We first examine the multiple populations or multiple treatments to test for statistical significance as evidence of among the parameters we want to compare. ANOVA F-test
, then a detailed follow-up analysis is legitimate.
If we planned our experiment with specific alternative hypotheses in mind ( gathering the data), we can test them using contrasts.
If we do not have specific alternatives, we can examine all pair-wise parameter comparisons to define which parameters differ from which, using multiple comparisons procedures.
An Overview of ANOVA