I'm conducting a meta-analysis on standardised mean difference scores. Some studies provide multiple effect sizes, thereby violating the assumption of independence. An example is given below (all effect sizes were calculated with regard to a pre-test). In study A, all participants received the same treatment (watching a video), and were tested repeatedly. In study B, there were two different treatment groups (one group watched a video, the other group listened to an audio book), and everyone was tested once. Study C provided only one effect size.
study treatment testing_moment effect_size A video immediately 0.6 A video delayed 0.5 B video immediately 0.9 B audio_book immediately 0.7 C audio_book delayed 0.4
I'm using the metafor package in R, in which you can fit a multilevel model to account for non-independent sampling errors.
What I've done:
rma.mv(effect_size_vector, variance_vector, mods = ~ testing_moment, random = ~ 1 | treatment/study, data = rev)
Could anyone please have a look whether this approach is correct? I'm especially unsure about whether I've correctly indicated the clustering using slash (/) (this decision was based on this page), and whether the model as a result indeed takes into account the non-independence of effect sizes.
I'm also wondering whether somehow it should be corrected that the samples in study A are dependent and in study B they are independent. Or is that already accounted for by virtue of the treatment variable being the same for both samples in study A?