I have the following problem: I am researching the difference in effects (as measured by standarized mean differences (SMD)) of two intervention types. (let's call them intervention 1 and intervention 2) by pooling the effects of the two different intervention types into pooled effect sizes using meta-analyses. To clarify what I mean: I ran a meta-analysis including 6 studies implementing intervention 1 and a separate analysis including 7 studies implementing intervention 2 and so far I have found that the pooled effect size of intervention 1 is d=0.3 and the pooled effect size of studies implementing intervention 2 is d=0.6. This seems like quite a difference but how do i statistically test whether these effects are significantly different?
If i disregard the meta-analysis and just test whether the mean SMD of studies implementing intervention 2 is significantly larger than studies implementing intervention 1 (t-test) I do not find a significant effect (p=.450). However in this t-test analyses the sample sizes of the individual studies are not taken into account and a SMD of a study with n=10 weighs as heavily as one with n=200. In the meta-analyses, the N of each study obviously does count and it appears that studies implementing intervention 2 with a large sample tend to have a more positive SMD hereby increasing the pooled effect size.
I have been searching the web for an answer to this question but I have yet to find an answer. Would it be viable to conduct an ANCOVA analysis with nominal variable=intervention type (1 or 2), covariate=N and independent variable=SMD?