Meta-Analysis - Calculating SE from given ES

Question

I have the following problem. I am trying to conduct a meta-analysis and I have an effect size estimation of some unpublished studies. Unfortunately, I don't have the Standard Errors for the mentioned Effect sizes.

Is it possible to calculate the Standard Error for the given Effect size?

Kind regards, Martha

Could you describe in your post what kind of effect sizes you’re working with? Correlations? Mean differences? — awhug, Sep 18 '19 at 10:26
I think there is no reliable way to get the exact SE. However, you can impute it, or assume a worst or best case scenario and try different analyses... — Giuseppe Biondi-Zoccai, Sep 18 '19 at 14:31
Sorry, I should have asked, are these $g$ from independent groups or is it repeated measures from pre- post-? — mdewey, Sep 18 '19 at 15:03
Please see my answer to a similar question before (https://stats.stackexchange.com/a/91313/24137). Simply stated, unless the authors give you the measure of variance, you can run several scenarios using imputed data. Good luck. — abousetta, Sep 18 '19 at 16:36

score 1 · Answer 1 · answered Sep 18 '19 at 17:18

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Let us work in terms of Cohen's $d$ and then convert to $g$.

It is known that the variance of $d$ is $$ V_d = \frac{n_1 + n_2}{n_1n_2} + \frac{d^2}{2(n_1 + n_2)} $$ where $n_1$ and $n_2$ are the sample sizes per group.

Suppose we in fact have $g$, we know that $$ g = J d $$ where $$ J = 1 - \frac{3}{4\nu - 1} $$ where $\nu$ is the df, that is $n_1 + n_2 - 2$ and $$ V_g = J^2 V_d $$

So by backcalculation from $g$ to $d$, computing the variance there and then converting back we get the sampling variance for $g$. The required standard error is then the square root. If only the overall sample size is known then setting $n_1 = n_2 = n/2$ would be defensible.

answered Sep 18 '19 at 17:18

mdewey

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If Hedge g is derived from data based on correlations, would I split the ntotal into n1 and n2? – Martha Sep 19 '19 at 11:46
No, that is a different situation. But why not meta-analyse the correlations (transformed using Fisher's $z$ transformation? – mdewey Sep 19 '19 at 12:07
Unfortunately I don't have the original data. Its unpublished data and I have only access to the Effect size of the study (Hedge g) and if the sutdy used categorial or correlational data – Martha Sep 19 '19 at 12:11
The problem is that I was answering under the assumption that the primary studies involved two group comparisons but now it seems that they involved a single group measured twice. In that case, if it is true, my answer does not apply. – mdewey Sep 19 '19 at 12:39
No its actually mixed. I have some studies that involve two group comparisons - for this studies your suggested convertations should work. But I have also studies that used correlations. If I understood correctly it is not possible to derive SE from this studies (with given g)? – Martha Sep 19 '19 at 12:53

Meta-Analysis - Calculating SE from given ES

1 Answers1