At its inception in the work of Skinner the nascent field of>behaviour analysis eschewed between-subject (group) averaging, Skinner (1938) remarking that [this] kind of science ? belongs on the non-statistical side (p443), and that individual prediction is of tremendous importance so long as the organism is to be treated scientifically (p444). Sidman (1960) strongly endorsed this, while allowing group averaging in specific circumstances. Nevertheless, from time to time, eminent behaviour analysts have called for the field to adopt group statistical methods requiring group averages, often on pragmatic grounds that this will help the field engage more with mainstream research. This paper will first consider why Skinner and Sidman argued as they did, and then consider several more recent arguments that support their position. The first is an argument that extends and generalizes Sidman?s from a biological perspective, noting that it is variability that drives natural selection, the most central process in biology, and that natural selection is blind to the average. Stephen J Gould argues that pre-occupation with group averages risks overshadowing proper attention to variability. The second argument considers the dangers of attempting to make inferences about within-subject processes from between-subject data (Quetelet?s fallacy), and the third, relatedly, considers the implications of measurement theory that specifies that inter-individual variation can only be used to explain intra-individual variation when the measurement system is ergodic. Most measurement in psychology and behaviour analysis, however, is non-ergodic. I conclude that the field should continue to eschew group averaging as a matter of principle, except in the instances that fit the conditions specified by Sidman and with due attention to variability (Gould).