Capacity limitations of working memory force people to rely on samples consisting of 7 +/- 2 items. The implications of these limitations for the early detection of correlations between binary variables were explored in a theoretical analysis of the sampling distribution of phi, the contingency coefficient. The analysis indicated that, for strong correlations (phi > .50), sample sizes of 7 +/- 2 are most likely to produce a sample correlation that is more extreme than that of the population. Another analysis then revealed that there is a similar cutoff point at which useful correlations (i.e., for which each variable is a valid predictor of the other) first outnumber correlations for which this is not the case. Capacity limitations are thus shown to maximize the chances for the early detection of strong and useful relations.
Adaptive decision making requires that contingencies between decision options and their relative assets be assessed accurately and quickly. The present research addresses the challenging notion that contingencies may be more visible from small than from large samples of observations. An algorithmic account for such a seemingly paradoxical effect is offered within a satisficing-choice framework. Accordingly, a choice is only made when the sample contingency describing the relative evaluation of the 2 options exceeds a critical threshold. Small samples, because of the high dispersion of their sampling distribution, facilitate above-threshold contingencies. Across a broad range of parameters, the resulting small-sample advantage in terms of hits is stronger than their disadvantage in false alarms. Computer simulations and experiments support the model predictions. The relative advantage of small samples is most apparent when information loss is low, when the threshold is high relative to the ecological contingency, and when the sampling process is self-truncated.
A theoretical analysis (Y. Kareev, 1995b) of the sampling distribution of correlations led to the surprising conclusion that the use of small samples has a potential advantage for the early detection of a correlation. This is so because the distribution is highly skewed, and the smaller the sample size, the more the distribution is skewed. This article describes 2 experiments that were designed as empirical tests of this conclusion. In Experiment I (N = 112), the authors compared the predictions of participants differing in their working-memory capacity (hence in the size of the samples they were likely to consider). In Experiment 2 (N = 144), the authors compared the predictions of participants who viewed samples of different sizes, whose size was determined by the authors. The results fully supported Y. Kareev's conclusion: In both experiments, participants with lower capacity (or smaller samples) indeed perceived the correlation as more extreme and were more accurate in their predictions.
People simulating a random generator fail in the rate of each event, which is too close to the theoretical rate, and in overalternation between events. It is suggested that both failures stem from attempts to produce within short-term memory (STM) limitations a typical sequence in the standard task. 398 Ss of 3 age groups performed 3 coin-tossing tasks: standard, guessing, and guessing with feedback. The proportion of events was more variable and alternation rate was higher in the guessing than in the standard task. High alternation rates are shown to be byproducts of typical sequences. An estimate of the window size within which people operate highly correlated with age (corresponding to changes in STM capacity), further supporting the typicality assumption. People's grasp of randomness is therefore concluded to be better than hitherto believed.I thank Judith Avrahami, Don Diener, Naftali Halberstadt, Howard Kaplan, Allen Neuringer, and an anonymus reviewer for their comments on earlier drafts.
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