Sample size bias in the estimation of means

Abstract

The present research concerns the hypothesis that intuitive estimates of the arithmetic mean of a sample of numbers tend to increase as a function of the sample size; that is, they reflect a systematic sample size bias. A similar bias has been observed when people judge the average member of a group of people on an inferred quantity (e.g., a disease risk; see Price, 2001; Price, Smith, & Lench, 2006). Until now, however, it has been unclear whether it would be observed when the stimuli were numbers, in which case the quantity need not be inferred, and "average" can be precisely defined as the arithmetic mean. In two experiments, participants estimated the arithmetic mean of 12 samples of numbers. In the first experiment, samples of from 5 to 20 numbers were presented simultaneously and participants quickly estimated their mean. In the second experiment, the numbers in each sample were presented sequentially. The results of both experiments confirmed the existence of a systematic sample size bias.