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I am interested in clarifying the distinctions between the two terms in the title to this query, the problem being that they can and have been used interchangeably in the literature.

Links to similar CV questions give a clear meaning to relative importance as a within model metric summarizing the magnitude or impact of a feature; this is distinct from but relatable to the statistical significance of that parameter. Also of note is the apparent fact that relative importance can be readily estimated within the context of statistical models but much less so, if at all, wrt many black box machine learning algorithms (NNs, RFs, xgboost, etc.).

Effect size can be used, on the one hand, wrt "the magnitude of the differences between groups" (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/); as well as, on the other, for determining optimal sample sizes as a function of the magnitude of a desired effect (https://stats.stackexchange.com/questions/18028/desired-effect-size-vs-expected-effect-size?r=SearchResults&s=1|67.3751) If there are additional uses for effect size, I'm interested in learning about them.

Ok, so both concepts evaluate the magnitude of something but effect size has wider meaning and uses than relative importance.

What is a precise definition of effect size?

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    What's your interest in finding an answer to this question? To me, *effect size* has a precise meaning and *relative importance* could mean different things to different people. You might get a better answer if you clarify where you're coming from. – abstrusiosity Dec 23 '20 at 16:17
  • @abstrusiosity I agree that clarification is needed. It's interesting that effect size has a precise meaning for you whereas relative importance is ambiguous. In my opinion, there is more redundancy in their meaning and use. Hopefully, you will elaborate on this view. –  Dec 24 '20 at 16:05
  • @abstrusiosity After three edits, I can't seem to arouse interest on CV, but for you. Since you have a precise meaning for effect size, would it be too much to ask you to share it? Thx. –  Dec 25 '20 at 20:04
  • It's Christmas. I would not be so surprised that people are away from message boards. – Dave Dec 25 '20 at 20:05

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