<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Hi,<div class=""><br class=""></div><div class="">first of all, I need to diclose that I am pretty much a newbie to meta-analysis. I am familiar with the general idea and the procedure of a „simple“ meta analysis. But I have an issue that seems to highly specific to me that I wasn’t able to find an answer in the literature or a previous posting, so I’d be happy for expert opinions.</div><div class=""><br class=""></div><div class="">I currently have a manuscript in peer review in whic the Editor asked us to do a mini meta-analysis over the four studies in the paper. All four studies use the same DV and manipulate the same factors, however, they differ in the implemented design:</div><div class=""><br class=""></div><div class="">In Studies 1 and 2, two of the factors (A and B) are manipulated between-subject and one within-subject (C). That is, each participant gives two responses in total. </div><div class=""><br class=""></div><div class="">In Studies 3 and 4, participants rate 40 stimuli that differ on two on factors A and B. Again, each stimulus is rated twice (factor C). So each participant gives 80 responses in total, the variables of interest are assessed within-subject and to analyze data. To analze, we used a linear mixed model/multilevel model with stimuli and participant as random factors. </div><div class=""><br class=""></div><div class="">The critical effect that the Editor is interested in is a rather complex three-way interaction AxBxC. Is it appropriate to summarize effect sizes of interaction terms in a meta analysis? From a former post on this mailing list I assumed it can be done: <a href="https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-February/000658.html" class="">https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-February/000658.html</a> However, I am wondering whether it is appropriate to combine effect sizes given the differences in the designs (between subjects elements in S1 and 2 but not in S3 and S4) and the different metric of the effect sizes (in the LMM in Studies 3 and 4 we use an approximation of d as suggested by Westfall (2014) that uses the the estimated variance components instead of the standard deviation). I read Morris& DeShon (2002) and understood that it is a potential problem to combine effect sizes that do not use the same metric - unfortunately, the transformation they suggest refers to combining effect sizes derived from comparisons of independent groups vs. repeated measures design and does not extend to linear mixed models.</div><div class=""><br class=""></div><div class="">One idea that I had is to follow the approach of Goh, Hall & Rosenthal (2016) for a random effects approach (which would mean to basically avagerage effect sizes and just ignore all differences in design, metric etc.) I’d be thankful for any thoughts on whether such a meta analysis can and should reasonably be done, any alternative suggestions, or whether due to the differences between the designs, it would be advisable to stay away from it.</div><div class=""><br class=""></div><div class="">Best,</div><div class=""><br class=""></div><div class="">Selma</div></body></html>