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I am trying to determine the appropriate effect size for a Wald's test. Does anyone know what effect size is typically reported for a Wald's test?

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  • $\begingroup$ The Wald test can be used to test a variety of hypotheses; it would be helpful to know more about your model and specifics on what the Wald will be testing. $\endgroup$
    – Bryan
    Mar 23, 2018 at 1:53

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I do not know of a general formula for an effect size for a Wald test, but I would suggest that an extrapolation from other analyses might be useful.  In particular, the relationship between Cohen’s $d$ and the $t$-ratio is $$d = t · \sqrt{\frac{1}{n}}$$ for a single sample, and $$d = t·\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$$ As the $t$-ratio is an example of a Wald statistic, and Cohen’s $d$ is an effect size, a possible general effect size may have the form $$z·\sqrt{\frac{1}{n}}$$ if a single sample, or $$z·\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$$ where $z$ is the Wald statistic.

Hope this is useful in some way.

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    $\begingroup$ Gregg, isn't an effect size index supposed to be independent of the sample size? "Unlike significance tests and P-values, indices like effect size are independent of sample size." (Source: sciencedirect.com/topics/medicine-and-dentistry/effect-size). $\endgroup$ Mar 23, 2018 at 1:43
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    $\begingroup$ Correct. At least for the t-ratios, these multiplication factors actually remove the dependence on the sample size. That is, if you write-out the formulas on the right-hand side, all the n's cancel. Making an assumption that the standard error for the target parameter in the Wald statistic depends on the sample size in a comparable way (which I acknowledge may be a BIG assumption), then the multiplication factors may do the same thing. $\endgroup$
    – Gregg H
    Mar 23, 2018 at 1:56
  • $\begingroup$ The Wald statistic is like an F-test in that it can, and generally does, reflect multiple parameters. Thus, it is a test of multiple effects, not a single effect. Furthermore, it is non-directional. As such, I see no reasonable way to get a meaningful effect size, assuming you want the effect size to reflect the direction and magnitude of a particular effect of interest. $\endgroup$
    – dbwilson
    Oct 12, 2020 at 9:47

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