Standard statistical tests cannot be used to test for equivalence.Ī conclusion of “no statistically significant difference” between treatments, simply means that you don't have strong enough evidence to persuade you that the two treatments lead to different outcomes. Standard statistical tests cannot be used to test for equivalence This can either be the entire goal of the study (for example to show that a new formulation of a drug works as well as the usual formulation) or it can just be the goal for analysis of a control experiment to prove that a system is working as expected, before moving on to asking the scientifically interesting questions. But in some situations, your goal is just the opposite - to prove that one treatment is indistinguishable from another, that any difference is of no practical consequence. In most experimental situations, your goal is to show that one treatment is better than another. You've really need to rethink how the test is set up. A conclusion of "no statistically significant difference" is not enough to conclude that two treatments are equivalent. But sometimes your goal is to prove that two sets of data are equivalent. Usually statistical tests are used to look for differences.
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