Power for equivalence tests

The power of a test estimates how likely it is that the test rejects the null hypothesis if the null hypothesis is indeed false. Because the null hypothesis for an equivalence test is often the opposite from the null hypothesis of a standard t-test of the population means, its power is expressed differently.

In equivalence testing, power is the likelihood that you will conclude that the population difference (or ratio) is within your equivalence limits when it actually is. If your test has low power, you may mistakenly conclude that you cannot claim equivalence when the difference (or ratio) is actually within the equivalence limits.

The following factors affect the power of your test.
Sample size
Larger samples give your test more power.
Difference
When the difference is close to the center of the two equivalence limits, your test has more power.
Standard deviation
Lower variability gives your test more power.
Alpha
Higher values for α give your test more power. However, α represents the probability of type I error. So increasing α increases your chance of claiming equivalence when it is not true.

To determine the power of an equivalence test, choose Stat > Power and Sample Size > Equivalence Tests and select the specific equivalence test that you want to use.

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