1
$\begingroup$

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 I am trying to conduct a meta-analysis and I have an effect size estimation of some unpublished studies.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

$\endgroup$
  • $\begingroup$ 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
1
$\begingroup$

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.

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 Its unpublished data and I have only access to the Effect size of the study (Hedge g) and if the sutdy used categorial or correlational data $\endgroup$ – Martha Sep 19 '19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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.