When and how to apply ANOVA and chi-square tests, including assumptions and how to interpret the test statistic.
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- What is a one-way ANOVA used for?
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Comparing the means of three or more independent groups- When should you use ANOVA instead of a t-test?
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When comparing three or more groups instead of exactly two groups- State the null hypothesis for ANOVA.
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All group means are equal- State the alternative hypothesis for ANOVA.
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At least one group mean differs from the others- What does the normality assumption require in ANOVA?
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The dependent variable is normally distributed within each group- What does homogeneity of variance mean in ANOVA?
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The variance of the dependent variable is equal across all groups- Why must observations be independent in ANOVA?
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So that each observation contributes unique information and does not influence other observations- What does the F-statistic represent in ANOVA?
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The ratio of between-group variance to within-group variance- What is between-group variance?
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The variability of group means around the overall mean- What is within-group variance?
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The variability of individual scores around their own group mean- How do you interpret a large F-statistic?
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Between-group variance is much larger than within-group variance, suggesting group means differ significantly- How do you interpret a small F-statistic?
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Between-group variance is similar to within-group variance, suggesting group means are similar- What is the relationship between F-statistic size and p-value?
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A larger F-statistic yields a smaller p-value- What purpose do post-hoc tests serve in ANOVA?
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To identify which specific group means differ after obtaining a significant ANOVA result- What does eta-squared measure in ANOVA?
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The proportion of variance in the dependent variable explained by the grouping variable
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