Computing the minimum effect size that can be detected with a specified level of statistical power
Rearranging the equation (Formula 1):
to solve d, we obtain:
Suppose we have only 25 cases available for study. What is the minimum effect size that we could expect to detect with power = 80% using one-tailed alpha = .05?
In this scenario, n = 25, and using the WISE p–z converter, we determine. Zα = 1.645 and Zβ = -0.842.
Applying the formula we find d = (2.487 / 5) = .497
This tells us that if the actual effect is smaller than about .50, then power for the contemplated study is less than 80%. We may decide that the study is not worth conducting because it is important to design a study that is likely to detect an effect that is less than .50, say .40.
If we can specify a minimum effect size that is important to detect, then we can use that value along with n and alpha error to compute power. In this example, if d = .40, alpha = .05, and n = 25, we can use the WISE Power Applet to find Power = .638. We may decide that it is not worth conducting the study with such low power.