Why Cohen’s effect size rule should be avoided

From Durlak (2009), How to select, calculate, and interpret effect sizes:

Many authors still routinely refer to Cohen’s (1988) comments made in reference to power analysis that SMDs of 0.20 are “small” in magnitude, those around 0.50 are “medium” and those around or above 0.80 are “large.” In terms of r, Cohen suggested corresponding figures of 0.10, 0.30, and 0.50. What many researchers do not realize is that Cohen offered these values cautiously as a general rule of thumb that might be followed in the absence of knowledge of the area and previous findings (Volker, 2006). Unfortunately, too many authors have applied these suggested conventions as iron-clad criteria without reference to the measurements taken, the study design, or the practical or clinical importance of the findings. Now that thousands of studies and meta-analyses have been conducted in the social sciences, Cohen’s (1988) general conventions do not automatically apply. Moreover, assuming that “large” effects are always more important than “small” or “medium” ones is unjustified. It is not only the magnitude of effect that is important, but also its practical or clinical value that must be considered.

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