// Numbas version: exam_results_page_options
{"name": "Calculate Pearson correlation coefficient", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"rr1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "rk(r1)", "description": "", "name": "rr1"}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.001", "description": "", "name": "tol"}, "r1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "darr(n,m,[random(1..20)])", "description": "", "name": "r1"}, "spxy": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sxy-t[0]*t[1]/n", "description": "", "name": "spxy"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "list(vector(rr1)-vector(rr2))", "description": 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"sum(map(r1[x]*r2[x],x,0..n-1))", "description": "", "name": "sxy"}, "r2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "tesarr(r1,darr(n,m,[random(1..m)]),9,m)", "description": "", "name": "r2"}, "tsqovern": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[t[0]^2/n,t[1]^2/n]", "description": "", "name": "tsqovern"}, "corrcoef": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(spxy/sqrt(ss[0]*ss[1]),3)", "description": "", "name": "corrcoef"}}, "ungrouped_variables": ["tsqovern", "obj", "r1", "r2", "ss", "m", "k", "ssq", "ssd", "n", "spcoef", "corrcoef", "vs", "spxy", "t", "tol", "v", "sxy", "rr2", "rr1", "d"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Calculate Pearson correlation coefficient", "functions": {"darr": {"type": "list", "language": "jme", "definition": "if(n=1,a,darr(n-1,m,[random(1..m except a)]+a))", 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"if(length(a)=2,max(a[0],a[1]),max(a[0],marr(a[1..length(a)])))", "parameters": [["a", "list"]]}}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "t[0]", "minValue": "t[0]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ssq[0]", "minValue": "ssq[0]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "t[1]", "minValue": "t[1]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ssq[1]", "minValue": "ssq[1]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "sxy", "minValue": "sxy", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ss[0]", "minValue": "ss[0]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ss[1]", "minValue": "ss[1]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "spxy", "minValue": "spxy", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "corrcoef+tol", "minValue": "corrcoef-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<table border=\"1\">\n      <tbody>\n      <tr><th align=\"left\">Wife $(X)$</th>\n      <td>$\\sum x=\\;$[[0]]</td>\n      <td>$\\sum x^2=\\;$[[1]]</td>\n      </tr>\n      <tr><th align=\"left\">Husband $(Y)$</th>\n      <td>$\\sum y=\\;$[[2]]</td>\n      <td>$\\sum y^2=\\;$[[3]]</td>\n      </tr>\n      </tbody>\n      </table>\n      <p>Also find $\\sum xy=\\;$[[4]] and then:</p>\n      <p>$\\displaystyle SSX = \\;$[[5]]</p>\n      <p>$\\displaystyle SSY = \\;$[[6]]</p>\n      <p>$\\displaystyle SPXY = \\;$[[7]]</p>\n      <p>Hence calculate the correlation coefficient $r$:</p>\n      <p>$r=\\;$[[8]]</p>\n      <p>&nbsp;</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "0.621", "minValue": "0.621", "correctAnswerFraction": false, "marks": 0.25, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "0.707", "minValue": "0.707", "correctAnswerFraction": false, "marks": 0.25, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "0.834", "minValue": "0.834", "correctAnswerFraction": false, "marks": 0.25, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "0.905", "minValue": "0.905", "correctAnswerFraction": false, "marks": 0.25, "showPrecisionHint": false}, {"displayType": "radiogroup", "choices": ["$p \\leq 0.002$, very strong evidence to reject the null hypothesis that there is no association.", "$0.002 \\lt p \\leq 0.01$, strong evidence to reject the null  hypothesis that there is no association.", "$0.01 \\lt p \\leq 0.05$, there is evidence to reject the null hypothesis that there is no association.", "$0.05 \\lt p \\leq 0.1$, weak evidence  against, do not reject the null hypothesis but consider further investigation.", "$p \\gt 0.1$, no evidence to reject the null hypothesis that there is no association."], "displayColumns": 1, "distractors": ["", "", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "v", "marks": 0}], "type": "gapfill", "prompt": "<p>Give the value of the correlation coefficient you have found, choose the range for the $p$ value by looking up the relevant table. Input the required values from the table here:</p>\n      <table border=\"1\">\n      <tbody>\n      <tr>\n      <td>$10\\%$</td>\n      <td>$5\\%$</td>\n      <td>$1\\%$</td>\n      <td>$0.2\\%$</td>\n      </tr>\n      <tr>\n      <td>[[0]]</td>\n      <td>[[1]]</td>\n      <td>[[2]]</td>\n      <td>[[3]]</td>\n      </tr>\n      </tbody>\n      </table>\n      <p>Then make a decision based on the $p$-value you have found by choosing one of these options:</p>\n      <p>[[4]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>It is well known that similarity in attitudes, beliefs and interests plays an important role in interpersonal attraction. A researcher developed a questionnaire which was completed by 8 married couples. One question sought to place each individual on a 20 point scale in which low scores represent liberal attitudes and high scores represent conservative attitudes. The data were:</p>\n  <table border=\"1\">\n  <tbody>\n  <tr><th align=\"left\">Couple</th><th>$\\var{obj[0]}$</th><th>$\\var{obj[1]}$</th><th>$\\var{obj[2]}$</th><th>$\\var{obj[3]}$</th><th>$\\var{obj[4]}$</th><th>$\\var{obj[5]}$</th><th>$\\var{obj[6]}$</th><th>$\\var{obj[7]}$</th></tr>\n  <tr><th align=\"left\">Wife $(X)$</th>\n  <td>$\\var{r1[0]}$</td>\n  <td>$\\var{r1[1]}$</td>\n  <td>$\\var{r1[2]}$</td>\n  <td>$\\var{r1[3]}$</td>\n  <td>$\\var{r1[4]}$</td>\n  <td>$\\var{r1[5]}$</td>\n  <td>$\\var{r1[6]}$</td>\n  <td>$\\var{r1[7]}$</td>\n  </tr>\n  <tr><th align=\"left\">Husband $(Y)$</th>\n  <td>$\\var{r2[0]}$</td>\n  <td>$\\var{r2[1]}$</td>\n  <td>$\\var{r2[2]}$</td>\n  <td>$\\var{r2[3]}$</td>\n  <td>$\\var{r2[4]}$</td>\n  <td>$\\var{r2[5]}$</td>\n  <td>$\\var{r2[6]}$</td>\n  <td>$\\var{r2[7]}$</td>\n  </tr>\n  </tbody>\n  </table>\n  <p>In this exercise you will find the Pearson correlation coefficent for the above paired data and&nbsp;comment on the significance of the calculated correlation.</p>\n  <p>The null hypothesis you are testing is:</p>\n  <p>$H_0$: There is no association between the attitudes of wives and husbands.</p>", "tags": ["checked2015", "correlation coefficient", "data analysis", "hypothesis testing", "Pearson correlation coefficient", "PSY2010", "statistics"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>30/09/2102:</strong></p>\n                                                                                                            <p>Introduced three functions:</p>\n                                                                                                            <p>1. To produce the ranking of a list of 8 numbers.</p>\n                                                                                                            <p>2. To produce a list of 8 numbers from a scale of 1..20 which are all distinct.</p>\n                                                                                                            <p>3. To produce the maximum of the numbers in a list.</p>\n                                                                                                            <p>4. Given an array such as in 2. to find another such array which has max diff between any two corresponding entries less than a given number. This is to ensure that the two array produced do not differ too much, as the point of the exercise is to show that there is a positive high correlation.</p>\n                                                                                                            <p>&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate the Pearson correlation coefficient on paired data and comment on the significance.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>The answers to all parts are given on revealing.</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}