The Same or not the same : Equivalence as an issue in educational research

In educational research, particularly in the sciences, a common research design calls for the establishment of a control and experimental group to determine the effectiveness of an intervention. As part of this design, it is often desirable to illustrate that the two groups were equivalent at the start of the intervention, based on measures such as standardized cognitive tests or student grades in prior courses. In this article we use SAT and ACT scores to illustrate a more robust way of testing equivalence. The method incorporates two one-sided t tests evaluating two null hypotheses, providing a stronger claim for equivalence than the standard method, which often does not address the possible problem of low statistical power. The two null hypotheses are based on the construction of an equivalence interval particular to the data, so the article also provides a rationale for and illustration of a procedure for constructing equivalence intervals. Our consideration of equivalence using this method also underscores the need to include sample sizes, standard deviations, and group means in published quantitative studies.