Effect sizes and F-ratios below 1.0: Sense or nonsense
Standard statistics texts indicate that the expected value of the F ratio is 1.0 (more precisely: N/(N-2)) in a completely balanced fixed-effects ANOVA, when the null hypothesis is true. Even though some authors suggest that the null hypothesis is rarely true in practice (e.g., Meehl, 1990), F ratios < 1.0 are reported quite frequently in the literature. However, standard effect size statistics (e.g., Cohen’s f) often yield positive values when F < 1.0, which appears to create confusion about the meaningfulness of effect size statistics when the null hypothesis may be true. Given the repeated emphasis on reporting effect sizes, it is shown that in the face of F < 1.0 it is misleading to only report sample effect size estimates as often recommended. Causes of F ratios < 1.0 are reviewed, illustrated by a short simulation study. The calculation and interpretation of corrected and uncorrected effect size statistics under these conditions are discussed. Computing adjusted measures of association strength and incorporating effect size confidence intervals are helpful in an effort to reduce confusion surrounding results when sample sizes are small. Detailed recommendations are directed to authors, journal editors, and reviewers.