I am reading Schmidt and Hunter - Methods of Meta-Analysis 3rd Edition to try and understand the theory behind meta-analysis. In chapter 3 they state the following: "To eliminate the effect of sampling error from a meta-analysis, we must derive the distribution of population correlations from the distribution of observed correlations." It was my understanding previously that we replicate studies time and time again in order to get a better idea of what the population correlation is. It is unclear to me why Schmidt and Hunter refer to population correlations (plural). Does each sample have its own population correlation?
the indivudual study correlation coefficients are regarded as samples from some universal (hypothetical) populaion with a population correlation coefficient and a population variance. These parameters are estimated from the sample (the individual studies in the meta analysis). It is the same concept as estimating the population mean and SD or SE from a sample (ie sample to population inference ).
further to my previous answer:
The first answer referred to a fixed effects made (one population corr coeff estimated)
In a random effects model a distribution of population corr coeffs is estimated.
this may explain the plural usage.
In random-effects modeling for meta-analysis, it is useful to think of each effect as coming from its own population. Across studies, then, we have the variance of observed effects, and we try to estimate a corresponding variance of population effects (by correcting the sample effects/distribution for measurement error variance, range restriction, etc.). If the population distribution ends up being zero, then the best fitting model assumes only one population value. But if it is non-zero, then there are assumed to be reliable differences between studies that give rise to varying effects. Piers Steel is in the business school at your university; he's a meta-analysis expert and would be a very useful contact on this front. Good luck!
Thank you everyone for your responses! These have been very helpful.
Frederick, Piers Steel is actually at the University of Calgary now!
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