Which statistical method is commonly used for comparing means across multiple groups?

The correct answer is ANOVA, which stands for Analysis of Variance. This statistical method is specifically designed to compare the means of three or more groups to determine if at least one group mean is statistically different from the others. ANOVA assesses the impact of one or more factors by comparing the means between the groups and using variance analysis to see if the observed differences are greater than what can be attributed to random chance.

When applied, ANOVA helps in situations where you have multiple groups and want to compare them simultaneously, thus avoiding multiple t-tests that can increase the risk of a Type I error (incorrectly rejecting the null hypothesis when it is true). It provides a more robust analysis by allowing the comparison in a single test instead of multiple individual comparisons.

For context, a t-test is suitable for comparing the means of only two groups, making it less effective for situations involving more than two. The Chi-square test is primarily used for categorical data to assess how expected counts compare to observed counts, rather than means of groups. Regression analysis focuses on the relationship between dependent and independent variables rather than the direct comparison of group means. Thus, ANOVA is rightly the go-to method for analyzing mean differences across multiple groups.