STATISTICAL POWER ANALYSIS IN WILDLIFE RESEARCH

Statistical power analysis can be used to increase the efficiency of r esearch efforts and to clarify research results, Power analysis is mos t valuable in the design or planning phases of research efforts. Such prospective (a priori) power analyses can be used to guide research de sign and to estimate the number of samples necessary to achieve a high probability of detecting biologically significant effects. Retrospect ive (a posteriori) power analysis has been advocated as a method to in crease information about hypothesis tests that were not rejected. Howe ver, estimating power for tests of null hypotheses that were not rejec ted with the effect size observed in tile study is incorrect; these po wer estimates will always be less than or equal to 0.50 when bias adju sted and have no relation to true power. Therefore, retrospective powe r estimates based on the observed effect size for hypothesis tests tha t were not rejected are misleading; retrospective power estimates are only meaningful when based on effect sizes other than the observed eff ect size, such as those effect sizes hypothesized to be biologically s ignificant. Retrospectively power analysis can be used effectively to estimate the number of samples or effect size that would have been nec essary for a completed study to have rejected a specific null hypothes is. Simply presenting confidence intervals can provide additional info rmation about null hypotheses that were not rejected, including inform ation about the size of the true effect and whether or not there is ad equate evidence to ''accept'' a null hypothesis as true, We suggest th at (1) statistical power analyses be routinely incorporated into resea rch planning efforts to increase their efficiency; (2) confidence inte rvals be used in lieu of retrospective power analyses for null hypothe ses that were not rejected to assess the likely size of the true effec t, (3) minimum biologically significant effect sizes be used for all p ower analyses, and (4) if retrospective power estimates are to be repo rted, then the alpha-level, effect sizes, and sample sizes used in cal culations must also be reported.