The recently completed CRONUS-Earth project broadly studied the production systematics of terrestrial in-situ cosmogenic nuclides and also incorporated an intercomparison study in which multiple labs measured various nuclides in homogenized geologic materials. Aliquots of these materials were measured in several labs for multiple nuclides, and the results combined to determine benchmark, consensus values. Results for some of these samples exhibited overdispersion, meaning that the measurements from the various labs differed by more than we would expect, given the quoted uncertainties. A traditional way to handle overdispersion is to add an extra amount to the variance of each lab. Another approach is to use a method that identifies potential outliers and then gives the outliers less weight in determining the final answer. A group of such methods is based on Bayesian thinking; one relatively simple member of this group was first proposed by Press (1997). We review the Press method and then apply it to the CRONUS data sets. We compare these results to those obtained by the added variance method and discuss the implications.