Many research hypotheses involve a difference between levels of the independent variable(s), in terms of a dependent variable of interest. A research hypothesis of an existing difference is matched with a statistical alternative hypothesis of two parameters (e.g., population means) being different, and a null hypothesis of no difference. For the purposes of this thesis, the type of statistical testing used in such cases is referred to as "difference testing". By contrast, statistical equivalence testing is a suitable approach in the less frequent situation where the research hypothesis involves the equivalence of several levels of the independent variable(s) in terms of a dependent variable. Once equivalence limits have been set, an equivalence test can be conducted, so as to test the null hypothesis of non-equivalence. The burden is on the researcher to accumulate enough empirical evidence to be able to reject this null hypothesis and conclude in favor of the alternative hypothesis of equivalence. After placing equivalence testing in context by reviewing its history, a formal definition and a numerical example of equivalence testing are given. Equivalence testing is then applied to the evaluation of the homogeneity of variance assumption, via a simulation study. An illustrative research example concerning classroom settings is also provided, in order to show how equivalence testing can be applied to research questions within Educational Psychology.
University of Minnesota Ph.D. dissertation. July 2009. Major: Educational Psychology. Advisor: Michael Rodriguez. 1 computer file (PDF); vii, 99 pages, appendices A-D. Ill. (some col.)
Gaillard, Philippe R..
Evaluating Tthe assumption of homogeneity of variance via equivalence testing..
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