THE DISTRIBUTION MATTERS - 2 TYPES OF SAMPLE-SIZE TASKS

Different studies on how well people take sample size into account hav e found a wide range of solution rates. In a recent review, Sedlmeier and Gigerenzer (1997) suggested that a substantial part of the variati on in results can be explained by the fact that experimenters have use d two different types of sample-size tasks, one involving fr frequency distributions and the other sampling distributions. This suggestion r ested on an analysis of studies that, with one exception, did not syst ematically manipulate type of distribution. In the research reported i n this paper, well-known sample-size tasks were used to examine the hy pothesis that frequency distribution versions of sample-size tasks yie ld higher solution rates than corresponding sampling distribution vers ions. In Study 1, a substantial difference between solution rates for the two types of task was found. Study 2 replicated this finding and r uled 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 distribut ion tasks. Finally, in Study 3 an attempt was made to reduce the gap b etween the solution rates for the two types of tasks by giving partici pants as many hints as possible for solving a sampling distribution ta sk. Even with hints, the gap in performance remained. A new computatio nal model of statistical reasoning specifies cognitive processes that might explain why people are better at solving frequency than sampling distribution tasks. (C) 1998 John Wiley & Sons, Ltd.