What does ANOVA compare?

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of three or more groups to determine if at least one group mean is statistically significantly different from the others. The main purpose of ANOVA is to analyze the variance within each group and between the groups.

When applying ANOVA, it assesses whether the variability in the data can be attributed to the effect of the treatment or group, as opposed to random variance. If the null hypothesis (which states that all group means are equal) is rejected, it indicates that at least one group mean is different, prompting further analysis to identify which specific groups differ.

This is essential in research where comparisons across multiple groups are needed, such as in clinical trials or experiments involving multiple treatment conditions. While t-tests can compare the means of two groups effectively, ANOVA extends this capability to handle comparisons involving three or more groups without increasing the risk of Type I errors associated with multiple two-group comparisons.