Chapter 10. Power analysis
This chapter covers
As a statistical consultant, I am often asked the question, “How many subjects do I need for my study?” Sometimes the question is phrased this way: “I have x number of people available for this study. Is the study worth doing?” Questions like these can be answered through power analysis, an important set of techniques in experimental design.
Power analysis allows you to determine the sample size required to detect an effect of a given size with a given degree of confidence. Conversely, it allows you 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, you’d be wise to alter or abandon the experiment.
In this chapter, you’ll learn how to conduct power analyses for a variety of statistical tests, including tests of proportions, t-tests, chi-square tests, balanced oneway ANOVA, tests of correlations, and linear models. Because power analysis applies to hypothesis testing situations, we’ll start with a brief review of null hypothesis significance testing (NHST). Then we’ll review conducting power analyses within R, focusing primarily on the pwr package. Finally, we’ll consider other approaches to power analysis available with R.