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D. Kahneman and A. Tversky (Cognitive Psychology, 1972 , 3, 430–454) claimed that “the notion that sampling variance decreases in proportion to sample size is apparently not part of man's repertoire of intuitions.” This study presents a series of experiments showing that it is possible to elicit judgments indicating that perceived sample accuracy increases with sample size. However, these judgments seem to reflect sensitivity to sample-to-population ratio rather than absolute sample size. In fact, people may trade sample size for sample-to-population ratio, even when this actually decreases expected sample accuracy. The widely held belief that the accuracy of a sample is connected with its relative size to the universe is mistaken. A sample smaller than 1%, taken from one universe, can be much more reliable than one comprising 10% of another. To determine with equal accuracy the average age of the population of New York City and of Peoria, Illinois, will require samples of equal size (variances of population being equal). ( Zeisel, 1960 ).

The question of sample size—how much is enough—has no simple answer. Magical numbers do not exist.

An experiment is reported in which S s are asked to compare pairs of binomial samples and judge which, if either, gives better evidence of asymmetry in their underlying population. The results indicate that whilst all S s are influenced by sample proportion only about one third give appropriate weighting to differences in sample size. However, according to the theory of ‘representativeness’ postulated by Kahneman and Tversky (1972) sample size should have been ignored altogether. A second experiment confirmed the hypothesis that their results reflected the use of over-complex problem presentation. When one of their problems was systematically simplified, a significant majority of S s showed insight into the role of sample size.

A formula is derived for the required number of subjects in a comparison group to test the equality of two Normal means when one sample size is fixed. Both the equal variances and the unequal variances cases are allowed for in one formula. This should be useful whenever a fixed number of subjects from one group is available, but an arbitrary number of comparison subjects could be employed. It is shown that when one sample size is fixed, some differences in means cannot be detected with a desired power regardless of how many comparison subjects might be available.

This paper explores a heuristic — representativeness — according to which the subjective probability of an event, or a sample, is determined by the degree to which it: (i) is similar in essential characteristics to its parent population; and (ii) reflects the salient features of the process by which it is generated. This heuristic is explicated in a series of empirical examples demonstrating predictable and systematic errors in the evaluation of uncertain events. In particular, since sample size does not represent any property of the population, it is expected to have little or no effect on judgment of likelihood. This prediction is confirmed in studies showing that subjective sampling distributions and posterior probability judgments are determined by the most salient characteristic of the sample (e.g., proportion, mean) without regard to the size of the sample. The present heuristic approach is contrasted with the normative (Bayesian) approach to the analysis of the judgment of uncertainty.

A double sample test for a hypothesis concerning the mean μ of a normal random variable with unknown variance σ2 is presented in this note. This test is an alternative to the usual single sample t test and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested here if the second sample is taken the information from the first sample is used in making the final decision. A table is included which is a tabulation of the rejection and acceptance points for various sample sizes and α = .05 and α = .01. Additional tables are included which give some power values and expected sample sizes for the new test and Owen's test. These power values are compared with power values of various single sample t tests. Conclusions about desirable sample sizes are presented for both the new test and Owen...