Which test is used to compare the means of three or more groups?

The test that is used to compare the means of three or more groups is ANOVA, which stands for Analysis of Variance. This statistical method allows analysts to determine whether there are any statistically significant differences between the means of three or more independent groups.

ANOVA works by analyzing the variances within each group and between the groups to see if observed differences are larger than what might be expected due to random chance. When the ANOVA test yields a significant result, it indicates that at least one group mean is different from the others, leading researchers to conduct further tests to identify where those differences lie.

In contrast, a t-test is designed for comparing the means of two groups only. The F-test, while it can be associated with the ANOVA method to assess variances, is not specifically used to compare group means. The Chi-square test is primarily used for categorical data to examine the association between two categorical variables and does not involve comparing means of groups. Therefore, ANOVA is the appropriate test for comparing the means across three or more groups.