The ''exchange paradox''-also referred to in the literature by a variety of other names, notably the ''two-envelopes problem''-is notoriously difficult, and experts are not all agreed as to its resolution. Some of the various expressions of the problem are open to more than one interpretation; some are stated in such a way that assumptions are required in order to fill in missing information that is essential to any resolution. In three experiments several versions of the problem were used, in each of which the information given was sufficient to determine an optimal choice strategy when it exists or to justify indifference regarding keeping or trading when such a strategy does not exist. College students who were presented with the various versions of the problem tended to base their choices on simple heuristics and to give little evidence of understanding the probabilistic implications of the differences in the problem statements.
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This experiment addressed the opinion prevailing among researchers that people are poor at producing random binary sequences. Participants tried to produce sets of sequences of outcomes of imaginary coin tosses that could not be distinguished statistically from sets expected from actual coin tossing. The results generally support the conclusion that people are not very good at this task, although the distributional properties of the sets of sequences produced are qualitatively similar to those expected of sets produced by a random process. The results do not support the common finding that people consistently produce substantially more alternations and fewer repetitions than would be produced by chance, nor do they provide evidence of the pervasive operation of a gambler’s fallacy manifesting itself in a tendency for an alternation to increase with the length of a preceding run.
Knowledge assessment via testing can be viewed from two vantage points: that of the test administrator and that of the test taker. From the administrator's perspective, the objective is to discover what an individual knows about a domain of interest. From that of the test taker, the challenge is to reveal what one knows. In this article we describe a procedure for administering and scoring multiple-choice tests that satisfies both of these objectives and we present experimental data that demonstrate its effectiveness. The method allows test takers to provide specific information about their confidence that each alternative for an item is the correct answer and makes guessing not only unnecessary but detrimental. From this information the administrator can derive measures of both knowledge and confidence, which, we argue, provides better estimates than systems that do not allow measurement of partial knowledge. The use of such measures for purposes of evaluation both of individual test takers' knowledge of a subject of interest and of the effectiveness of instruction with respect to that subject is discussed.
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