Which analysis compares mean values of a dependent variable across multiple categories or groups?

Which analysis compares mean values of a dependent variable across multiple categories or groups?

• A. ANOVA
• B. t-test
• C. Chi-square test
• D. Correlation analysis

Answer: (A)

The main idea here is comparing average outcomes across more than two groups. ANOVA (Analysis of Variance) does exactly that by testing whether the means across multiple categories differ more than would be expected by random variation. It does this by partitioning the total variability into variation between groups and variation within groups and forming an F statistic from those components. A significant F indicates that at least one group mean is different from the others, and post-hoc tests (like Tukey or Bonferroni) can tell you which groups differ. This method relies on assumptions such as independence of observations, roughly normal residuals, and equal variances across groups. If you only have two groups, a t-test would be used, but with three or more groups, ANOVA is appropriate to control the Type I error rate. The other analyses don’t fit because a t-test compares two means, chi-square tests categorical relationships, and correlation looks at association between two continuous variables rather than comparing multiple means.

The main idea here is comparing average outcomes across more than two groups. ANOVA (Analysis of Variance) does exactly that by testing whether the means across multiple categories differ more than would be expected by random variation. It does this by partitioning the total variability into variation between groups and variation within groups and forming an F statistic from those components. A significant F indicates that at least one group mean is different from the others, and post-hoc tests (like Tukey or Bonferroni) can tell you which groups differ.

This method relies on assumptions such as independence of observations, roughly normal residuals, and equal variances across groups. If you only have two groups, a t-test would be used, but with three or more groups, ANOVA is appropriate to control the Type I error rate. The other analyses don’t fit because a t-test compares two means, chi-square tests categorical relationships, and correlation looks at association between two continuous variables rather than comparing multiple means.