Abstract
We examine the ability of observers to extract summary statistics (such as the mean and the relative-variance) from rapid numerical sequences of two digit numbers presented at a rate of 4/s. In four experiments (total N = 100), we find that the participants show a remarkable ability to extract such summary statistics and that their precision in the estimation of the sequence-mean improves with the sequence-length (subject to individual differences). Using model selection for individual participants we find that, when only the sequence-average is estimated, most participants rely on a holistic process of frequency based estimation with a minority who rely on a (rule-based and capacity limited) mid-range strategy. When both the sequence-average and the relative variance are estimated, about half of the participants rely on these two strategies. Importantly, the holistic strategy appears more efficient in terms of its precision. We discuss implications for the domains of two pathways numerical processing and decision-making.
Highlights
Imagine a stock-market operator viewing a rapid sequence of stock returns on which she needs to make a fast buy/sell decision, or alternatively, a person who faces a crowd of people, each exhibiting a distinct emotional expression toward the person, who needs to decide if to approach or not
The results of these experiments demonstrate that human observers have a high capacity to extract two major summary statistics—the average and the relative variance, and to evaluate them with a relatively high accuracy when viewing rapid numerical sequences presented at a rate of 4/s
The results indicate significant variability in the strategy that the observers deploy in these estimations. This variability is indicated in the variation of the average-estimation precision, in the variation of the sequence length effect and the curvature of the U-shape in the decision weights for ranked sequence elements (Figure 5). As all of these factors distinguish between the strategies we labeled as holistic-normative vs. mid-range, it is Summary Statistics of Rapid Numerical Sequences likely that they reflect a variability in the strategy the participants deploy
Summary
Imagine a stock-market operator viewing a rapid sequence of stock returns on which she needs to make a fast buy/sell decision, or alternatively, a person who faces a crowd of people, each exhibiting a distinct emotional expression toward the person, who needs to decide if to approach or not. In situations such as this, the rapid extraction of summary statistics of the elements (numerical returns or emotional expressions), in particular their average, has obvious advantages. In a recent study, Summary Statistics of Rapid Numerical Sequences
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