\n const ciLeft= meanDiff - ci\n const ciRight = meanDiff + ci\n const significant= ((0 {\n \n const grandMean = d3.mean(data.flat())\n \n // Sum of Squares (Within)\n const ssw = d3.sum(data.map(values=>{\n const meanWithin = d3.mean(values)\n return d3.sum(values.map(value=>Math.pow(value-meanWithin, 2)))\n }))\n \n // Degrees of Freedom (Within)\n const dfw = d3.sum(data.map(values=>{\n return values.length - 1\n }))\n \n // Mean Square (Within)\n const msw = ssw / dfw\n \n // Sum of squares between\n const ssb = d3.sum(data.map(values=>{\n const meanWithin = d3.mean(values)\n return values.length * Math.pow(meanWithin - grandMean, 2)\n }))\n \n // Degrees of freedom between\n const dfb = data.length - 1\n \n // Mean Square (Between)\n const msb = ssb / dfb\n \n const fScore = (ssb/dfb)/(ssw/dfw)\n \n const pValue = fTable(fScore, dfb, dfw)\n \n // Strength of Association\n const eta2= ssb / (ssb+ssw)\n\n return {ssw, dfw, msw, ssb, dfb, msb, fScore, pValue, eta2}\n // d3.sum(ds.map(d=>Math.pow(d[key]-meanWithin, 2)))\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":83,"value":"fTable = (fScore, p1,p2) => {\t\n//view-source:https://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/pvalues.htm#rfdist\n //\n \tvar Pi=Math.PI; var PiD2=Pi/2; var PiD4=Pi/4; var Pi2=2*Pi\n\tvar e=2.718281828459045235; var e10 = 1.105170918075647625\n\tvar Deg=180/Pi\n function FishF(f,n1,n2) {\n\t\tvar x=n2/(n1*f+n2)\n\t\tif((n1%2)==0) { return StatCom(1-x,n2,n1+n2-4,n2-2)*Math.pow(x,n2/2) }\n\t\tif((n2%2)==0){ return 1-StatCom(x,n1,n1+n2-4,n1-2)*Math.pow(1-x,n1/2) }\n\t\tvar th=Math.atan(Math.sqrt(n1*f/n2)); var a=th/PiD2; var sth=Math.sin(th); var cth=Math.cos(th)\n\t\tif(n2>1) { a=a+sth*cth*StatCom(cth*cth,2,n2-3,-1)/PiD2 }\n\t\tif(n1==1) { return 1-a }\n\t\tvar c=4*StatCom(sth*sth,n2+1,n1+n2-4,n2-2)*sth*Math.pow(cth,n2)/Pi\n\t\tif(n2==1) { return 1-a+c/2 }\n\t\tvar k=2; while(k<=(n2-1)/2) {c=c*k/(k-.5); k=k+1 }\n\t\treturn 1-a+c\n\t\t}\n\tfunction StatCom(q,i,j,b) {\n\t\tvar zz=1; var z=zz; var k=i; while(k<=j) { zz=zz*q*k/(k-b); z=z+zz; k=k+2 }\n\t\treturn z\n\t\t}\n \n return FishF(fScore,p1,p2)\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"import {table} from \"@tmcw/tables/2\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 32:"$31:body"