// Numbas version: finer_feedback_settings
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"definition": "sig1", "description": "", "name": "sig3"}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(vr>=11.34,[1,0,0,0,0],vr>=6.36,[0,1,0,0,0],vr>=3.68,[0,0,1,0,0],vr>=2.7,[0,0,0,1,0],[0,0,0,0,1])", "description": "", "name": "v"}, "m2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(mean(r2),2)", "description": "", "name": "m2"}, "stderror": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(sqrt(mrs)/sqrt(n1),2)", "description": "", "name": "stderror"}, "mbt": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(BTSS/dfbt,2)", "description": "", "name": "mbt"}, "r2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(round(normalsample(mu2,sig2)),6)", "description": "", "name": "r2"}, "mu3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(24..32#0.5)", "description": "", "name": "mu3"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sum(t)", "description": "", "name": "g"}, "tsqovern": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[t[0]^2/n1,t[1]^2/n2,t[2]^2/n3]", "description": "", "name": "tsqovern"}, "u": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(v[0]=1,0,v[1]=1,1,v[2]=1,2,v[3]=1,3,4)", "description": "", "name": "u"}, "sd2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(pstdev(r2),2)", "description": "", "name": "sd2"}}, "ungrouped_variables": ["sd1", "sd2", "sd3", "mrs", "r2", "vr", "mbt", "pmsg", "stderror", "dfrs", "m1", "m3", "m2", "btss", "u", "tss", "dfbt", "tol", "ssq", "sig1", "v1", "sig3", "sig2", "cmsg", "rss", "tsqovern", "mu1", "g", "mu3", "mu2", "ss", "k", "r3", "n", "r1", "stovern", "t", "v", "n1", "n2", "n3", "pvalue"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Perform a one-way ANOVA", "functions": {"pstdev": {"type": "number", "language": "jme", "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "parameters": [["l", "list"]]}}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "m1", "maxValue": "m1", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd1", "maxValue": "sd1", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[0]", "maxValue": "t[0]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[0]", "maxValue": "ssq[0]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "m2", "maxValue": "m2", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd2", "maxValue": "sd2", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[1]", "maxValue": "t[1]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[1]", "maxValue": "ssq[1]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "m3", "maxValue": "m3", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd3", "maxValue": "sd3", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[2]", "maxValue": "t[2]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[2]", "maxValue": "ssq[2]", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "g", "maxValue": "g", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "ss", "maxValue": "ss", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}], "type": "gapfill", "prompt": "\n      <p>First fill in this table with the appropriate values, all decimals to 2 decimal places:</p>\n      <table border=\"1\">\n      <tbody>\n      <tr>\n      <td>&nbsp;</td>\n      <td>$\\overline{x}_i$</td>\n      <td>$s_i$</td>\n      <td>$T_i$</td>\n      <td>$\\sum x^2$</td>\n      <td>$n_i$</td>\n      </tr>\n      <tr><th align=\"left\">Group A</th>\n      <td>[[0]]</td>\n      <td>[[1]]</td>\n      <td>[[2]]</td>\n      <td>[[3]]</td>\n      <td>6</td>\n      </tr>\n      <tr><th align=\"left\">Group B</th>\n      <td>[[4]]</td>\n      <td>[[5]]</td>\n      <td>[[6]]</td>\n      <td>[[7]]</td>\n      <td>6</td>\n      </tr>\n      <tr><th align=\"left\">Group C</th>\n      <td>[[8]]</td>\n      <td>[[9]]</td>\n      <td>[[10]]</td>\n      <td>[[11]]</td>\n      <td>6</td>\n      </tr>\n      <tr>\n      <td>&nbsp;</td>\n      <td>&nbsp;</td>\n      <td>&nbsp;</td>\n      <td>$G=\\;$[[12]]</td>\n      <td>Sum of Squares=[[13]]</td>\n      <td>$N=18$</td>\n      </tr>\n      </tbody>\n      </table>\n      <p>Note that in doing this you will have supplied the sample means and sample standard deviations for the three groups.</p>\n      ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "tss", "minValue": "tss", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "btss", "minValue": "btss", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rss", "minValue": "rss", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}], "type": "gapfill", "prompt": "\n      <p>Now find the following, all to 2 decimal places:</p>\n        <p>$\\displaystyle TSS\\;=\\;$[[0]],&nbsp;$\\displaystyle BTSS\\;=\\;$[[1]],&nbsp;$\\displaystyle RSS\\;=\\;$[[2]]</p>\n      ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "dfbt", "maxValue": "dfbt", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "btss", "maxValue": "btss", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "mbt", "maxValue": "mbt", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "vr", "maxValue": "vr", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": true, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "dfrs", "maxValue": "dfrs", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "rss", "maxValue": "rss", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "mrs", "maxValue": "mrs", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "n-1", "maxValue": "n-1", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "tss", "maxValue": "tss", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 0.5}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "stderror-tol", "maxValue": "stderror+tol", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": "<p>Now complete the ANOVA table using the values to 2 decimal places obtained above:</p>\n<table border=\"1\">\n<tbody>\n<tr><th align=\"left\">Source</th><th>df</th><th>SS</th><th>MS</th><th>VR</th></tr>\n<tr><th align=\"left\">Between Treatments</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr><th align=\"left\">Residual</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>[[6]]</td>\n<td>-</td>\n</tr>\n<tr><th align=\"left\">Total</th>\n<td>[[7]]</td>\n<td>[[8]]</td>\n<td>-</td>\n<td>-</td>\n</tr>\n</tbody>\n</table>\n<p>Also calculate the estimated standard error of the mean : [[9]]</p>\n<p>Note that <strong>VR&nbsp;</strong>is found by taking the ratio of two of the values in this table.