Approximating power for significance tests with one degree of freedom

Shortcut approximate equations are described that provide estimates of the sample size required for 50% power (alpha = 0.05, two-tailed) for 1 degree of freedom tests of significance for simple correlations, differences between 2 independent group means, and Pearson's chi-square test for 2 x 2 contingency tables. These sample sizes should be thought of as minima, because power equal to 50% means that the chance of a significant finding is that of flipping a fair coin. A more desirable sample size can be computed by simply doubling the 50% sample sizes, which is shown to result in power between 80% and 90%. With these simple tools, power can be estimated rapidly, which, it is hoped, will lead to greater use and understanding of power in the teaching of statistics and in research.