28:null 29:["$","title",null,{"children":"Exam scores on True/False problems | Mattias Villani | Observable"}] 2f:[] 2c:{"id":"adeda856a8e5db68","slug":null,"title":"Exam scores on True/False problems","thumbnail":"29d43af13b859dc3acac6424d9d6a49824af23ae6d47d0f7adcb5939fdfdcafe","access_level":"public","create_time":"$D2025-05-21T18:25:16.532Z","update_time":"$D2025-05-21T20:17:56.672Z","view_time":null,"first_public_time":"$D2025-05-21T20:12:41.906Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":176,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"},{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Exam scores on True/False problems","cells":[{"id":0,"value":"# Exam scores on True/False problems","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"This widget computes the probability distribution for the score on an exam problem with a certain number of true/false questions. A correct answer gives 1 point, but wrong answers give negative points to discourage random guessing. But how large should this penalty be?\n\nYou can choose the total number of questions in the problem and the number of those questions that the student guesses with a probability of success of 0.5. The remaining questions are assumed to have been answered correctly.","pinned":false,"hidden":false,"mode":"md"},{"id":9,"value":"viewof nQuestions = Inputs.range([2, 20], {value: 10, label: \"Number of questions\", step: 1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"viewof nGuess = Inputs.range([0, nQuestions], {value: 10, label: \"Number of questions with random guessing\", step: 1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"viewof negScore = Inputs.range([-2, 0], {value: -1, label: \"Score for wrong answer\", step: 0.25})","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"viewof minimumScore = Inputs.range([-nQuestions, 0], {value: 0, label: \"Lowest possible overall score\", step: 1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"Plot.plot({\n x: {\n domain: d3.sort(scoreProbDist, d => d.score).map(d => d.score)\n },\n y: {\n grid: true\n },\n marks: [\n Plot.barY(scoreProbDist, {x: \"score\", y: \"prob\", fill: \"steelblue\"})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":92,"value":"
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n---\n#### 🙈 Appendix 🙈\n\nHere is just some code and details that you probably don't want to see.","pinned":false,"hidden":false,"mode":"md"},{"id":25,"value":"// JavaScript equivalent of probDistScore function\nfunction probDistScore(nQuestions, nGuess, negScore, minimumScore, nSim = 10000) {\n let scores = [];\n \n for (let i = 0; i < nSim; i++) {\n let nRightGuess = d3.randomBinomial(nGuess, 0.5)()\n let nWrongGuess = nGuess - nRightGuess;\n let score = (nQuestions - nGuess) + nRightGuess * 1 + nWrongGuess * negScore;\n \n if (score < 0) {\n score = minimumScore;\n }\n \n scores.push(score);\n }\n return scores;\n}\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":32,"value":"scores = probDistScore(nQuestions, nGuess, negScore, minimumScore)","pinned":false,"hidden":false,"mode":"ojs"},{"id":138,"value":"scoresNoPenalty = probDistScore(nQuestions, nGuess, 0, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":62,"value":"scoreProbDist = { \n let uniqueScores = []\n scores.forEach(item => {\n if (!uniqueScores.includes(item)) {\n uniqueScores.push(item)\n }\n })\n // initialize\n let scoreDistribution = {};\n for (let score of uniqueScores){\n scoreDistribution[score] = 0;\n }\n scores.forEach(score => {\n scoreDistribution[score]++;\n });\n \n // Normalize to get probabilities\n let scoreDict = [];\n for (let score of uniqueScores) {\n scoreDict.push({\"score\": score, \"prob\": scoreDistribution[score] /= nSim})\n }\n return scoreDict\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":140,"value":"scoreProbDistNoPenalty = { \n let uniqueScores = []\n scoresNoPenalty.forEach(item => {\n if (!uniqueScores.includes(item)) {\n uniqueScores.push(item)\n }\n })\n // initialize\n let scoreDistribution = {};\n for (let score of uniqueScores){\n scoreDistribution[score] = 0;\n }\n scoresNoPenalty.forEach(score => {\n scoreDistribution[score]++;\n });\n \n // Normalize to get probabilities\n let scoreDict = [];\n for (let score of uniqueScores) {\n scoreDict.push({\"score\": score, \"prob\": scoreDistribution[score] /= nSim})\n }\n return scoreDict\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":27,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"nSim = 10000","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2d:"$2c:body"