I'm aware of the limitations of these simple rules of thumb, but in the research context in which I'm currently working, I can't avoid them.

This Cambridge University website cites the rules of thumb of Cohen (1988) for $η^2$ as being

0.01 = small effect
0.06 = medium effect
0.14 = large effect

Their figures seem to come from the table on p283, but it seems to me that straightfowardly reading the values off that table isn't right because the table represents $η^2$ as a function of f. However, according to my recording of the original document here (specifically p283-284) I worked it out that an $η^2$ of

0.100 = small effect
0.243 = medium effect
0.372 = large effect

The Cohen text is not very easy to read, and so I wonder that perhaps I have made a mistake. Am I missing something obvious here?

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd edition). Hillsdale, New Jersey: L.


Both of them are right; it's easy to see the answer returns the square.

eta = 0.100  --->  (eta)^2 =0.01   small effect
eta = 0.243  --->  (eta)^2 =0.06   medium effect
eta = 0.372  --->  (eta)^2 =0.14   large effect

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