// Numbas version: finer_feedback_settings
{"name": "A comparison of the means of four groups (1).", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"pstdev": {"definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)", "type": "number", "parameters": [["l", "list"]], "language": "jme"}}, "ungrouped_variables": ["cval", "dfamong", "dftotal", "dfwithin", "fratio", "ftable", "grp1", "grp2", "grp3", "mean1", "mean2", "mean3", "msamong", "mswithin", "object", "objects", "outcome", "s1", "s2", "s3", "sig1", "slip", "ssamong", "sstotal", "sswithin", "sumallx", "sumsq1", "sumsq2", "sumsq3", "sumx1", "sumx2", "sumx3", "treat1", "treat2", "treat3", "tuk12", "tuk12sig", "tuk13", "tuk13sig", "tuk23", "tuk23sig", "tukse", "tukssd", "tukval", "var1", "var2", "var3"], "name": "A comparison of the means of four groups (1).", "tags": ["average", "data analysis", "differences", "elementary statistics", "hypothesis testing", "mean", "mean of differences", "paired t-test", "standard deviation", "standard deviation of differences", "statistics", "stats", "t-test", "variance"], "advice": "<p><strong>Summary statistics</strong></p>\n<p>Calculate means and variances for both groups: variance ($s^2$) is just the standard deviation ($s$ or $sd$) squared.</p>\n<p>Mean 1 = {mean1}; Mean 2 = {mean2}; Mean 3 = {mean3}</p>\n<p>Variance 1 = {var1}; Variance 2 = {var2}; Variance 3 = {var3}</p>\n<p>Cochran's value = {cval}; Table value = 0.707. If Cochran's value &gt; 0.707, transformation of the data may be required. (This will be ignored in this example because it would greatly complicate the code.)</p>\n<p>n1 = 6; n2 = 6; n3 = 6</p>\n<p><strong>Intermediate terms</strong></p>\n<p>Caalculate&nbsp;the following:</p>\n<p>Sum of Group 1 = {sumx1};&nbsp;<span>Sum of Group 2&nbsp;{sumx2}= ;&nbsp;Sum of Group 3&nbsp;=&nbsp;{sumx3}</span></p>\n<p><span>Sum of all values = {sumallx}</span></p>\n<p><span>Sum of squares of all values = &nbsp;{s2}</span></p>\n<p>Calculate&nbsp;the S terms:</p>\n<p>S1 = {s1}</p>\n<p>S2 = {s2}</p>\n<p>S3 = {s3}</p>\n<p><strong>Complete the ANOVA table</strong></p>\n<p>Fill in the values (3 decimal places, except for df).</p>\n<table>\n<tbody>\n<tr>\n<td>Source</td>\n<td>SS</td>\n<td>df</td>\n<td>MS</td>\n<td>F-ratio</td>\n</tr>\n<tr>\n<td>Among</td>\n<td>{ssamong}</td>\n<td>{dfamong}</td>\n<td>{msamong}</td>\n<td>{fratio}</td>\n</tr>\n<tr>\n<td>Within</td>\n<td>{sswithin}</td>\n<td>{dfwithin}</td>\n<td>{mswithin}</td>\n<td></td>\n</tr>\n<tr>\n<td>Total</td>\n<td>{sstotal}</td>\n<td>{dftotal}</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p><strong>Outcome</strong></p>\n<p>Is the null hypothesis (all means equal) rejected? A 0 means&nbsp;\"no\" and a 1 means&nbsp;\"yes\".</p>\n<p style=\"padding-left: 30px;\">Outcome = {outcome}</p>\n<p></p>\n<p><strong>Complete Tukey's test</strong></p>\n<p>1.&nbsp;Find the appropriate q-value (k = 3, df = 15):</p>\n<p style=\"padding-left: 30px;\">table q = {tukval}</p>\n<p>2. Calculate the standard error (square-root(MSwithin/n)):</p>\n<p style=\"padding-left: 30px;\">SE = {tukse}</p>\n<p>3. Calculate the smallest significant difference (SSD or Least Significant Difference, LSD):</p>\n<p style=\"padding-left: 30px;\">SSD = {tukssd}</p>\n<p>4. Calculate the differences between all pairs of means (ignore the sign):</p>\n<p style=\"padding-left: 30px;\">Mean 1 - Mean 2 = {tuk12}<br/>Mean 1 - Mean 3 = {tuk13}<br/>Mean 2 - Mean 3 = {tuk23}</p>\n<p>5. Compare each difference to the SSD. If the difference is greater than SSD, then the means differ. Enter 0 below if the&nbsp;means are equal and 1 if they differ:</p>\n<p style=\"padding-left: 30px;\"><span>Mean 1 - Mean 2 = {tuk12sig}<br/>Mean 1&nbsp;- Mean 3&nbsp;=&nbsp;{tuk13sig}<br/>Mean 2&nbsp;- Mean 3&nbsp;=&nbsp;{tuk23sig}<br/></span></p>\n<p>Note that this test can give inconclusive results.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p><strong>Summary statistics</strong></p>\n<p>Calculate means and variances for both groups: variance ($s^2$) is just the standard deviation ($s$ or $sd$) squared.</p>\n<p><strong>Note: All values, except df and outcome, should be given to 3&nbsp;decimal places.</strong></p>\n<p>Mean 1 = [[0]]; Mean 2 =&nbsp;[[1]]; Mean 3 =&nbsp;[[2]]</p>\n<p>Variance 1 = [[3]]; Variance 2 =&nbsp;[[4]]; Variance 3 =&nbsp;[[5]]</p>\n<p>n1 = 6; n2 = 6; n3 = 6</p>\n<p>Cochran's value =&nbsp;[[6]]</p>\n<p><em>(Normally, we would compare the Cochran's value to the table (0.707) and transform the data if required, but this makes this too complicated, so we will assume that the calculated value is always lower than the table value.)