Much research in the last two decades has demonstrated that human responses deviate from the performance deemed normative according to various models of decision making and rational judgment (e.g., the basic axioms of utility theory). This gap between the normative and the descriptive can be interpreted as indicating systematic irrationalities in human cognition. However, four alternative interpretations preserve the assumption that human behavior and cognition is largely rational. These posit that the gap is due to (1) performance errors, (2) computational limitations, (3) the wrong norm being applied by the experimenter, and (4) a different construal of the task by the subject. In the debates about the viability of these alternative explanations, attention has been focused too narrowly on the modal response. In a series of experiments involving most of the classic tasks in the heuristics and biases literature, we have examined the implications of individual differences in performance for each of the four explanations of the normative/descriptive gap. Performance errors are a minor factor in the gap; computational limitations underlie non-normative responding on several tasks, particularly those that involve some type of cognitive decontextualization. Unexpected patterns of covariance can suggest when the wrong norm is being applied to a task or when an alternative construal of the task should be considered appropriate.