What statistical test is used to compare the means of multiple distributions?

The ANOVA test, or Analysis of Variance, is specifically designed to compare the means of multiple distributions or groups to determine if there are any statistically significant differences among them. When researchers want to assess whether different categories or groups have differing average outcomes, ANOVA is the preferred method because it can simultaneously evaluate multiple groups, whereas other tests might only handle two groups at a time.

In situations where there are three or more groups, using a T-test, which is more suited for comparing just two means, would not be appropriate as it increases the risk of Type I error. The Chi-squared test is used when dealing with categorical data to assess how likely it is that an observed distribution is due to chance, and it does not measure means. Regression analysis, on the other hand, is primarily used to examine the relationships between variables, rather than to compare the means of different groups. Thus, ANOVA stands out as the correct statistical test for this purpose.