// Numbas version: exam_results_page_options
{"name": "Andrew's copy of Perform a one-way ANOVA", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "m1", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "m1"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd1", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "sd1"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[0]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "t[0]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[0]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "ssq[0]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "m2", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "m2"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd2", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "sd2"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[1]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "t[1]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[1]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "ssq[1]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "m3", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "m3"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "sd3", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "sd3"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "t[2]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "t[2]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "ssq[2]", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "ssq[2]"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "g", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "g"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "ss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "ss"}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "marks": 0, "type": "gapfill", "prompt": "<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>\n<th align=\"left\">Treatment 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>\n<th align=\"left\">Treatment 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>\n<th align=\"left\">Treatment 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>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "tss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "tss"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "btss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "btss"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "rss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "rss"}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "marks": 0, "type": "gapfill", "prompt": "<p>Now find the following, all to 2 decimal places:</p>\n<p>$\\displaystyle SS Total\\;=\\;$[[0]],&nbsp;$\\displaystyle SST\\;=\\;$[[1]],&nbsp;$\\displaystyle SSE\\;=\\;$[[2]]</p>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "dfbt", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "dfbt"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "btss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "btss"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "mbt", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "mbt"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "vr", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "vr"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "dfrs", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "dfrs"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "rss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "rss"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "mrs", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "mrs"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "n-1", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "n-1"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "minValue": "tss", "correctAnswerStyle": "plain", "marks": 0.5, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "tss"}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "marks": 0, "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>\n<th align=\"left\">Source of Variation</th>\n<th>df</th>\n<th>Sums of Squares</th>\n<th>Mean Square</th>\n<th>F</th>\n</tr>\n<tr>\n<th align=\"left\">Treatments</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr>\n<th align=\"left\">Error</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>[[6]]</td>\n<td>-</td>\n</tr>\n<tr>\n<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>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "displayColumns": 1, "scripts": {}, "maxMarks": 0, "shuffleChoices": false, "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>"], "minMarks": 0, "matrix": "v", "marks": 0, "type": "1_n_2", "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>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "displayColumns": 0, "scripts": {}, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "choices": ["Very strong", "Strong", "Moderate", "Weak", "None"], "minMarks": 0, "matrix": "v", "marks": 0, "type": "1_n_2", "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>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "displayColumns": 1, "scripts": {}, "maxMarks": 0, "shuffleChoices": false, "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."], "minMarks": 0, "matrix": "v", "marks": 0, "type": "1_n_2", "prompt": "<p>Hence what is your decision based on the above ANOVA analysis?</p>", "variableReplacementStrategy": "originalfirst"}], "preamble": {"js": "", "css": ""}, "extensions": ["stats"], "advice": "", "tags": [], "name": "Andrew's copy of Perform a one-way ANOVA", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["sd1", "sd2", "sd3", "vr", "mbt", "pmsg", "mu3", "stderror", "n", "m1", "tol", "m2", "btss", "stovern", "tss", "dfbt", "m3", "ssq", "sig1", "v1", "sig3", "sig2", "dfrs", "cmsg", "rss", "tsqovern", "mu1", "g", "r2", "mu2", "ss", "k", "r3", "mrs", "r1", "u", "t", "v", "n1", "n2", "n3", "pvalue"], "functions": {"pstdev": {"type": "number", "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "language": "jme", "parameters": [["l", "list"]]}}, "statement": "<p>Grand MeanThe 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>\n<th align=\"left\">Treatment 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>\n<th align=\"left\">Treatment 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>\n<th align=\"left\">Treatment 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>", "metadata": {"description": "<p>One-way ANOVA example</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"g": {"group": "Ungrouped variables", "definition": "sum(t)", "name": "g", "description": "", "templateType": "anything"}, "sd2": {"group": "Ungrouped variables", "definition": "precround(pstdev(r2),2)", "name": "sd2", "description": "", "templateType": "anything"}, "t": {"group": "Ungrouped variables", "definition": "[sum(r1),sum(r2),sum(r3)]", "name": "t", "description": "", "templateType": "anything"}, "sd3": {"group": "Ungrouped variables", "definition": "precround(pstdev(r3),2)", "name": "sd3", "description": "", "templateType": "anything"}, "sd1": {"group": "Ungrouped variables", "definition": "precround(pstdev(r1),2)", "name": "sd1", "description": "", "templateType": "anything"}, "stderror": {"group": "Ungrouped variables", "definition": "precround(sqrt(mrs)/sqrt(n1),2)", "name": "stderror", "description": "", "templateType": "anything"}, "r1": 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"switch(pvalue<=0.001,[1,0,0,0,0],pvalue<=0.01,[0,1,0,0,0],pvalue<=0.05,[0,0,1,0,0],pvalue<=0.1,[0,0,0,1,0],[0,0,0,0,1])", "name": "v1", "description": "", "templateType": "anything"}, "sig1": {"group": "Ungrouped variables", "definition": "random(3..5#0.2)", "name": "sig1", "description": "", "templateType": "anything"}, "dfrs": {"group": "Ungrouped variables", "definition": "N-k", "name": "dfrs", "description": "", "templateType": "anything"}}, "variable_groups": [], "type": "question", "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}]}], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}