The distribution matters: two types of sample-size tasks

Different studies on how well people take sample size into account have found a wide range of solution rates. In a recent review, Sedlmeier and Gigerenzer (1997) suggested that a substantial part of the variation in results can be explained by the fact that experimenters have used two different types of sample-size tasks, one involving frequency distributions and the other sampling distributions. This suggestion rested on an analysis of studies that, with one exception, did not systematically manipulate type of distribution. In the research reported in this paper, well-known sample-size tasks were used to examine the hypothesis that frequency distribution versions of sample-size tasks yield higher solution rates than corresponding sampling distribution versions. In Study 1, a substantial difference between solution rates for the two types of task was found. Study 2 replicated this finding and ruled out an alternative explanation for it, namely, that the solution rate for sampling distribution tasks was lower because the information they contained was harder to extract than that in frequency distribution tasks. Finally, in Study 3 an attempt was made to reduce the gap between the solution rates for the two types of tasks by giving participants as many hints as possible for solving a sampling distribution task. Even with hints, the gap in performance remained. A new computational model of statistical reasoning specifies cognitive processes that might explain why people are better at solving frequency than sampling distribution tasks. Copyright© 1998 John Wiley & Sons, Ltd.