// Numbas version: finer_feedback_settings
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[], "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": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "m1", "minValue": "m1", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "sd1", "minValue": "sd1", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"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": "m2", "minValue": "m2", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "sd2", "minValue": "sd2", "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": "m3", "minValue": "m3", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "sd3", "minValue": "sd3", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "t[2]", "minValue": "t[2]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ssq[2]", "minValue": "ssq[2]", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "g", "minValue": "g", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ss", "minValue": "ss", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}], "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        \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": "<p>Now find the following, all to 2 decimal places:</p>\n<p>$\\displaystyle SST\\;=\\;$[[0]],&nbsp;$\\displaystyle SSG\\;=\\;$[[1]],&nbsp;$\\displaystyle SSW\\;=\\;$[[2]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "dfbt", "minValue": "dfbt", "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": "mbt", "minValue": "mbt", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "vr", "minValue": "vr", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "dfrs", "minValue": "dfrs", "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}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "mrs", "minValue": "mrs", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "n-1", "minValue": "n-1", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "tss", "minValue": "tss", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}], "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>F</th></tr>\n<tr><th align=\"left\">Between groups</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr><th align=\"left\">Within groups</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>Note that <strong>F&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": "<p>Give the value of $F$ 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>", "distractors": ["", "", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "v", "marks": 0}, {"displayType": "radiogroup", "choices": ["Very strong", "Strong", "Moderate", "Weak", "None"], "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": ["We reject the null hypothesis at the $0.1\\%$ level", "We reject the null hypothesis at the $1\\%$ level.", "We reject the null hypothesis at the $5\\%$ level.", "We do not reject the null hypothesis but consider further investigation.", "We do not reject the null hypothesis."], "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": "<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.</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>", "tags": ["ACE2013", "ANOVA", "average", "checked2015", "data analysis", "degrees of freedom", "F-test", "hypothesis testing", "mean", "mean ", "one-way ANOVA", "one-way Anova", "standard deviation", "statistics", "stats", "variance"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n    \t\t                            \t\t<p><strong>11/07/2012:</strong></p>\n    \t\t                            \t\t                                                                <p><strong><br /></strong>Added tags.</p>\n    \t\t                            \t\t                                                                <p>Calculation not yet tested.</p>\n    \t\t                            \t\t                                                                <p><strong>23/07/2012:</strong></p>\n    \t\t                            \t\t                                                                <p>Added description.</p>\n    \t\t                            \t\t                                                                <p>Checked calculation.</p>\n    \t\t                            \t\t                                                                <p><strong>3/08/2012:</strong></p>\n    \t\t                            \t\t                                                                <p>Added tags.</p>\n    \t\t                            \t\t                                                                <p>Question appears to be working correctly.</p>\n    \t\t                            \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/"}]}