</em></p>\n<p>In the next part, you enter the values for the intermediate terms.</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{mean1}+{slip}", "minValue": "{mean1}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{mean2}+{slip}", "minValue": "{mean2}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{mean3}+{slip}", "minValue": "{mean3}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{var1}+{slip}", "minValue": "{var1}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{var2}+{slip}", "minValue": "{var2}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{var3}+{slip}", "minValue": "{var3}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{cval}+{slip}", "minValue": "{cval}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p><strong>Intermediate terms</strong></p>\n<p>Enter the following:</p>\n<p>Sum of Group 1 = [[0]];&nbsp;<span>Sum of Group 2&nbsp;= [[1]];&nbsp;Sum of Group 3&nbsp;=&nbsp;[[2]]</span></p>\n<p><span>Sum of all values =&nbsp;[[3]]</span></p>\n<p><span>Sum of squares of all values =&nbsp;[[4]]</span></p>\n<p>Enter the S terms:</p>\n<p>S1 = [[5]]</p>\n<p>S2 = [[6]]</p>\n<p>S3 =&nbsp;[[7]]</p>\n<p>In the next part, you complete the analysis of variance.</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sumx1}+{slip}", "minValue": "{sumx1}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sumx2}+{slip}", "minValue": "{sumx2}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sumx3}+{slip}", "minValue": "{sumx3}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sumallx}+{slip}", "minValue": "{sumallx}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{s2}+{slip}", "minValue": "{s2}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{s1}+{slip}", "minValue": "{s1}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{s2}+{slip}", "minValue": "{s2}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{s3}+{slip}", "minValue": "{s3}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p><strong>Complete the ANOVA table</strong></p>\n<p>Fill in the values (3 decimal places, except for df).</p>\n<table>\n<tbody>\n<tr>\n<td>Source</td>\n<td>SS</td>\n<td>df</td>\n<td>MS</td>\n<td>F-ratio</td>\n</tr>\n<tr>\n<td>Among</td>\n<td>[[0]]</td>\n<td>[[3]]</td>\n<td>[[6]]</td>\n<td>[[8]]</td>\n</tr>\n<tr>\n<td>Within</td>\n<td>[[1]]</td>\n<td>[[4]]</td>\n<td>[[7]]</td>\n<td></td>\n</tr>\n<tr>\n<td>Total</td>\n<td>[[2]]</td>\n<td>[[5]]</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p><strong>Outcome</strong></p>\n<p>Is the null hypothesis (all means equal) rejected? Enter 0 for \"no\" and 1 for \"yes\".</p>\n<p>[[9]]</p>\n<p>If the null hypothesis is rejected, Tukey's test can be used to determine which means differ.</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{ssamong}+{slip}", "minValue": "{ssamong}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sswithin}+{slip}", "minValue": "{sswithin}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{sstotal}+{slip}", "minValue": "{sstotal}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": "0", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{dfamong}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "minValue": "{dfamong}", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": "0", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{dfwithin}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "minValue": "{dfwithin}", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "scripts": {}, "maxValue": "{dftotal}", "minValue": "{dftotal}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{msamong}+{slip}", "minValue": "{msamong}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{mswithin}+{slip}", "minValue": "{mswithin}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{fratio}+{slip}", "minValue": "{fratio}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": "0", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{outcome}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "minValue": "{outcome}", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p><strong>Complete Tukey's test</strong></p>\n<p>1.