// Numbas version: exam_results_page_options
{"shuffleQuestions": false, "questions": [], "type": "exam", "name": "Regression for psychology", "feedback": {"showtotalmark": true, "showanswerstate": true, "advicethreshold": 0, "allowrevealanswer": true, "showactualmark": true}, "metadata": {"notes": "", "description": ""}, "percentPass": 0, "allQuestions": true, "pickQuestions": 0, "showQuestionGroupNames": false, "duration": 0, "question_groups": [{"name": "", "pickQuestions": 0, "questions": [{"name": "Stephanie's copy of Pearson1", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Stephanie Greaves", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/340/"}], "functions": {"darr": {"definition": "if(n=1,a,darr(n-1,m,[random(1..m except a)]+a))", "type": "list", "language": "jme", "parameters": [["n", "number"], ["m", "number"], ["a", "list"]]}, "rk": {"definition": "\n      /*This gives the ranking of the entries in a, c counts the ties */\n        var out = [];\n      for(var j=0;j<a.length;j++){\n        var s=0;\n        var c=0;\n        for(var i=0;i<a.length;i++){\n      if(a[j]>a[i]){s+=1;}\n      else\n        if(a[j]==a[i]){c+=1;}\n        }\n      out[j]=(2*s+c+1)/2;\n      }\n      return out;\n      ", "type": "list", "language": "javascript", "parameters": [["a", "list"]]}, "pstdev": {"definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "type": "number", "language": "jme", "parameters": [["l", "list"]]}, "marr": {"definition": "if(length(a)=2,max(a[0],a[1]),max(a[0],marr(a[1..length(a)])))", "type": "number", "language": "jme", "parameters": [["a", "list"]]}, "tesarr": {"definition": "if(marr(map(abs(x),x,list(vector(a)-vector(b))))<d,b,tesarr(a,darr(length(a),m,[random(1..m)]),d,m))", "type": "list", "language": "jme", "parameters": [["a", "list"], ["b", "list"], ["d", "number"], ["m", "number"]]}}, "tags": ["Pearson correlation coefficient", "correlation coefficient", "data analysis", "hypothesis testing", "statistics"], "type": "question", "advice": "<p>The answers to all parts are given on revealing.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"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>$\\displaystyle \\sum(x_i-\\bar{x})^2 = \\;$[[5]]</p>\n<p>$\\displaystyle \\sum(y_i-\\bar{y})^2= \\;$[[6]]</p>\n<p>$\\displaystyle \\sum(x_iy_i -n\\bar{x}\\bar{y})= \\;$[[7]]</p>\n<p>Hence calculate the correlation coefficient $r$:</p>\n<p>$r=\\;$[[8]]</p>\n<p>&nbsp;</p>", "marks": 0, "gaps": [{"marks": 0.5, "maxValue": "t[0]", "minValue": "t[0]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "ssq[0]", "minValue": "ssq[0]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "t[1]", "minValue": "t[1]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "ssq[1]", "minValue": "ssq[1]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "sxy", "minValue": "sxy", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "ss[0]", "minValue": "ss[0]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "ss[1]", "minValue": "ss[1]", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 0.5, "maxValue": "spxy", "minValue": "spxy", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"marks": 1, "maxValue": "corrcoef+tol", "minValue": "corrcoef-tol", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "\n  <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>\n  ", "variable_groups": [], "progress": "ready", "preamble": {"css": "", "js": ""}, "variables": {"tsqovern": {"definition": "[t[0]^2/n,t[1]^2/n]", "templateType": "anything", "group": "Ungrouped variables", "name": "tsqovern", "description": ""}, "obj": {"definition": "['A','B','C','D','E','F','G','H']", "templateType": "anything", "group": "Ungrouped variables", "name": "obj", "description": ""}, "r1": {"definition": "darr(n,m,[random(1..20)])", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "r2": {"definition": "tesarr(r1,darr(n,m,[random(1..m)]),9,m)", "templateType": "anything", "group": "Ungrouped variables", "name": "r2", "description": ""}, "ss": {"definition": "[ssq[0]-t[0]^2/n,ssq[1]-t[1]^2/n]", "templateType": "anything", "group": "Ungrouped variables", "name": "ss", "description": ""}, "ssq": {"definition": "[sum(map(x^2,x,r1)),sum(map(x^2,x,r2))]", "templateType": "anything", "group": "Ungrouped variables", "name": "ssq", "description": ""}, "k": {"definition": 3, "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "m": {"definition": 20, "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "ssd": {"definition": "sum(map(x^2,x,d))", "templateType": "anything", "group": "Ungrouped variables", "name": "ssd", "description": ""}, "n": {"definition": 8, "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "spcoef": {"definition": "precround(6*ssd/(n*(n^2-1)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "spcoef", "description": ""}, "corrcoef": {"definition": "precround(spxy/sqrt(ss[0]*ss[1]),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "corrcoef", "description": ""}, "vs": {"definition": "switch(spcoef >=0.952,[1,0,0,0,0],spcoef>=0.881,[0,1,0,0,0],spcoef>=0.738,[0,0,1,0,0],spcoef>=0.643,[0,0,0,1,0],[0,0,0,0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "vs", "description": ""}, "spxy": {"definition": "sxy-t[0]*t[1]/n", "templateType": "anything", "group": "Ungrouped variables", "name": "spxy", "description": ""}, "t": {"definition": "[sum(r1),sum(r2)]", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "tol": {"definition": 0.001, "templateType": "anything", "group": "Ungrouped variables", "name": "tol", "description": ""}, "v": {"definition": "switch(corrcoef >=0.905,[1,0,0,0,0],corrcoef>=0.834,[0,1,0,0,0],corrcoef>=0.707,[0,0,1,0,0],corrcoef>=0.621,[0,0,0,1,0],[0,0,0,0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "sxy": {"definition": "sum(map(r1[x]*r2[x],x,0..n-1))", "templateType": "anything", "group": "Ungrouped variables", "name": "sxy", "description": ""}, "rr2": {"definition": "rk(r2)", "templateType": "anything", "group": "Ungrouped variables", "name": "rr2", "description": ""}, "rr1": {"definition": "rk(r1)", "templateType": "anything", "group": "Ungrouped variables", "name": "rr1", "description": ""}, "d": {"definition": "list(vector(rr1)-vector(rr2))", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "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;<strong>26/01/2013:</strong></p>\n    <p>No advice as yet.</p>", "description": "<p>Calculate the Pearson correlation coefficient on paired data and comment on the significance.</p>"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}], "pickingStrategy": "all-ordered"}], "navigation": {"browse": true, "showfrontpage": true, "preventleave": true, "onleave": {"message": "", "action": "none"}, "reverse": true, "allowregen": true, "showresultspage": "never"}, "timing": {"timedwarning": {"message": "", "action": "none"}, "timeout": {"message": "", "action": "none"}, "allowPause": true}, "contributors": [{"name": "Stephanie Greaves", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/340/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}