# Appropriate homogeneity test for meta-analysis

I'm looking at measures from different studies (for a meta-analysis) and hoping to provide an aggregate effect size. I'm trying to identify hetero-/homo-geneity to determine whether I should use a random or fixed effects model. I do not have the original data - but rather effect sizes calculated from the individual studies. As such, I have Cohen's d, variance, n1, and n2 for each study/measure.

With this data, (how) can I calculate Cochran's q (or other test for homogeneity)?

Do I need to? Anderson-Darling shows that it's normally distributed.

• This link has useful information and a calculation tool (to do exactly what I hoped for - determine homogeneity of Cohen's d values - but the link to the tools is down. arxiv.org/abs/0906.2999 – d-cubed Apr 23 '14 at 0:49
• Here's the article with a working link. ncbi.nlm.nih.gov/pubmed/20528863 – d-cubed Apr 23 '14 at 1:00
• I have a doubt that either of the two - hetero-/homo-geneity determine whether I should use a random or fixed effects model. – Subhash C. Davar Aug 1 '20 at 12:30

## 1 Answer

The R package metafor is very useful for conducting a meta-analysis. If you estimate a model using rma.uni you can get a $Q$-test as output with the model to assess the heterogeneity with.

Although it may be possible, I do not know how one would perform the Anderson Darling test while accounting for the precision of the included studies. I think you should still test for heterogeneity. Additionally, you may also want to take a look at a funnel plot. Although it is typically used to help identify publication bias, you can also sometimes get a visual sense of heterogeneity in the studies by looking at one. If the Anderson Darling test was only performed on the effect estimates from the study, this plot may be informative in that it can reveal differences in distribution of the effect estimates as a function of the precision. This, and many other useful meta-analysis tools, are available in that package as well.

• I'd been looking at the metafor (and other packages). I thought I couldn't use rma.uni unless I'd determined the homogeneity first. My Q is 60 and p < .0001 with the rma.uni test - so am I to assume homogeneity? – d-cubed Apr 22 '14 at 19:30
• The test might also be implemented in rma.uni for method = "FE". I think you still get the heterogeniety test from the fixed effects model. In any event, coming from rma.uni, the test is valid as long as the sample is large enough (small samples affect the heterogeneity tests badly). But it looks like you have heterogeneity. As a side note, you also get some other tests like the $I^2$ in that package. – Deathkill14 Apr 22 '14 at 19:39