What is the difference between fixed effects model and random effects model for a meta-analysis of sample correlations? Fixed effects model seems to differ from random effects model for a meta-analysis of sample correlations in terms of assumptions. What is key assumption for a fixed effect model?
 A: In a fixed-effects model, you are assuming that the true correlation estimated in each study is the same. In the Random effects model you accept that there is variation in the true correlation being estimate in each study.
Thus, the fixed-effects model assumes that observed variation in estimated correlations is due only to effect of random sampling.
It deciding between the two, you would often use a combination of theoretical knowledge and observed data. Theory will often suggest that the true correlation should vary somewhat between studies. You can also examine various test statistics on the observed correlations to assess whether the variation appears more than you would expect based on random sampling (e.g., see this discussion about Cochran's Q and related indices).
A: *

*Fixed-effect model


This model assumes that there is one true effect size; which underlies all the studies in the analysis, and that all differences in observed effects are due to sampling error. While we follow the practice of calling this a fixed-effect model, a more descriptive term would be a common-effect model. In either case, we use the singular (effect) since there is only one true effect.


*Random-effects model


Under this random-effects model we allow that the true effect could vary from study to study. For example, the effect size might be higher or lower in studies. Because studies will differ in the mixes of participants and in the implementations of interventions, among other reasons, there may be different effect sizes underlying different studies. If it were possible to perform an infinite number of studies (based on the inclusion criteria for analysis), the true effect sizes for these studies would be distributed about some mean. The effect sizes in the studies that actually were performed are assumed to represent a random sample of these effect sizes (hence the term random effects).
