Power Analysis and Sample Size Estimation Using R

This chapter demonstrates some of the facilities in R for computing power and estimating required sample size for a few statistical models, focusing much of attention on interpreting what the given power estimate and analysis means. Statistical power is the probability of rejecting a null hypothesis given that the null hypothesis is actually false. That is, if the null hypothesis under test is, in reality not true, power is a probability of detecting that falsity. The level of statistical power is determined by four elements: effect size, population dispersion or variability, and sample size. Having demonstrated power principles through a t-test, the chapter then briefly surveys these same principles in a one-way ANOVA. Estimating power for a one-way ANOVA is about as easy as for a t-test. The chapter considers the case of estimating power for correlations, specifically the Pearson product-moment correlation coefficient.