// Numbas version: exam_results_page_options
{"name": "ANOVA (one-way): drug effect", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "<p>This questions assesses the ability to conduct an ANOVA and interpret the results.</p><p>Adaptive marking: an error in calculating F can be carried over to the calculation of the p-value as well as the test conclusion.</p>"}, "tags": [], "statement": "<p>A trial was conducted to investigate any difference in blood cholesterol reduction when comparing $\\var{k-1}$&nbsp;different drugs. A total of $\\var{n}$ subjects was randomly allocated to $\\var{k}$ groups (one group for each drug plus a placebo group), with each group comprising $\\var{ni}$ subjects.</p>", "functions": {}, "variables": {"dfE": {"definition": "n-k", "description": "", "templateType": "anything", "name": "dfE", "group": "Analysis"}, "F": {"definition": "siground(MSG/MSE,3)", "description": "", "templateType": "anything", "name": "F", "group": "Analysis"}, "v": {"definition": "switch(p_pc<=alpha_pc,[3,0],p_pc>alpha_pc,[0,3])", "description": "<p>The \"3\" is the amount of marks available.</p>", "templateType": "anything", "name": "v", "group": "Ungrouped variables"}, "MSE": {"definition": "siground(SSE/dfE,3)", "description": "", "templateType": "anything", "name": "MSE", "group": "Analysis"}, "alpha_pc": {"definition": "random(0.1,1,5,10)", "description": "<p>Significance level as percentage.</p>", "templateType": "anything", "name": "alpha_pc", "group": "Setup"}, "p": {"definition": "siground(ftest(F,dfG,dfE),3)", "description": "", "templateType": "anything", "name": "p", "group": "Analysis"}, "SSE": {"definition": "random(700..800)", "description": "", "templateType": "anything", "name": "SSE", "group": "Setup"}, "k": {"definition": "random(4,5,10)", "description": "<p>Number of groups.</p>", "templateType": "anything", "name": "k", "group": "Setup"}, "dfG": {"definition": "k-1", "description": "", "templateType": "anything", "name": "dfG", "group": "Analysis"}, "MSG": {"definition": "siground(SSG/dfG,3)", "description": "", "templateType": "anything", "name": "MSG", "group": "Analysis"}, "tol": {"definition": "0.05", "description": "<p>Tolerance to allow for up to 5% rounding errors.</p>", "templateType": "anything", "name": "tol", "group": "Ungrouped variables"}, "SST": {"definition": "siground(SSG+SSE,3)", "description": "", "templateType": "anything", "name": "SST", "group": "Analysis"}, "SSG": {"definition": "random(10..15#0.1)", "description": "", "templateType": "anything", "name": "SSG", "group": "Setup"}, "dfTot": {"definition": "n-1", "description": "", "templateType": "anything", "name": "dfTot", "group": "Analysis"}, "n": {"definition": "random(100..900#100)", "description": "<p>Total number of subjects.</p>", "templateType": "anything", "name": "n", "group": "Setup"}, "p_pc": {"definition": "100*siground(ftest(F,dfG,dfE),3)", "description": "", "templateType": "anything", "name": "p_pc", "group": "Analysis"}, "ni": {"definition": "n/k", "description": "<p>Number of subjects per group.</p>", "templateType": "anything", "name": "ni", "group": "Setup"}}, "name": "ANOVA (one-way): drug effect", "ungrouped_variables": ["tol", "v"], "extensions": ["stats"], "variable_groups": [{"variables": ["n", "k", "ni", "SSG", "SSE", "alpha_pc"], "name": "Setup"}, {"variables": ["dfG", "dfE", "dfTot", "MSG", "MSE", "F", "SST", "p", "p_pc"], "name": "Analysis"}], "advice": "<p>For general aspects of ANOVA, see relevant literature (e.g., section 7.5 of <a href=\"https://leanpub.com/openintro-statistics\">OpenIntro Statistics</a>).</p>\n<p>The p-value can be calculated from the F value using Excel's&nbsp;F.DIST.RT function.</p>", "preamble": {"css": "", "js": ""}, "parts": [{"scripts": {}, "prompt": "<p>Fill in the gaps in the ANOVA table:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\"></th>\n<th>df</th>\n<th>Sum Sq</th>\n<th>Mean Sq</th>\n<th>F value</th>\n</tr>\n<tr>\n<th align=\"left\">drug</th>\n<td>[[0]]</td>\n<td style=\"text-align: center;\">$\\var{SSG}$</td>\n<td>[[3]]</td>\n<td>[[5]]</td>\n</tr>\n<tr>\n<th align=\"left\">Residuals</th>\n<td>[[1]]</td>\n<td style=\"text-align: center;\">$\\var{SSE}$</td>\n<td>[[4]]</td>\n<td></td>\n</tr>\n<tr>\n<th align=\"left\">Total</th>\n<td>[[2]]</td>\n<td>[[6]]</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>", "gaps": [{"minValue": "dfG", "maxValue": "dfG", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "dfE", "maxValue": "dfE", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "dfTot", "maxValue": "dfTot", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "MSG*(1-tol)", "maxValue": "MSG*(1+tol)", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "MSE*(1-tol)", "maxValue": "MSE*(1+tol)", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "F*(1-tol)", "maxValue": "F*(1+tol)", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}, {"minValue": "SST*(1-tol)", "maxValue": "SST*(1+tol)", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "0.5", "adaptiveMarkingPenalty": 0, "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "correctAnswerStyle": "plain"}], "marks": 0, "unitTests": [], "useCustomName": false, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"scripts": {}, "prompt": "<p>Calculate the p-value and convert to the corresponding percentage:</p>\n<p>$p=$ [[0]]$=$ [[1]]$\\%$</p>", "gaps": [{"minValue": "p*(1-tol)", "maxValue": "p*(1+tol)", "type": "numberentry", "showFractionHint": true, "allowFractions": false, "useCustomName": false, "marks": "2", "adaptiveMarkingPenalty": "0.5", "correctAnswerFraction": false, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": 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"extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "prompt": "<p>What is the conclusion of the test considering a significance level $\\alpha=\\var{alpha_pc}\\%$?</p>", "marks": 0, "maxMarks": 0, "showFeedbackIcon": true, "adaptiveMarkingPenalty": "0", "variableReplacements": [{"must_go_first": false, "part": "p1g1", "variable": "p_pc"}], "customMarkingAlgorithm": "", "scripts": {}, "choices": ["Reject the null hypothesis as at least one group mean is different.", "Do not reject the null hypothesis as all group means are equal."], "displayColumns": "1", "useCustomName": false, "customName": "", "variableReplacementStrategy": "alwaysreplace", "displayType": "radiogroup", "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "unitTests": [], "matrix": "v", "showCellAnswerState": true}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}]}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}