Which test would you use to compare means across three or more groups?

Which test would you use to compare means across three or more groups?

• A. ANOVA
• B. t-test
• C. Regression
• D. Correlation

Answer: (A)

When you want to compare means across three or more groups, you need a method that tests whether any group differs from the others without inflating the chance of finding a difference just by chance. One-way ANOVA does this by partitioning the total variation into variation between groups and variation within groups; if all group means are equal, the between-group variation is small, yielding a small F-statistic, whereas a real difference among means increases the between-group variation and the F-statistic, signaling a significant result. ANOVA relies on assumptions of normality within groups, independence of observations, and roughly equal variances across groups. If you find a significant result, you’d use post hoc tests (like Tukey) to determine which specific groups differ while controlling the overall error rate. Other methods, like a t-test, only compare two means at a time and would inflate the Type I error rate if used repeatedly across three or more groups, while regression and correlation focus on relationships rather than comparing multiple group means.

When you want to compare means across three or more groups, you need a method that tests whether any group differs from the others without inflating the chance of finding a difference just by chance. One-way ANOVA does this by partitioning the total variation into variation between groups and variation within groups; if all group means are equal, the between-group variation is small, yielding a small F-statistic, whereas a real difference among means increases the between-group variation and the F-statistic, signaling a significant result. ANOVA relies on assumptions of normality within groups, independence of observations, and roughly equal variances across groups. If you find a significant result, you’d use post hoc tests (like Tukey) to determine which specific groups differ while controlling the overall error rate. Other methods, like a t-test, only compare two means at a time and would inflate the Type I error rate if used repeatedly across three or more groups, while regression and correlation focus on relationships rather than comparing multiple group means.