Power Analysis
Power analysis is an important aspect of experimental design. It allows us to determine the sample size required to detect an effect of a given size with a given degree of confidence. Conversely, it allows us to determine the probability of detecting an effect of a given size with a given level of confidence, under sample size constraints. If the probability is unacceptably low, we would be wise to alter or abandon the experiment.
The following four quantities have an intimate relationship:
Given any three, we can determine the fourth. The methods given below use R's Power Analysis (Pwr) package; this implements power analysis as outlined by Cohen (1988). The R functions that are made available here are listed below. A more detailed description is given here.
For each of these functions, you enter three of the four quantities (effect size, sample size, significance level, power) and the fourth is calculated. The significance level defaults to 0.05, but you can remove it if this is the quantity you would like to calculate. Specifying an effect size can be a daunting task. ES formulas and Cohen's suggestions (based on social science research) are provided here. Cohen's suggestions should only be seen as very rough guidelines. Your own subject matter experience should be brought to bear.