&nbsp;Find the appropriate q-value (k = 3, df = 15):</p>\n<p style=\"padding-left: 30px;\">table q =&nbsp;[[0]]</p>\n<p>2. Calculate the standard error (square-root(MSwithin/n)):</p>\n<p style=\"padding-left: 30px;\">SE =&nbsp;[[1]]</p>\n<p>3. Calculate the smallest significant difference (SSD or Least Significant Difference, LSD):</p>\n<p style=\"padding-left: 30px;\">SSD =&nbsp;[[2]]</p>\n<p>4. Calculate the differences between all pairs of means (ignore the sign):</p>\n<p style=\"padding-left: 30px;\">Mean 1 - Mean 2 =&nbsp;[[3]]<br/>Mean 1 - Mean 3 =&nbsp;[[4]]<br/>Mean 2 - Mean 3 =&nbsp;[[5]]</p>\n<p>5. Compare each difference to the SSD. If the difference is greater than SSD, then the means differ. Enter 0 below if the&nbsp;means are equal and 1 if they differ:</p>\n<p style=\"padding-left: 30px;\"><span>Mean 1 - Mean 2 =&nbsp;[[6]]<br/>Mean 1&nbsp;- Mean 3&nbsp;=&nbsp;[[7]]<br/>Mean 2&nbsp;- Mean 3&nbsp;=&nbsp;[[8]]<br/></span></p>\n<p>Note that this test can give inconclusive results.</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tukval}+{slip}", "minValue": "{tukval}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tukse}+{slip}", "minValue": "{tukse}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tukssd}+{slip}", "minValue": "{tukssd}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tuk12}+{slip}", "minValue": "{tuk12}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tuk13}+{slip}", "minValue": "{tuk13}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "scripts": {}, "precision": "3", "maxValue": "{tuk23}+{slip}", "minValue": "{tuk23}-{slip}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": "50", "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{tuk12sig}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "marks": 1, "minValue": "{tuk12sig}", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": "50", "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{tuk13sig}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "minValue": "{tuk13sig}", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": "50", "integerAnswer": true, "allowFractions": false, "scripts": {}, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{tuk23sig}", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "marks": 1, "minValue": "{tuk23sig}", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "<p>A biologist studied the effects of season and population density (number of animals in the area) on egg production in a marine snail [5]. A partially completed analysis of the study is shown below. State appropriate null hypotheses, then complete the analysis and draw conclusions about these null hypotheses, and about the effects of density and season.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"mswithin": {"definition": "sswithin/dfwithin", "templateType": "anything", "group": "Ungrouped variables", "name": "mswithin", "description": ""}, "mean1": {"definition": "precround(mean(grp1),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mean1", "description": ""}, "mean2": {"definition": "precround(mean(grp2),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mean2", "description": ""}, "mean3": {"definition": "precround(mean(grp3),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "mean3", "description": ""}, "sumsq1": {"definition": "sumsqrd(grp1)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumsq1", "description": ""}, "sumsq3": {"definition": "sumsqrd(grp3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumsq3", "description": ""}, "sumsq2": {"definition": "sumsqrd(grp2)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumsq2", "description": ""}, "slip": {"definition": "0.025", "templateType": "anything", "group": "Ungrouped variables", "name": "slip", "description": ""}, "sstotal": {"definition": "s2-s1", "templateType": "anything", "group": "Ungrouped variables", "name": "sstotal", "description": ""}, "grp3": {"definition": "repeat(precround(normalsample(treat3,sig1),1),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "grp3", "description": ""}, "grp2": {"definition": "repeat(precround(normalsample(treat2,sig1),1),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "grp2", "description": ""}, "grp1": {"definition": "repeat(precround(normalsample(treat1,sig1),1),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "grp1", "description": ""}, "sswithin": {"definition": "s2-s3", "templateType": "anything", "group": "Ungrouped