// Numbas version: finer_feedback_settings
{"name": "One-way ANOVA", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "functions": {"pstdev": {"type": "number", "language": "jme", "parameters": [["l", "list"]], "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)"}}, "parts": [{"showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "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      ", "marks": 0, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", 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"showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "t[2]", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "t[2]"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "ssq[2]", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "ssq[2]"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "g", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "g"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "ss", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "ss"}]}, {"showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "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      ", "marks": 0, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "tss", "marks": 0.5, "unitTests": [], "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "maxValue": "tss"}, {"notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "btss", "marks": 0.5, "unitTests": [], "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "maxValue": "btss"}, {"notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "mustBeReduced": false, "minValue": "rss", "marks": 0.5, "unitTests": [], "showCorrectAnswer": true, "allowFractions": false, "correctAnswerFraction": false, "scripts": {}, "maxValue": "rss"}]}, {"showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "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>", "marks": 0, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "dfbt", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "dfbt"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "btss", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "btss"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "mbt", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "mbt"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": true, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "vr", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "vr"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "dfrs", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "dfrs"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "rss", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "rss"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "mrs", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "mrs"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "n-1", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "n-1"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "tss", "mustBeReduced": false, "marks": 0.5, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "tss"}, {"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "showPrecisionHint": false, "mustBeReducedPC": 0, "strictPrecision": false, "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "precision": "2", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minValue": "stderror-tol", "mustBeReduced": false, "marks": 1, "allowFractions": false, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "stderror+tol"}]}, {"shuffleChoices": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "1_n_2", "minMarks": 0, "customMarkingAlgorithm": "", "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      ", "matrix": "v", "displayColumns": 1, "marks": 0, "unitTests": [], "showCorrectAnswer": true, "displayType": "radiogroup", "scripts": {}, "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>"], "maxMarks": 0}, {"shuffleChoices": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "1_n_2", "minMarks": 0, "customMarkingAlgorithm": "", "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>", "matrix": "v", "displayColumns": 0, "marks": 0, "unitTests": [], "showCorrectAnswer": true, "displayType": "radiogroup", "scripts": {}, "choices": ["<p>Very Strong Evidence</p>", "<p>Strong Evidence</p>", "<p>Evidence</p>", "<p>Weak Evidence</p>", "<p>No Evidence</p>"], "maxMarks": 0}, {"shuffleChoices": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "1_n_2", "minMarks": 0, "customMarkingAlgorithm": "", "prompt": "<p>Hence what is your decision based on the above ANOVA analysis?</p>", "matrix": "v", "displayColumns": 1, "marks": 0, "unitTests": [], "showCorrectAnswer": true, "displayType": "radiogroup", "scripts": {}, "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>"], "maxMarks": 0}], "metadata": {"description": "<p>One-way ANOVA example</p>", "licence": "Creative Commons Attribution 4.0 International"}, "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 $2$ units over one hour and Group C had $4$ units over one 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\">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>\n<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>\n<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 the 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>", "tags": [], "variable_groups": [], "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"], "advice": "", "variables": {"pmsg": {"description": "", "group": "Ungrouped variables", "name": "pmsg", "templateType": "anything", "definition": "[' is less than $0.001$',' lies between $0.001$ and $0.01$',' lies between $0.01$ and $0.05$',' lies between $0.05$ and $0.10$',' is greater than $0.10$']"}, "mrs": {"description": "", "group": "Ungrouped variables", "name": "mrs", "templateType": "anything", "definition": "precround(RSS/dfrs,2)"}, "dfbt": {"description": "", "group": "Ungrouped variables", "name": "dfbt", "templateType": "anything", "definition": "k-1"}, "v1": {"description": "", "group": "Ungrouped