How does pooling affect variance? Suppose you are looking at the prevalence of a certain disease and you can detect this disease in fecal samples. How does having a bunch of pooled fecal samples (i.e., taking a fecal sample from 5 individuals and pooling them together to get "one" sample) affect the variance compared to having a bunch of individual samples where each sample represents one person. 
I am doing a series of meta-analyses on the prevalence of a certain disease. The meta-analyses where the disease is detected in pooled fecal samples tends to have a lower heterogeneity compared to the meta-analyses where the disease is detected in individual fecal samples (individual-level sampling). What could explain this?
 A: Not sure in what sense you mean "pooling". In epidemiology, there's a concept of composite sampling. That is, for a rare disease and sensitive assay, you can collate a fraction of biospecimen and provide the diagnostic for 10 to 100 unique samples and, pending a positive result, subsample from the cluster to identify which participant was prevalent for disease. The process goes back to Dorfman who in 1943 suggested the approach as a cost effective way to test US military recruits for syphilis. For prevalence estimates, it's not necessary to subsample.
Meta-analyses also usually discuss pooled analyses where a weighted regression is used to combine the results from a number of studies that are considered to be "sufficiently homogeneous". Personally, I don't think this is the point of a good meta-analysis, since a bunch of underpowered studies does not one adequately powered study make. There's lots of reasons (early termination, publication bias, exploratory analyses published as confirmatory analyses) "the literature" is not a good database, though it contains some very good records.
Ultimately, if the choice boils down to an epidemiologic study that uses composite sampling or individual sampling, the composite study is superior because you can come up with the exact same prevalence estimate (unbiasedness) for either a lot less money or a lot more participants. I wager the researchers who are smart enough to composite also chose to recruit a bigger N. I very much doubt the heterogeneity differs significantly for an individual sampled vs compositely sampled study of the same N.
