Effect Size - "Small", "medium", "large"

"Small", "medium", "large"

Some fields using effect sizes apply words such as "small", "medium" and "large" to the size of the effect. Whether an effect size should be interpreted small, medium, or large depends on its substantial context and its operational definition. Cohen's conventional criteria small, medium, or big are near ubiquitous across many fields. Power analysis or sample size planning requires an assumed population parameter of effect sizes. Many researchers adopt Cohen's standards as default alternative hypotheses. Russell Lenth criticized them as T-shirt effect sizes

This is an elaborate way to arrive at the same sample size that has been used in past social science studies of large, medium, and small size (respectively). The method uses a standardized effect size as the goal. Think about it: for a "medium" effect size, you'll choose the same n regardless of the accuracy or reliability of your instrument, or the narrowness or diversity of your subjects. Clearly, important considerations are being ignored here. "Medium" is definitely not the message!

For Cohen's d an effect size of 0.2 to 0.3 might be a "small" effect, around 0.5 a "medium" effect and 0.8 to infinity, a "large" effect. (But note that the d might be larger than one)

Cohen's text anticipates Lenth's concerns:

"The terms 'small,' 'medium,' and 'large' are relative, not only to each other, but to the area of behavioral science or even more particularly to the specific content and research method being employed in any given investigation....In the face of this relativity, there is a certain risk inherent in offering conventional operational definitions for these terms for use in power analysis in as diverse a field of inquiry as behavioral science. This risk is nevertheless accepted in the belief that more is to be gained than lost by supplying a common conventional frame of reference which is recommended for use only when no better basis for estimating the ES index is available." (p. 25)

In an ideal world, researchers would interpret the substantive significance of their results by grounding them in a meaningful context or by quantifying their contribution to knowledge. Where this is problematic, Cohen's effect size criteria may serve as a last resort.