</p>\n<p>Input all numbers to 2 decimal places.</p>", "showCorrectAnswer": true, "marks": 0}, {"displayType": "radiogroup", "choices": ["<p>$p$ less than $0.1\\%$</p>", "<p>$p$ lies between $0.1\\%$ and $1\\%$</p>", "<p>$p$ lies between  $1 \\%$ and $5\\%$</p>", "<p>$p$ lies between  $5 \\%$ and $10\\%$</p>", "<p>$p$ is greater than $10\\%$</p>"], "displayColumns": 1, "prompt": "\n      <p>Give the value of $VR$ you have found, choose the range for the $p$ value by looking up the critical values of $F_{2,15}$ (one-sided).</p>\n      <table border=\"1\">\n      <tbody>\n      <tr>\n      <td>$10\\%$</td>\n      <td>$5\\%$</td>\n      <td>$1\\%$</td>\n      <td>$0.1\\%$</td>\n      </tr>\n      <tr>\n      <td>$2.70$</td>\n      <td>$3.68$</td>\n      <td>$6.36$</td>\n      <td>$11.34$</td>\n      </tr>\n      </tbody>\n      </table>\n      ", "distractors": ["", "", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "v", "marks": 0}, {"displayType": "radiogroup", "choices": ["<p>Very Strong Evidence</p>", "<p>Strong Evidence</p>", "<p>Evidence</p>", "<p>Weak Evidence</p>", "<p>No Evidence</p>"], "displayColumns": 0, "prompt": "<p>Given the $p$-value and the range you have found, what is the strength of evidence against the null hypothesis that the mean times taken are the same for the three groups?</p>", "distractors": ["", "", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "v", "marks": 0}, {"displayType": "radiogroup", "choices": ["<p>We reject the null hypothesis at the $0.1\\%$ level</p>", "<p>We reject the null hypothesis at the $1\\%$ level.</p>", "<p>We reject the null hypothesis at the $5\\%$ level.</p>", "<p>We do not reject the null hypothesis but consider further investigation.</p>", "<p>We do not reject the null hypothesis.</p>"], "displayColumns": 1, "prompt": "<p>Hence what is your decision based on the above ANOVA analysis?</p>", "distractors": ["", "", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "v", "marks": 0}], "statement": "\n  <p>The following data arose in a comparison of the effects of alcohol on the time taken to complete a task. There were three groups of subjects; Group A had no alcohol, Group B had two units over 1 hour and Group C had 4 units over 1 hour. The responses are the times (in seconds) taken to complete a word-matching task.</p>\n    <table border=\"1\">\n    <tbody>\n    <tr><th align=\"left\">Group A (0 units)</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    </tr>\n    <tr><th align=\"left\">Group B (2 units)</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    </tr>\n    <tr><th align=\"left\">Group C (4 units)</th>\n    <td>$\\var{r3[0]}$</td>\n    <td>$\\var{r3[1]}$</td>\n    <td>$\\var{r3[2]}$</td>\n    <td>$\\var{r3[3]}$</td>\n    <td>$\\var{r3[4]}$</td>\n    <td>$\\var{r3[5]}$</td>\n    </tr>\n    </tbody>\n    </table>\n    <ul>\n    <li>Write down the sample mean and standard deviation for each group together with an estimate of the standard error of a mean, $\\displaystyle\\frac{s}{\\sqrt{n}}$, to 2 decimal places.</li>\n    <li>Test the null hypothesis that the alcohol consumption does not affect the mean time taken to complete the task.</li>\n    </ul>\n    <p>&nbsp;</p>\n  ", "tags": ["ANOVA", "average", "checked2015", "data analysis", "degrees of freedom", "F-test", "hypothesis testing", "mean", "mean ", "one-way Anova", "one-way ANOVA", "PSY2010", "standard deviation", "statistics", "stats", "variance"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n                            \t\t<p><strong>11/07/2012:</strong></p>\n                            \t\t                                                                <p><strong><br /></strong>Added tags.</p>\n                            \t\t                                                                <p>Calculation not yet tested.</p>\n                            \t\t                                                                <p><strong>23/07/2012:</strong></p>\n                            \t\t                                                                <p>Added description.</p>\n                            \t\t                                                                <p>Checked calculation.</p>\n                            \t\t                                                                <p><strong>3/08/2012:</strong></p>\n                            \t\t                                                                <p>Added tags.</p>\n                            \t\t                                                                <p>Question appears to be working correctly.</p>\n                            \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>One-way ANOVA example</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "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/"}]}