# Meta-Analysis - Calculating SE from given ES

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 I am trying to conduct a meta-analysis and I have an effect size estimation of some unpublished studies.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 use mean differences. Effect size is Hedge g. – Martha Sep 18 '19 at 11:30
• Do you have the sample sizes? – mdewey Sep 18 '19 at 13:27
• I have the number of the total sample size – Martha Sep 18 '19 at 13:29
• 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... – Joe_74 Sep 18 '19 at 14:31

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.

• 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 Its unpublished data and I have only access to the Effect size of the study (Hedge g) and if the sutdy used categorial or correlational data – Martha Sep 19 '19 at 12:11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