A one-way ANOVA is a statistical test for comparing and making inferences about means associated with two or more groups. Once we have rejected the null hypothesis that all means are equal, we will want to further investigate the individual pair-wise differences in the means, to know which mean(s) are different.

This leads us to the next logical question—which means are different? Because we have rejected the idea that the null hypothesis is true (rejecting the idea that all means are equal), we can perform multiple comparisons to identify the differences.