Frequently, a series of similar experiments are performed each yielding an estimate of a parameter, such as the affinity of a ligand for receptor. To obtain the best estimate of the parameter, the results from the assays are often pooled and a common mean and standard error are derived. Commonly, the reciprocal of the observed variance is used to determine the weight of each estimate. This is appropriate for data which do not display a variance which is functionally related to the mean. However, this type of weighting is not appropriate for radioactivity such as is used in receptor binding assays that has the property that the variability of each measurement is proportional to the mean. Many parameter estimates derived from analysis of these data will also exhibit variability which is functionally related to the mean. We suggest more suitable weights for these type of data, present formulas for the weighted mean and standard error, and investigate the behavior of tests of homogeneity using simulation.
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