A Note on Statistical Power

Formal hypothesis testing consists of a series of steps: designation of the null (H0) and alternative (H^) hypotheses, collection of data to discriminate between these hypotheses, and then statistical analysis of the data. If the probability of an observed result is less than 5% (P < 0.05), we generally accept H^ and reject Ho. Conversely, if P > 0.05, we have failed to reject the null hypothesis. Most analyses stop here. If the null hypothesis is not rejected, however, the statistical power of the test should be evaluated. Power analysis adds another important dimension to hypothesis testing, and failure to evaluate power may result in false inferences. A recent example illustrates these points. Edwards et al. (1988) presented evidence that a correlation exists between the sex ratios of fledgling Golden Eagles (Aquila chrysaetos) and the abundance of food (jackrabbit density), presumably because the larger females have an advantage in sibling competition when food is short. Bortolotti (1989) and Arnold (1989) raised a number of criticisms, many of which Edwards and Collopy (1989) addressed; but, the question of whether there is evidence that sex ratio covaries with food remains. Using a Spearman's rank correlation, Arnold reanalyzed Edwards et al.'s data (their fig. 1 and table 1) and found a near zero correlation (rs = -0.003, P = 0.99) between food and sex ratio. Edwards et al. (1988: 795), however, used a dif-