Group Comparisons with Scale Dependent Variables
摘要
This chapter covers both parametric and nonparametric methods for comparing groups. Parametric approaches include the independent samples t-test and the one-way analysis of variance (ANOVA), which assess differences in a scale variable between two or more groups. Post-hoc tests are discussed for cases in which the ANOVA omnibus test is statistically significant. Nonparametric alternatives are introduced for situations where assumptions of normality or homogeneity of variance are violated. The Mann–Whitney U test serves as the nonparametric counterpart to the t-test, and the Kruskal–Wallis test parallels ANOVA. When the Kruskal–Wallis test is significant, post-hoc comparisons can be conducted using Dunn’s test to identify specific group differences. Parametric tests generate test statistics such as t (for the t-test) and F (for ANOVA), whereas nonparametric tests produce rank-based statistics. Finally, measures of effect size, such as Cohen’s d for t-tests and eta-squared (η2) for ANOVA, quantify the strength of group differences.