Thread by @datepsych

"Correlation size is not field-dependent." The guy who gave us the conventions for interpreting effect sizes said they were.

https://twitter.com/BobMcElrath/status/1659184768531984384

An R-squared of .2, so a Pearson's R of about .4, is a moderate-to-large correlation per Cohen's guidelines by the way.

Effect size conventions are entirely arbitrary. Simply derived from what is common in a field. You can never look at an r or d and know from the size if it's meaningful or not without understanding the practical significance of it.

Also from Cohen:

Also funny in the whole "small correlation" debacle is that small effects are supposed to be basically indistinguishable by sight.

Many people confused that because the dots on the chart don't pop out as a clear patten that it means there is no mathematical relationship.

In any case, understanding how meaningful the size of an effect is can only be done within the context of your field and further with a good understanding of what you are measuring.

So going back to this chart as an example (and ignoring the issues unrelated to interpreting effect sizes more generally):

How many additional homicides is explained by a change in X? It might be a "small" relationship that represents thousands of murders.

To use another recent example: the effect of antidepressants on depression is very small.

Yet, across a population this may represent tens and thousands of people who don't commit suicide, or who don't leave the workplace, due ro depression.

There is a name for this paradox in statistics where small relationships have large implications (particularly on a population level, but also occasionally on individual or interpersonal levels).

Obesity and many health outcomes are like this.

For a more recent take on this, Daniel Lakens' textbook (perhaps one of the more influential living statisticians today):

lakens.github.io/statistical_in…

And here is my video on effect sizes for anyone who would prefer to listen (no math):