2f:[] 2d:{"title":"Signal Detection for Two Groups with Difference Prevalences","cells":[{"id":0,"value":"# Signal Detection for Two Groups with Difference Prevalences","pinned":false,"hidden":false,"mode":"md"},{"id":144,"value":"The top graphs show the normal distributions for the group with the higher prevalence. These distributions are simply shifted rightward relative to the middle graphs for the group with lower prevalence. The assumption is that all the distributions are the same except for shifts. The diagnosticity, i.e,, the distance between the true (right) and false (left) distributions is the same for both groups. Move the outpoint slider to change the outpoint and observe how the respective HR and FAR change. They are always higher for the more prevalent group. You can follow the HR and FAR for each group in the ROC in the third row. Except near the ends, the HR and FAR points remain the same distance apart for the two groups. And they are of course always on the same ROC curve.","pinned":false,"hidden":false,"mode":"md"},{"id":51,"value":"viewof cut = Inputs.range([-3,7], {label: \"Cut Point\", step: 0.1, start: 2})","pinned":false,"hidden":false,"mode":"ojs"},{"id":253,"value":"viewof dPrime = Inputs.range([0,3], {label: \"d'\", step: 0.05, start: 0.7})","pinned":false,"hidden":false,"mode":"ojs"},{"id":63,"value":"\\small HR = P(\"YES\" | true positive) = ${round2(ahr)}","pinned":false,"hidden":false,"mode":"tex"},{"id":77,"value":"\\small FAR = P(\"YES\" | true negative) = ${round2(afar)}","pinned":false,"hidden":false,"mode":"tex"},{"id":16,"value":"Plot.plot({\n height: 200,\n x: {domain: [-3,7]},\n marks: [\n Plot.ruleY([0]),\n Plot.areaY(apos, {x: \"x\", y: \"y\", fill: graphColors.red, opacity: 0.5}),\n Plot.areaY(aneg, {x: \"x\", y: \"y\", fill: graphColors.blue, opacity: 0.5}),\n Plot.ruleX([cut], {strokeWidth: 3})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":99,"value":"\\small HR = P(\"YES\" | true positive) = ${round2(bhr)}","pinned":false,"hidden":false,"mode":"tex"},{"id":101,"value":"\\small FAR = P(\"YES\" | true negative) = ${round2(bfar)}","pinned":false,"hidden":false,"mode":"tex"},{"id":44,"value":"Plot.plot({\n height: 200,\n x: {domain: [-3,7]},\n marks: [\n Plot.ruleY([0]),\n Plot.areaY(bpos, {x: \"x\", y: \"y\", fill: graphColors.orange, opacity: 0.5}),\n Plot.areaY(bneg, {x: \"x\", y: \"y\", fill: \"gray\", opacity: 0.5}),\n Plot.ruleX([cut], {strokeWidth: 3})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":248,"value":"### ROC and Normalized ROC ","pinned":false,"hidden":false,"mode":"md"},{"id":217,"value":"\n \n \n \n

\n ${roc1}\n

\n ${roc2}\n

\n \n","pinned":false,"hidden":false,"mode":"html"},{"id":105,"value":"roc1 = Plot.plot({\n height: width/2,\n width: width/2,\n\n marks: [\n Plot.frame(),\n Plot.ruleY([0]),\n Plot.lineY(roc, {x: \"far\", y: \"hr\"}),\n Plot.dot([{hr: bhr, far: bfar}], {x: \"far\", y: \"hr\", fill: graphColors.orange, r: 10}),\n Plot.dot([{hr: ahr, far: afar}], {x: \"far\", y: \"hr\", fill: \"black\", r: 10 }),\n Plot.line([{x: 0, y:0},{x:1,y:1}], {x: \"x\", y: \"y\", strokeWidth: 1})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":205,"value":"roc2 = Plot.plot({\n height: width/2,\n width: width/2,\n x: {domain: [-3,3]},\n y: {domain: [-3,3]},\n marks: [\n Plot.frame(),\n Plot.dot([{x: z(afar), y: z(ahr)}], {x: \"x\", y: \"y\", r: 10, fill: \"black\"}),\n Plot.dot([{x: z(bfar), y: z(bhr)}], {x: \"x\", y: \"y\", r: 10, fill: graphColors.orange}),\n Plot.line([{x: -3, y:-3},{x:3,y:3}], {x: \"x\", y: \"y\", strokeWidth: 1}),\n Plot.line([{x: -3, y: -3+dPrime},{x:3-dPrime, y:3}], {x: \"x\", y: \"y\"})\n]})","pinned":false,"hidden":false,"mode":"ojs"},{"id":61,"value":"## Setup","pinned":false,"hidden":false,"mode":"md"},{"id":227,"value":"width = 600","pinned":true,"hidden":false,"mode":"ojs"},{"id":189,"value":"function z(p) {\n let z = jStat.normal.inv(p,0,1)\n// if(z <= -3) return -3;\n// else if(z >= 3) return 3;\n return round2(z);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":232,"value":"function round2(x) {\n return Math.round(x*100)/100\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":68,"value":"ahr = 1-jStat.normal.cdf(cut,aposd,1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":91,"value":"afar = 1-jStat.normal.cdf(cut,groupOffset,1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":95,"value":"bhr = 1-jStat.normal.cdf(cut,bposd,1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"bfar = 1 - jStat.normal.cdf(cut,0,1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":28,"value":"groupOffset = 0.5","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"aposd = bposd + groupOffset","pinned":false,"hidden":false,"mode":"ojs"},{"id":36,"value":"bposd = dPrime","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"apos = {let dd = [];\n for(let i=-3+aposd; i <= 3+aposd; i=i+.05)\n dd.push({x: i, y: jStat.normal.pdf(i, aposd, 1)})\n\n return dd;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"aneg = {let dd =[];\n for(let i=-3+groupOffset; i <= 3 + groupOffset; i = i + 0.05)\n dd.push({x: i, y: jStat.normal.pdf(i, groupOffset, 1)})\n return dd;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":38,"value":"bpos = {let dd = [];\n for(let i=-3+bposd; i <= 3+bposd; i=i+.05)\n dd.push({x: i, y: jStat.normal.pdf(i, bposd, 1)})\n return dd;}\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":40,"value":"bneg = {let dd =[];\n for(let i=-3; i <= 3; i = i + 0.05)\n dd.push({x: i, y: jStat.normal.pdf(i, 0, 1)})\n return dd;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":103,"value":"roc = { let dd = [];\n for(let i=-3; i<=3; i=i+0.05)\n dd.push({hr: 1- jStat.normal.cdf(i,bposd,1), far: 1-jStat.normal.cdf(i,0,1)})\n return dd;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"jStat = require('jStat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":25,"value":"graphColors = ({\n blue: \"#4e79a7\",\n orange: \"#f2832d\",\n red: \"#e15759\"\n})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W2f","stdlib":"1","titling":"auto"}