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).

Social sampling and expressed attitudes: Authenticity preference and social extremeness aversion lead to social norm effects and polarization.

“…Another question is whether people’s estimations of distributions take the form of continually updated estimates of the distribution’s parameters, or are based on small samples retrieved at the time the distribution must be estimated. Most evidence supports the latter assumption (Lindskog, 2015; Lindskog & Winman, 2014; Lindskog, Winman, & Juslin, 2013a), consistent with the idea that people are naïve intuitive samplers (Juslin et al, 2007). Here, we make no strong commitment about when social norms are estimated; all that is essential for SST is that people have access to knowledge about the prevailing social norm at the time they decide what attitude to express, and that the knowledge they have is sufficient to enable estimation of their relative rank.…”

“…Here, we make no strong commitment about when social norms are estimated; all that is essential for SST is that people have access to knowledge about the prevailing social norm at the time they decide what attitude to express, and that the knowledge they have is sufficient to enable estimation of their relative rank. SST assumes that the expressed attitudes of all eight social network neighbors inform people’s estimation of the neighborhood social norm; people infer at least something about distributions from as few as four data points (Lindskog, 2015), and the assumption that eight observations are considered does not seem too inconsistent with small-sampling assumptions.…”

When does more mean worse? Accuracy of judgmental forecasting is nonlinearly related to length of data series

“…Studies in which people have been presented with data and required to make judgments about their means, variances or distributional properties have shown the expected effects of sample size in some cases [19,20] but not in others [21,32,33,34,50]. As a result, Pollard [42, p 15] concluded that: "On the basis of these often conflicting results, there is insufficient support for the Peterson and Beach idea that descriptive tasks can be viewed as tasks on which subjects make inferences that are properly influenced by sample size".…”

Sample size weighting follows a curvilinear function.

“…This suggests that people feel that the amount of data they will gain from subsequent samples rapidly diminishes such that further information is of little value. Thus, although larger samples may be viewed as more reliable (Kaufmann & Betsch, 2009), once one has a handful of cases, those data may feel sufficiently representative of a population (Tversky & Kahneman, 1971; also see Lindskog, 2015).…”