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In 1988 Cohen suggested the following interpretation for effect size: "small~0.20, Medium~0.50, Large~0.80". I'm aware that these values are rather arbitrary and that an extensive disclaimer in this respect is already in Cohen's work.

Yet, is there a similar interpretation for Cliff's delta?

I found something similar for Cramer's V Small 0.1 0.2, Medium 0.3 0.5, Large 0.5. But nothing about Cliff's delta.

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You can name effect sizes whatever you want and your names would be no less valid than Cohen's "T-shirt effect sizes". The thing about the T-shirt effect sizes is that, despite their widespread use, there's nothing to recommend them beyond "Cohen said so". (Meanwhile, Cohen said a lot of other, more important things about data analysis, but these have been largely ignored, probably because they would require taking data analysis more seriously.) A $d$ of .2 could be small in one context and large in another, which is unavoidable considering that $d$ is standardized and hence throws away the original units.

In general, if you're confronted with an effect and want to know how big it is in an intuitive sense, you should compare it to a plot of the data it came from, rather than standardizing it and looking for T-shirt sizes for the standardized form.

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Vargha and Delaney (2000) give interpretations of their A statistic:

small, >= 0.56; medium, >= 0.64; large, >= 0.71

The corresponding values they give for Cliff's delta are:

small, >= 0.11; medium, >= 0.28; large, >= 0.43

Be cautious in evaluating negative Cliff's delta values and A values less than 0.50.

But, because both VDA and Cliff's delta are easy to express as probabilities (e.g., of an observation in one group being larger than an observation in another group), there is less need with these statistics than perhaps with some others to convey the small, medium, large interpretations.

Reference:

Vargha, A. and H.D. Delaney. A Critique and Improvement of the CL Common Language Effect Size Statistics of McGraw and Wong. 2000. Journal of Educational and Behavioral Statistics 25(2):101–132.

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