Size invariance in visual number discrimination

This study deals with the observer's ability to discriminate the numerosity of two random dot-patterns irrespective of their relative size. One of these two patterns was a reference one that was always composed of 32 dots randomly distributed within a K x K invisible square window (K = 1.92 degrees). The second one was the test pattern with one of the five magnifications (K = 0.64 degrees, 1.28 degrees, 1.92 degrees, 2.56 degrees, 3.20 degrees) and the relative number of dots varied on 11 levels (N = -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, or 15 dots). The observer's task was to indicate which of the two patterns contained more dots. The results show that the stimulus size, as an irrelevant stimulus attribute, can be ignored in the judgements about relative numerosity. This means that the perceived numerosity is size invariant, at least for a 1.6-times magnification and a 3-times reduction of the test pattern. The size invariance observed constrains the range of potential models, since the perceived numerosity can be identified only by means of a feature of the stimulus that will remain invariant after any change in the absolute stimulus size.