A-Priori Comparisons of Least Observed Squares Means vs. Post-hoc Comparisons of Means

For planned comparisons, STATISTICA uses least-squares means or "predicted means" in user-specified contrasts. That is, specific hypotheses are tested according to the overall model that was fitted to the data. This is consistent with the purpose and theory of planned comparisons, which must be a-priori and within the framework of the given model. Post-Hoc comparisons, however, are not a-priori, so one should be able to perform comparisons between any observed means in the design regardless of whether those comparisons are consistent with the a-priori model (note that some least-squares means may not be estimable in some designs, even though observed means may indeed exist).

STATISTICA will always compute post-hoc tests using observed means, taking the estimate of Sigma (when appropriate, i.e., when called for by the respective test) from the overall analysis (ANOVA). For ANCOVA designs, even though all post-hoc tests are performed on observed means, the estimate of Sigma for the tests will be "adjusted" by the presence of covariates in the model (because the MS-error for the between-group design will have been effectively adjusted).

To further illustrate this approach in an example, suppose a researcher had an a-priori model, but none of the effects that were anticipated proved to be statistically significant, while several other (non-anticipated) effects were found to be statistically significant. If this researcher then did post-hoc comparisons on least squares (predicted) means, he or she would have the paradox of testing post-hoc hypotheses on means predicted from a model that is already known to be unsupported by the data. At that point, it would make more sense to go back to the "simple" observed data (weighted means), and perform post-hoc comparisons to see whether any of the effects (differences) that were found are reliable or consistent with an overall null-hypothesis (no differences anywhere) given the overall design and number of cell means in the design.