We are currently doing a research on physiological changes of platelet aggregation during three trimesters of pregnancy and postnatal period, then we compare these groups to each other and the control arm as well. We have recruited 10 patients per each trimester, 10 postnatal and 6 as control arm. The total sample size is 46. We wonder how we can calculate the study power? FYI we used Kruskal-Wallis Test to compare mean of the five groups, then if the resulted P-value was significant or close, we tried to perform post hoc Mann-Whitney Test. We also used same agonist (interference) for all groups but the participants are different in demographic point of view.
When computing power, you have to state what hypothetical effect size you are trying to detect. As Peter mentioned, computing the power to detect the results you actually detected is rarely useful.
The key paragraph: If your study reached a conclusion that the difference is not statistically significant, then -- by definition-- its power to detect the effect actually observed is very low. You learn nothing new by such a calculation. It can be useful to compute the power of the study to detect a difference that would have been scientifically or clinically worth detecting. It is not worthwhile to compute the power of the study to detect the difference (or effect) actually observed.
Here are five related peer-reviewed articles:
- SN Goodman and JA Berlin, The Use of Predicted Confidence Intervals When Planning Experiments and the Misuse of Power When Interpreting the Results, Annals Internal Medicine 121: 200-206, 1994.
- Hoenig JM, Heisey DM, The abuse of power, The American Statistician. February 1, 2001, 55(1): 19-24. doi:10.1198/000313001300339897.
- Lenth, R. V. (2001), Some Practical Guidelines for Effective Sample Size Determination, The American Statistician, 55, 187-193
- M Levine and MHH Ensom, Post Hoc Power Analysis: An Idea Whose Time Has Passed, Pharmacotherapy 21:405-409, 2001.
- Thomas, L, Retrospective Power Analysis, Conservation Biology Vol. 11 (1997), No. 1, pages 276-280
First, post-hoc power analysis is problematic (see, e.g. this
Second, if you decide to proceed anyway, there are two general approaches to power calculation. The simpler choice is to find a program that will calculate power for you. The more complex is to simulate the data. The former makes assumptions (sometimes unwarranted assumptions); if you go this route, you'd probably want to use the power programs for a one-way ANOVA and then note that in limitations. The latter requires you to create hypothetical data. Both have been discussed here a lot. How to simulate will depend on what software you are using.
Third, regarding power for the KW test, this article seems apropos, but I have not read it (beyond the abstract) as it is behind a pay wall.