What does ANOVA primarily help to determine?

• A. Difference between two population means
• B. Equivalence of three or more population means
• C. Correlation between two variables
• D. Distribution of a single population mean

Answer: (B)

ANOVA, which stands for Analysis of Variance, is a statistical method primarily used to determine if there are statistically significant differences between the means of three or more independent groups. This technique allows researchers to test the null hypothesis that all group means are equal against an alternative hypothesis that at least one group mean is different.

When comparing multiple groups, simply using techniques that evaluate pairwise comparisons can increase the risk of Type I error, where false positives occur due to multiple testing. ANOVA mitigates this risk by assessing group means in a single comprehensive test, making it ideal for studies involving three or more populations.

Understanding the context is important, as other options focus on different statistical concepts. The examination of differences between only two means might be more directly associated with t-tests rather than ANOVA. Similarly, correlation pertains to the relationship between two variables, not the differences between means, and focusing solely on the distribution of a single population mean does not align with the core purpose of ANOVA either. Thus, ANOVA serves as a robust tool to assess the equivalence or differences among multiple population means simultaneously.