A widespread and popular belief posits that humans possess a cognitive capacity that is limited to keeping track of and maintaining stable relationships with approximately 150 people. This influential number, ‘Dunbar's number’, originates from an extrapolation of a regression line describing the relationship between relative neocortex size and group size in primates. Here, we test if there is statistical support for this idea. Our analyses on complementary datasets using different methods yield wildly different numbers. Bayesian and generalized least-squares phylogenetic methods generate approximations of average group sizes between 69–109 and 16–42, respectively. However, enormous 95% confidence intervals (4–520 and 2–336, respectively) imply that specifying any one number is futile. A cognitive limit on human group size cannot be derived in this manner.