variables", "name": "sswithin", "description": ""}, "cval": {"definition": "precround(max([var1,var2,var3])/sum([var1,var2,var3]),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "cval", "description": ""}, "sumallx": {"definition": "(sumx1+sumx2+sumx3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumallx", "description": ""}, "treat2": {"definition": "random(65..75#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "treat2", "description": ""}, "treat3": {"definition": "random(60..70#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "treat3", "description": ""}, "treat1": {"definition": "random(45..55#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "treat1", "description": ""}, "s3": {"definition": "(sumx1^2)/6+(sumx2^2)/6+(sumx3^2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "s3", "description": ""}, "s2": {"definition": "sumsqrd(grp1)+sumsqrd(grp2)+sumsqrd(grp3)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "(sumallx^2)/18", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "var2": {"definition": "precround((pstdev(grp2)^2),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "var2", "description": ""}, "tuk12": {"definition": "abs(mean1-mean2)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk12", "description": ""}, "tuk13": {"definition": "abs(mean1-mean3)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk13", "description": ""}, "dfamong": {"definition": "2", "templateType": "anything", "group": "Ungrouped variables", "name": "dfamong", "description": ""}, "sumx1": {"definition": "sum(grp1)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumx1", "description": ""}, "sumx2": {"definition": "sum(grp2)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumx2", "description": ""}, "sumx3": {"definition": "sum(grp3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sumx3", "description": ""}, "var1": {"definition": "precround((pstdev(grp1)^2),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "var1", "description": ""}, "var3": {"definition": "precround((pstdev(grp3)^2),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "var3", "description": ""}, "msamong": {"definition": "ssamong/dfamong", "templateType": "anything", "group": "Ungrouped variables", "name": "msamong", "description": ""}, "object": {"definition": "'Athlete'", "templateType": "anything", "group": "Ungrouped variables", "name": "object", "description": ""}, "tukssd": {"definition": "precround(tukval*tukse,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "tukssd", "description": ""}, "dfwithin": {"definition": "15", "templateType": "anything", "group": "Ungrouped variables", "name": "dfwithin", "description": ""}, "sig1": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "sig1", "description": ""}, "objects": {"definition": "'Athletes'", "templateType": "anything", "group": "Ungrouped variables", "name": "objects", "description": ""}, "ssamong": {"definition": "s3-s1", "templateType": "anything", "group": "Ungrouped variables", "name": "ssamong", "description": ""}, "tuk12sig": {"definition": "if(tuk12>tukssd,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk12sig", "description": ""}, "fratio": {"definition": "precround(msamong/mswithin,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "fratio", "description": ""}, "tuk13sig": {"definition": "if(tuk13>tukssd,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk13sig", "description": ""}, "tuk23": {"definition": "abs(mean2-mean3)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk23", "description": ""}, "tuk23sig": {"definition": "if(tuk23>tukssd,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "tuk23sig", "description": ""}, "tukval": {"definition": "3.67", "templateType": "anything", "group": "Ungrouped variables", "name": "tukval", "description": ""}, "ftable": {"definition": "3.68", "templateType": "anything", "group": "Ungrouped variables", "name": "ftable", "description": ""}, "dftotal": {"definition": "17", "templateType": "anything", "group": "Ungrouped variables", "name": "dftotal", "description": ""}, "tukse": {"definition": "precround(sqrt(mswithin/6),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "tukse", "description": ""}, "outcome": {"definition": "if(fratio>ftable,1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "outcome", "description": ""}}, "metadata": {"notes": "<p>Incomplete.</p>", "description": "<p>A comparison of the means of four&nbsp;groups.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Keith McGuinness", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/523/"}]}]}], "contributors": [{"name": "Keith McGuinness", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/523/"}]}