Where did that come from?—Identifying the source of a sample

Abstract

People's ability to summarize their knowledge of an observed numerical variable has been extensively studied. However, many real-life situations require people to go beyond summary statistics and infer which process or distribution has generated a sample. The present study investigates the extent to which people can make such inferences when the experienced variable is continuous and when they have had previous experience with instances of the variable. It also tests specific predictions derived from three possible cognitive processes of how inferences about a generating distribution are made. The results indicate that participants are efficient and flexible intuitive statisticians, requiring only as little as four observations in a sample to successfully infer which distribution it came from. Further, the results indicate that the cognitive process supporting the inference uses statistical properties of both an experienced distribution and a presented test sample, as suggested by the Naïve Sampling Model (NSM).

Keywords:

• Intuitive statistics
• Sample
• Inference
• Naïve intuitive statistician
• Naïve sampling model

The author is indebted to Anders Winman, Peter Juslin, Håkan Nilsson, and Hedvig Söderlund for reading and commenting on earlier versions of the manuscript and to Johnny Halldin for help with the data collection of Experiments 1 and 3

The Swedish Research Council sponsored this research.

Notes

¹Permutation tests are a class of nonparametric test that rely on permutation and resampling techniques and make minimal assumptions about the data.