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 I am trying to conduct a meta-analysis and I have an effect size estimation of some unpublished studies.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

  • $\begingroup$ Could you describe in your post what kind of effect sizes you’re working with? Correlations? Mean differences? $\endgroup$ – awhug Sep 18 '19 at 10:26
  • $\begingroup$ I use mean differences. Effect size is Hedge g. $\endgroup$ – Martha Sep 18 '19 at 11:30
  • $\begingroup$ Do you have the sample sizes? $\endgroup$ – mdewey Sep 18 '19 at 13:27
  • $\begingroup$ I have the number of the total sample size $\endgroup$ – Martha Sep 18 '19 at 13:29
  • $\begingroup$ 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... $\endgroup$ – 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.

  • $\begingroup$ If Hedge g is derived from data based on correlations, would I split the ntotal into n1 and n2? $\endgroup$ – Martha Sep 19 '19 at 11:46
  • $\begingroup$ No, that is a different situation. But why not meta-analyse the correlations (transformed using Fisher's $z$ transformation? $\endgroup$ – mdewey Sep 19 '19 at 12:07
  • $\begingroup$ 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 Its unpublished data and I have only access to the Effect size of the study (Hedge g) and if the sutdy used categorial or correlational data $\endgroup$ – Martha Sep 19 '19 at 12:11
  • $\begingroup$ 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. $\endgroup$ – mdewey Sep 19 '19 at 12:39
  • $\begingroup$ 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)? $\endgroup$ – Martha Sep 19 '19 at 12:53

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