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Both absolute and relative brain size vary greatly among and within the major vertebrate lineages. Scientists have long debated how larger brains in primates and hominins translate into greater cognitive performance, and in particular how to control for the relationship between the non-cognitive functions of the brain and body size. One solution to this problem is to establish the slope of cognitive equivalence, that is the line connecting organisms with an identical bauplan but different body sizes. Here, we suggest that intraspecific slopes provide the best available estimate of this measure. This approach was abandoned because slopes were too low by an unknown margin due to estimation error. We control for the error problem by focusing on highly dimorphic primate species with large sample sizes and fitting a line through the mean values for adult females and males. We obtain the best estimate for the slope of ca 0.27, a value much lower than those constructed using all mammal species, and close to the value expected based on the genetic correlation between brain size and body size. We also find that the estimate of cognitive brain size based on cognitive equivalence fits empirical cognitive studies better than the encephalization quotient (EQ), which should therefore be avoided in future studies on primates, and presumably mammals and birds in general. The use of residuals from the line of cognitive equivalence may change conclusions concerning the cognitive abilities of extant and extinct primate species, including hominins.