GLM Hypothesis Testing - Planned Comparisons of Least Square Means
Usually, experimental hypotheses are stated in terms that are more specific than simply main effects or interactions. We may have the specific hypothesis that a particular textbook will improve math skills in males, but not in females, while another book would be about equally effective for both genders, but less effective overall for males. Now generally, we are predicting an interactions here: the effectiveness of the book is modified (qualified) by the student's gender. However, we have a particular prediction concerning the nature of the interactions: we expect a significant difference between genders for one book, but not the other. This type of specific prediction is usually tested by testing planned comparisons of least squares means (estimates of the population marginal means), or as it is sometimes called, contrast analysis.
Briefly, contrast analysis allows us to test the statistical significance of predicted specific differences in particular parts of our complex design. The four-step procedure for testing specific hypotheses is used to specify and test specific predictions. Contrast analysis is a major and indispensable component of the analysis of many complex experimental designs.
To learn more about the logic and interpretation of contrast analysis refer to the ANOVA/MANOVA module Overview section; examples of how to specify contrasts are also discussed there in the Notes section, for between-group designs as well as repeated measures designs.
Whole Model Tests
Error Terms for Tests
Testing Hypotheses for Repeated Measures and Dependent Variables
See also GLM - Index.