Perception of the mean and sum size of geometric forms

Abstract

Human efficacy in mean and sum size estimation was tested in this thesis. Kahneman (2011) proposed mean and sum size of geometric figures to be estimated by different systems – System1 and System 2. Effortless and automatic System 1 allows estimating mean size with considerable accuracy. Sum size, which requires multiplication of the means, however, can be only computed by a more elaborate higher order system, System 2. Two experiments, sharing the test elements, but with different reference and instruction, were conducted to test Kahneman’s proposal. In the first experiment the observers were asked to estimate mean size of a set of elements; in the second, the task was to estimate the sum size of the same elements. We expected to see great differences in the accuracy of size and sum discrimination if the underlying operations used in these tasks were different. The results show sudden drop in the accuracy if participants were required to estimate the sum size instead of mean size. Instead of assuming multiplication in sum size estimation, we proposed a model, where all the elements are set side-by-side, following an imaginary line, with the sum distance occupied by the adjoining elements being estimated instead. Accuracy is lowered in the sum size discrimination task by the measurement error of single elements, which is likely to be increased by the additional requirement – mental transposition of the elements – that one could estimate the required property. In addition, we could see that the mean size of a set of similar elements can be estimated only by using a subset of 2 –3 of all elements. Therefore, accuracy in the sum size estimation task can be reduced not only by the transposition need, but also by the requirement to use all the elements for creating an estimate.