From a note
A Priori Power Analysis. This is an important part of planning research. You determine how many cases you will need to have a good chance of detecting an effect of a specified size with the desired amount of power. See my document Estimating the Sample Size Necessary to Have Enough Power for required number of cases to have 80% for common designs.
A Posteriori Power Analysis. Also know as “post hoc” power analysis. Here you find how much power you would have if you had a specified number of cases. Is it “a posteriori” only in the sense that you provide the number of number of cases, as if you had already conducted the research. Like “a priori” power analysis, it is best used in the planning of research – for example, I am planning on obtaining data on 100 cases, and I want to know whether or not would give me adequate power.
Retrospective Power Analysis. Also known as “observed power.” There are several types, but basically this involves answering the following question: “If I were to repeat this research, using the same methods and the same number of cases, and if the size of the effect in the population was exactly the same as it was in the present sample, what would be the probability that I would obtain significant results?” Many have demonstrated that this question is foolish, that the answer tells us nothing of value, and that it has led to much mischief. See this discussion from Edstat-L. I also recommend that you read Hoenig and Heisey (The American Statistician, 2001, 55, 19-24). A few key points:
- Some stat packs (SPSS) give you “observed power” even though it is useless.
- “Observed power” is perfectly correlated with the value of p – that is, it provides absolutely no new information that you did not already have.
- It is useless to conduct a power analysis AFTER the research has been completed. What you should be doing is calculating confidence intervals for effect sizes.
I was confused what differences and relation are between Retrospective Power Analysis and A Posteriori power analysis? I think they both have a given sample size and try to estimate the power?
What does "the size of the effect in the population was exactly the same as it was in the present sample" mean?
Thanks and regards!