A farewell to Bonferroni: the problems of low statistical power and publication bias

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Abstract
Recently, Jennions and Møller (2003) carried out a meta-analysis on statistical power in the field of behavioral ecology and animal behavior, reviewing 10 leading journals including Behavioral Ecology. Their results showed dismayingly low average statistical power (note that a meta-analytic review of statistical power is different from post hoc power analysis as criticized in Hoenig and Heisey, 2001). The statistical power of a null hypothesis (Ho) significance test is the probability that the test will reject Ho when a research hypothesis (Ha) is true. Knowledge of effect size is particularly important for statistical power analysis (for statistical power analysis, see Cohen, 1988; Nakagawa and Foster, in press). There are many kinds of effect size measures available (e.g., Pearson's r, Cohen's d, Hedges's g), but most of these fall into one of two major types, namely the r family and the d family (Rosenthal, 1994). The r family shows the strength of relationship between two variables while the d family shows the size of difference between two variables. As a benchmark for research planning and evaluation, Cohen (1988) proposed ‘conventional’ values for small, medium, and large effects: r =.10,.30, and.50 and d =.20,.50, and.80, respectively (in the way that p values of.05,.01, and.001 are conventional points, although these conventional values of effect size have been criticized; e.g., Rosenthal et al., 2000).

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