What is the primary goal of an Analysis of Variance (ANOVA)?

The primary goal of an Analysis of Variance (ANOVA) is indeed to analyze variance among three or more groups. ANOVA is a statistical method used to determine whether there are statistically significant differences between the means of different groups. It does this by comparing the variance within each group to the variance between the groups. When there are three or more groups involved, conducting multiple t-tests to compare each pair of groups would increase the risk of Type I error. ANOVA offers a more robust method to evaluate these differences simultaneously.

In the context of the other options, while testing the correlation between two variables involves examining the relationship between them, it is not the focus of ANOVA. The option regarding comparing the means of two independent groups would apply more directly to a t-test, which is designed for that specific purpose. Finally, measuring regression coefficients pertains to regression analysis, assessing the impact of one or more independent variables on a dependent variable, which is distinct from the objectives of ANOVA. Thus, ANOVA is primarily concerned with comparing means across multiple groups to understand the effects of categorical independent variables on a dependent variable.