What people really know about probability and statistics: The effects of problem characteristics on beliefs

The first set of experiments shows that the beliefs people express about random sampling vary according to the computations required to obtain alternative answers to the problems; such variations are called computation effects. In several studies, it is demonstrated that the gambler's fallacy emerges only under conditions where the fallacious answer can be easily computed. The experiments in this section support the view that some beliefs are constructed as a function of the computational difficulty of responses based on those beliefs.;The third section examines people's performances on weighted mean problems. In the first study, people answered a series of questions that varied in computational difficulty. In most cases, the correct method of solving the problems was used regardless of computational difficulty, showing that performance is stable across problems that require well-learned algorithms. In the second study, performance on weighted mean problems improved with practice, apparently because a correct, known schema for the problems was triggered across trials. These results suggest that when solving problems that require well-learned algorithms, errors in performance diminish when people remember pre-computed schemas for solving problems. Thus on such tasks, inconsistent performance across trials can be attributed to difficulties accessing schemas, rather than to the processes involved in constructing on-line beliefs.;Misconceptions in a variety of domains have been characterized as deeply entrenched and difficult to change. The "teaching for conceptual change" approach was developed to deal with these kinds of misconceptions. However, the studies reported here show that the beliefs people express in judgment and statistical reasoning tasks are highly influenced by task characteristics, which suggests that teaching for stable knowledge may be more productive in these areas than teaching for conceptual change. (Abstract shortened by UMI.).;The second series of studies shows how belief construction varies according to the manner in which beliefs are reported; such variations are called format effects. People answered sampling problems in free-response or multiple-choice response formats. Although the problems were otherwise identical, these relatively minor changes in response formats led to different distributions of answers. In particular, people were more likely to see different outcomes as "equally likely" when responding in a multiple-choice format than when answering in a free-response format.