// Numbas version: finer_feedback_settings
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print and refer to the coding sheet if you wish.</p>\n<ul>\n<li>To answer each of the questions, think about how it applies to the caregiver interacting with this specific child.</li>\n<li>Code based on initial reactions / general impressions; don&rsquo;t over think any of the items; code quickly.</li>\n<li>Use all available information to form a reaction including nonverbals</li>\n<li>Try to use the entire 5-point scale, do not leave items blank (give each item your best guess)</li>\n<li>Watch five minutes only (if it goes on beyond five minutes, discontinue)</li>\n</ul>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Couple</th>\n<th>$\\var{obj[0]}$</th>\n<th>$\\var{obj[1]}$</th>\n<th>$\\var{obj[2]}$</th>\n<th>$\\var{obj[3]}$</th>\n<th>$\\var{obj[4]}$</th>\n<th>$\\var{obj[5]}$</th>\n<th>$\\var{obj[6]}$</th>\n<th>$\\var{obj[7]}$</th>\n<th>$\\var{obj[8]}$</th>\n<th>$\\var{obj[9]}$</th>\n</tr>\n<tr>\n<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<td>$\\var{r1[8]}$</td>\n<td>$\\var{r1[9]}$</td>\n</tr>\n<tr>\n<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<td>$\\var{r2[8]}$</td>\n<td>$\\var{r2[9]}$</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>", "extensions": ["stats"], "advice": "<p>The answers to all parts are given on revealing.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "functions": {"pstdev": {"language": "jme", "parameters": [["l", "list"]], "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "type": "number"}, "darr": {"language": "jme", "parameters": [["n", "number"], ["m", "number"], ["a", "list"]], "definition": "if(n=1,a,darr(n-1,m,[random(1..m except a)]+a))", "type": "list"}, "tesarr": {"language": "jme", "parameters": [["a", "list"], ["b", "list"], ["d", "number"], ["m", "number"]], "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"}, "rk": {"language": "javascript", "parameters": [["a", "list"]], "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 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"originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "ss[0]", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.5, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "ss[1]", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "ss[1]", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.5, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "spxy", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "spxy", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.5, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "corrcoef+tol", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "corrcoef-tol", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "customMarkingAlgorithm": "", "type": "numberentry"}], "extendBaseMarkingAlgorithm": true, "prompt": "\n      <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>\n      ", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill"}, {"gaps": [{"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "0.549", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "0.549", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.25, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "0.632", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "0.632", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.25, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "0.765", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "0.765", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.25, "customMarkingAlgorithm": "", "type": "numberentry"}, {"allowFractions": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "maxValue": "0.847", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "minValue": "0.847", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "marks": 0.25, "customMarkingAlgorithm": "", "type": "numberentry"}, {"minMarks": 0, "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."], "scripts": {}, "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "variableReplacements": [], "showCorrectAnswer": true, "displayColumns": 1, "maxMarks": 0, "marks": 0, "matrix": "v", "customMarkingAlgorithm": "", "type": "1_n_2"}], "extendBaseMarkingAlgorithm": true, "prompt": "\n      <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>\n      ", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill"}], "name": "Michael's copy of Derek's copy of Calculate Pearson correlation coefficient", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate the Pearson correlation coefficient on paired data and comment on the significance.</p>"}, "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Derek Hunt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2889/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Derek Hunt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2889/"}]}