variables", "name": "v1", "templateType": "anything", "definition": "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])"}, "sd3": {"description": "", "group": "Ungrouped variables", "name": "sd3", "templateType": "anything", "definition": "precround(pstdev(r3),2)"}, "n1": {"description": "", "group": "Ungrouped variables", "name": "n1", "templateType": "anything", "definition": "6"}, "m2": {"description": "", "group": "Ungrouped variables", "name": "m2", "templateType": "anything", "definition": "precround(mean(r2),2)"}, "stovern": {"description": "", "group": "Ungrouped variables", "name": "stovern", "templateType": "anything", "definition": "sum(tsqovern)"}, "sig2": {"description": "", "group": "Ungrouped variables", "name": "sig2", "templateType": "anything", "definition": "sig1"}, "n3": {"description": "", "group": "Ungrouped variables", "name": "n3", "templateType": "anything", "definition": "6"}, "ss": {"description": "", "group": "Ungrouped variables", "name": "ss", "templateType": "anything", "definition": "sum(ssq)"}, "sd2": {"description": "", "group": "Ungrouped variables", "name": "sd2", "templateType": "anything", "definition": "precround(pstdev(r2),2)"}, "sd1": {"description": "", "group": "Ungrouped variables", "name": "sd1", "templateType": "anything", "definition": "precround(pstdev(r1),2)"}, "n": {"description": "", "group": "Ungrouped variables", "name": "n", "templateType": "anything", "definition": "n1+n2+n3"}, "t": {"description": "", "group": "Ungrouped variables", "name": "t", "templateType": "anything", "definition": "[sum(r1),sum(r2),sum(r3)]"}, "u": {"description": "", "group": "Ungrouped variables", "name": "u", "templateType": "anything", "definition": "switch(v[0]=1,0,v[1]=1,1,v[2]=1,2,v[3]=1,3,4)"}, "rss": {"description": "", "group": "Ungrouped variables", "name": "rss", "templateType": "anything", "definition": "precround(ss-stovern,2)"}, "dfrs": {"description": "", "group": "Ungrouped variables", "name": "dfrs", "templateType": "anything", "definition": "N-k"}, "n2": {"description": "", "group": "Ungrouped variables", "name": "n2", "templateType": "anything", "definition": "6"}, "k": {"description": "", "group": "Ungrouped variables", "name": "k", "templateType": "anything", "definition": "3"}, "cmsg": {"description": "", "group": "Ungrouped variables", "name": "cmsg", "templateType": "anything", "definition": "['do reject','do reject','do not reject','do not reject','do not reject']"}, "m1": {"description": "", "group": "Ungrouped variables", "name": "m1", "templateType": "anything", "definition": "precround(mean(r1),2)"}, "ssq": {"description": "", "group": "Ungrouped variables", "name": "ssq", "templateType": "anything", "definition": "[sum(map(x^2,x,r1)),sum(map(x^2,x,r2)),sum(map(x^2,x,r3))]"}, "tss": {"description": "", "group": "Ungrouped variables", "name": "tss", "templateType": "anything", "definition": "precround(ss-G^2/N,2)"}, "pvalue": {"description": "", "group": "Ungrouped variables", "name": "pvalue", "templateType": "anything", "definition": "precround(ftest(VR,2,15),3)"}, "vr": {"description": "", "group": "Ungrouped variables", "name": "vr", "templateType": "anything", "definition": "precround(MBT/MRS,2)"}, "mu3": {"description": "", "group": "Ungrouped variables", "name": "mu3", "templateType": "anything", "definition": "random(24..32#0.5)"}, "stderror": {"description": "", "group": "Ungrouped variables", "name": "stderror", "templateType": "anything", "definition": "precround(sqrt(mrs)/sqrt(n1),2)"}, "m3": {"description": "", "group": "Ungrouped variables", "name": "m3", "templateType": "anything", "definition": "precround(mean(r3),2)"}, "sig3": {"description": "", "group": "Ungrouped variables", "name": "sig3", "templateType": "anything", "definition": "sig1"}, "mbt": {"description": "", "group": "Ungrouped variables", "name": "mbt", "templateType": "anything", "definition": "precround(BTSS/dfbt,2)"}, "r1": {"description": "", "group": "Ungrouped variables", "name": "r1", "templateType": "anything", "definition": "repeat(round(normalsample(mu1,sig1)),6)"}, "tsqovern": {"description": "", "group": "Ungrouped variables", "name": "tsqovern", "templateType": "anything", "definition": "[t[0]^2/n1,t[1]^2/n2,t[2]^2/n3]"}, "r3": {"description": "", "group": "Ungrouped variables", "name": "r3", "templateType": "anything", "definition": "repeat(round(normalsample(mu3,sig3)),6)"}, "v": {"description": "", "group": "Ungrouped variables", "name": "v", "templateType": "anything", "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])"}, "tol": {"description": "", "group": "Ungrouped variables", "name": "tol", "templateType": "anything", "definition": "0.001"}, "btss": {"description": "", "group": "Ungrouped variables", "name": "btss", "templateType": "anything", "definition": "precround(stovern-G^2/N,2)"}, "r2": {"description": "", "group": "Ungrouped variables", "name": "r2", "templateType": "anything", "definition": "repeat(round(normalsample(mu2,sig2)),6)"}, "sig1": {"description": "", "group": "Ungrouped variables", "name": "sig1", "templateType": "anything", "definition": "random(3..5#0.2)"}, "mu1": {"description": "", "group": "Ungrouped variables", "name": "mu1", "templateType": "anything", "definition": "random(20..25#0.5)"}, "g": {"description": "", "group": "Ungrouped variables", "name": "g", "templateType": "anything", "definition": "sum(t)"}, "mu2": {"description": "", "group": "Ungrouped variables", "name": "mu2", "templateType": "anything", "definition": "random(22..28#0.5)"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "One-way ANOVA", "extensions": ["stats"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "type": "question", "contributors": [{"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Lauren Frances Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2490/"}]}]}], "contributors": [{"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Lauren Frances Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2490/"}]}