11.6 The null hypothesis for ANOVA posits no difference among population means, as in other hypothesis tests, but the research hypothesis in this case is a bit different. Why? Solution The research hypothesis states that at least two of the means differ, but it does not indicate which ones. Post-hoc tests can then be used to determine more in the case you reject the null hypothesis in the initial ANOVA. In fact the research hypothesis for ANOVA doesn.