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Meta-analysis studies a set of estimates of one parameter with three basic tools: The funnel diagram is the distribution of the estimates as a function of their precision; the funnel asymmetry test, FAT; and the meta average, where PET is an estimate. The FAT-PET MRA is a meta regression analysis, on the data of the funnel, which jointly estimates the FAT and the PET. Ideal funnels are lean and symmetric. Empirical funnels are wide, and most have asymmetries biasing the plain average. Many asymmetries are due to censoring made during the research-publication process. The PET is tooled to correct the average for censoring. We show that estimation faults and misspecification may cause natural asymmetries, which the PET does not correct. If the MRA includes controls for omitted variables, the PET does correct for omitted variables bias. Thus, it is important to know the reason for an asymmetry.

Natural Funnel Asymmetries: A Simulation Analysis of the Three Basic Tools of Meta Analysis