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