StatDave_sas, I'm glad you responded. The title of the note you cited indicates that it is about testing equality, but it really looks like the standard treatment of demonstrating difference by rejecting the null hypothesis of equality.The example in the article says that the chi-squared test shows that the null hypothesis (of equivalence) is rejected, which is great in this example, so I know the two groups are not equivalent. However, I am looking for a measure of how similar they are, and I need to flip the hypotheses. My "null hypothesis" is that they are different, and I want to be able to reject that. I have found some literature on this topic, but there doesn't seem to be much treatment of this situation. Some literature suggests that using a conventional chi-squared test and seeing a p-value of 0.06, for example, would demonstrate that the two groups were similar, but I object that this is not a strict enough test. That simply means that there is still a 94% chance that they are different, right? (Note that some fields of study seem to think p<0.10 shows a significant difference.) Naively, I would expect to need a p-value > 0.95 in order to say with 95% confidence that the two sets of responses are likely to be the same. From what I have read, the TOST table generated by the RISKDIFF option seems the appropriate statistic to use to test equivalence in the 2x2 case, but I have no idea what to do in 2x3 (two groups, three response categories) or higher tables. What are your thoughts? Thanks!
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