Power Analysis

Power, by definition, is the ability to find a statistically significant difference when the null hypothesis is in fact false, in other words power is your ability to find a difference when a real difference exists. The power of a study is determined by three factors: the sample size, the alpha level, and the effect size.

Most of the time when a researcher is concerned about issues regarding power it is when a study if first being proposed prior to collection of any data. In this situation, the investigator wants to determine what an appropriate sample size would be or justify a proposed sample size. In order to answer this question, the researcher needs to know the other two parts of the equation: alpha level and effect size. Determining an alpha level is usually a pretty easy task, figuring out the effect size is another matter.

Cohen, regarded as the deity of power analysis, (1977, 1988) justifies these levels of effect sizes.

Effect size Index Small Medium Large
t-test on Means d 0.20 0.50 0.80
t-test on Correlations r 0.10 0.30 0.50
F-test ANOVA f 0.10 0.25 0.40
F-test regression f2 0.02 0.15 0.35
Chi-Square Test w 0.10 0.30 0.50

There are a number of web resources related to statistical power analyses