A brief narrative description of the journal article, document, or resource. Analyzed 150 articles from the "Journal of Applied Psychology" (JAP) from 1940 to 1999 to determine statistical reporting practices related to null hypothesis significance testing, American Psychological Association guidelines, and reform recommendations. Findings show little evidence that decades of cogent criticisms by reformers have resulted in changes in statistical reporting practices in JAP
Arguments are presented to support increased emphasis on logical aspects of formal methods of analysis, depending on probability in the sense of R. A. Fisher. Formulating probabilistic models that convey uncertain knowledge of objective phenomena and using such models for inductive reasoning are central activities of individuals that introduce limited but necessary subjectivity into science. Statistical models are classified into overlapping types called here empirical, stochastic and predictive, all drawing on a common mathematical theory of probability, and all facilitating statements with logical and epistemic content. Contexts in which these ideas are intended to apply are discussed via three major examples.
The authors tested the thesis that people find the Monty Hall dilemma (MHD) hard because they fail to understand the implications of its causal structure, a collider structure in which 2 independent causal factors influence a single outcome. In 4 experiments, participants performed better in versions of the MHD involving competition, which emphasizes causality. This manipulation resulted in more correct responses to questions about the process in the MHD and a counterfactual that changed its causal structure. Correct responses to these questions were associated with solving the MHD regardless of condition. In addition, training on the collider principle transferred to a standard version of the MHD. The MHD taps a deeper question: When is knowing about one thing informative about another?
We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students' representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students' partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.
When participants assess the relationship between two variables, each with levels of presence and absence, the two most robust phenomena are that: (a) observing the joint presence of the variables has the largest impact on judgment and observing joint absence has the smallest impact, and (b) participants' prior beliefs about the variables' relationship influence judgment. Both phenomena represent departures from the traditional normative model (the phi coefficient or related measures) and have therefore been interpreted as systematic errors. However, both phenomena are consistent with a Bayesian approach to the task. From a Bayesian perspective: (a) joint presence is normatively more informative than joint absence if the presence of variables is rarer than their absence, and (b) "failing" to incorporate prior beliefs is a normative error. Empirical evidence is reported showing that joint absence is seen as more informative than joint presence when it is clear that absence of the variables, rather than their presence, is rare.
This case study examines the validity of 1 measure of representation and employs multiple measures to examine whether they provide mutually informative or independent pieces of information. These measures include (a) concept maps, which measure how individuals represent their content knowledge of a domain as a whole; (b) problem sorts, which measure how individuals represent a specific aspect of their knowledge on word problems; and (c) structured interviews, which identify the reasons underlying sorting and concept mapping performance. Data from statistics instructors showed that the sorting task was a useful measure of representation when supplemented with instructors explanations of their rationales. Moreover, concept maps assisted in the interpretation of performance on the sorting task. Concept maps and problem sorts were mutually informative, with the former providing a broader picture and the latter illustrating how particular concepts became salient when applied to a different context.
It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to<br>the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends<br>on reasoners' interpretation of the expressions "probability" and "and." We report two experiments<br>designed to clarify the normative status of typical responses to conjunction problems.
The study of heuristics and biases in judgment has been criticized in several publications by G.<br>Gigerenzer, who argues that "biases are not biases" and "heuristics are meant to explain what does<br>not exist" (1991, p. 102). This article responds to Gigerenzer's critique and shows that it misrepresents<br>the authors' theoretical position and ignores critical evidence. Contrary to Gigerenzer's central<br>empirical claim, judgments of frequency - not only subjective probabilities - are susceptible to large<br>and systematic biases. A postscript responds to Gigerenzer's (1996) reply.
One event cannot be more probable than another that includes it. Judging P(A & B) to be higher<br>than P(A) has been caIled the conjunction fallacy- This study examined a disjullctioll fallaQ< Ss<br>received brief case descriptions and ordered 7 categories according to 1 of 4 criteria: (a) probability<br>of membership, (b) wiIlingness to bet on membership, (c) inclination to predict membership, and (d)<br>suitability for membership. The list included nested pairs of categories (e.g., Brazil-South America).<br>Ranking a category more probable than its superordinate, or betting on it rather than its superordinate,<br>is fallacious. Prediction, however, may be guided by maximizing informativeness, and suitability<br>need conform to no formal rule. Hence, for these 2 criteria, such a ranking pattern is not<br>fallacious. Yet ranking of categories higher than their superordinates was equally common on all 4<br>criteria. The results support representativeness against alternative interpretations.