True/false question type to assess knowledge of basic aspects of ANOVA.
", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "Identify each of the following statements as true or false in relation to the analysis of variance (ANOVA) method:
", "advice": "Revise ANOVA, e.g., Section 7.5 of OpenIntro Statistics (4th edition).
\nNote in particular:
\nwith $k$ the number of groups.
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", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "random(1,5,10)", "description": "", "templateType": "anything", "can_override": false}, "dfG": {"name": "dfG", "group": "Ungrouped variables", "definition": "k-1", "description": "Degrees of freedom of the mean square between groups (MSG).
", "templateType": "anything", "can_override": false}, "t_statements": {"name": "t_statements", "group": "Statements", "definition": "[ \"Null hypothesis (H$_0$): The mean is the same across all groups.\", \"Alternative hypothesis (H$_A$): At least one mean is different.\", \"It is inappropriate to examine all data by eye (informal testing) and only afterwards decide which groups to formally test.\", \"For $\\\\var{k}$ groups and $\\\\var{n}$ total observations, $df_G=\\\\var{dfG}$.\", \"For $\\\\var{k}$ groups and $\\\\var{n}$ total observations, $df_E=\\\\var{dfE}$.\", \"The larger the variability between group means relative to the within-group variability, the stronger the evidence against the null hypothesis.\", \"For $\\\\var{k}$ groups and an original significance level $\\\\alpha=\\\\var{alpha}\\\\%$, testing all possible pairs requires a modified significance level $\\\\alpha^*=\\\\var{alphaStar}\\\\%$.\", \"All else being equal, larger differences in means between groups increase the evidence favouring the alternative hypothesis.\", \"All else being equal, larger within-group variations decrease the evidence favouring the alternative hypothesis.\", \"Rejecting the null hypothesis indicates evidence that at least one group mean is different from one another.\", \"If the null hypothesis is true, any variation in the sample means is due to chance.\", \"Rejecting the null hypothesis does not imply that a significant difference in the pairwise comparisons can be found.\", \"As the number of groups increases, the modified significance level for pairwise tests decreases.\" ]", "description": "", "templateType": "list of strings", "can_override": false}, "K_bonf": {"name": "K_bonf", "group": "Ungrouped variables", "definition": "k*(k-1)/2", "description": "Bonferroni correction
", "templateType": "anything", "can_override": false}, "dfE": {"name": "dfE", "group": "Ungrouped variables", "definition": "n-k", "description": "Degrees of freedom for the mean square error (MSE).
", "templateType": "anything", "can_override": false}, "statement_marks": {"name": "statement_marks", "group": "Statements", "definition": "map([2,0],x,t_statements)+map([0,2],x,f_statements)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Statements", "definition": "shuffle(0..len(statements)-1)[0..6]", "description": "", "templateType": "anything", "can_override": false}, "f_statements": {"name": "f_statements", "group": "Statements", "definition": "[ \"Null hypothesis (H$_0$): At least one mean is different.\", \"Alternative hypothesis (H$_A$): The mean is the same across all groups.\", \"It is appropriate to examine all data by eye (informal testing) and only afterwards decide which groups to formally test.\", \"For $\\\\var{k}$ groups and $\\\\var{n}$ total observations, $df_G=\\\\var{n-1}$.\", \"For $\\\\var{k}$ groups and $\\\\var{n}$ total observations, $df_E=\\\\var{dfG}$.\", \"The larger the within-group variability relative to variability between group means, the stronger the evidence against the null hypothesis.\", \"For $\\\\var{k}$ groups and an original significance level $\\\\alpha=\\\\var{alpha}\\\\%$, testing all possible pairs does not require a modified significance level as long as the conditions of independence, normality and constant variance are satisfied.\", \"All else being equal, larger differences in means between groups decrease the evidence favouring the alternative hypothesis.\", \"All else being equal, larger within-group variations increase the evidence favouring the alternative hypothesis.\", \"Rejecting the null hypothesis indicates evidence that all the means are different from one another.\", \"If the alternative hypothesis is true, any variation in the sample means is due to chance.\", \"Rejecting the null hypothesis implies that a significant difference in the pairwise comparisons can always be found.\", \"As the number of groups increases, the modified significance level for pairwise tests increases as well.\" ]", "description": "", "templateType": "list of strings", "can_override": false}, "alphaStar": {"name": "alphaStar", "group": "Ungrouped variables", "definition": "siground((alpha/K_bonf),3)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "Total number of observations.
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