Subjects judged whether binary strings had been generated by a random or a nonrandom process.
Subjects judged whether binary strings had been generated by a random or a nonrandom process.
Significance testing is one of the most controversial subjects in research (Morrison and Henkel, 1970) and also one of the most misunderstood topics in the learning of statistics (Falk, 1986: Falk and Greenbaum (in print)). In this paper we present the results from a theoretical and experimental study concerning University students' understanding about the logic of statistical testing. The theoretical study discusses epistemological issues concerning Fisher's and Neyman-Pearson's approach to hypothesis testing and their relationship to the problem of induction in experimental sciences. The experiment sample included 436 students from 7 different university majors. Some of these students had a theoretically oriented course in statistics, such as those reading Mathematics, whereas others had a practically oriented course in statistics, such as those reading Psychology. The item presented in this paper is part of a larger questionnaire, which includes 20 items, and refers to the kind of proof provided by the results of a test of hypotheses. Following the analysis of these students' arguments, we identify three main conceptions: a) the test of hypotheses as a decision rule which provides a criterion for accepting one of the hypotheses; b) the test of hypotheses as mathematical proof of the truth of one of the hypotheses and c) the test of hypothesis as an inductive procedure which allows us to compute the "a posteriori" probability of the null hypothesis.
This study was undertaken with the goal of inferring an informal approach to probability that would explain, among other things, why subject responses to problems involving uncertainty deviate from those prescribed by formal theories. On the basis of an initial set of interviews such as an informal approach was hypothesized and described as outcome-oriented. In a second set of interviews, the outcome approach was used to successfully predict the performance of subjects on a different set of problems. In this chapter I will elaborate on the importance of understanding that subjects' performance in situations involving uncertainty is based on a theoretical framework that is different in important respects from any formal theory of probability. Additionally, I will argue that the outcome approach is reasonable given the nature of the decisions people face in a natural environment. To this end, I will review research which suggests some reasons why causal as opposed to statistical explanations of events are salient and functionally adaptive.
The present study investigated a model used by non-mathematically oriented students in solving problems in descriptive statistics. Analyses show that college students mistakenly assume that a set of means together with simple mean computation constitutes a mathematical group satisfying the four axioms of closure, associativity, identity, and inverse. this set of misconceptions is so deeply ingrained in a students' underlying knowledge base that mere exposure to a more advanced course in statistics is not sufficient to overcome those misconceptions. However, results of an experiment indicated that most students were able to acquire the appropriate schema of statistical concepts by engaging in diagnostic activities embedded within a feedback-corrective procedure.
Behavioral decision theory can contribute in many ways to the management and regulation of risk. In recent years, empirical and theoretical research on decision making under risk has produced a body of knowledge that should be of value to those who seek to understand and improve societal decisions. This paper describes several components of this research, which is guided by the assumption that all those involved with high-risk technologies as promoters, regulators, politicians, or citizens need to understand how they and the others think about risk. Without such understanding, well-intended policies may be ineffective, perhaps even counterproductive.
In two experiments, subjects were asked to judge whether the probability of A give B was greater than, equal to, or less than the probability of B given A for various events A and B. In addition, in Experiment 2, subjects were asked to estimate the conditional probabilities and also to calculate conditional probabilities from contingency data. For problems in which one conditional probability was objectively larger than the other, performance ranged from about 25-80% correct, depending on the nature of A and B. Changes in the wording of problems also affected performance, although less dramatically. Patterns of responses consistent with the existence of a causal bias in judging probabilities were observed with one of the wordings used but not with the other. Several features of the data suggest that a major source of error was the confusion between conditional and joint probabilities.
Performance on problems included in the most recent administration of NAEP suggest that the majority of secondary students believe in the independence of random events. In the study reported here a high percentage of high-school and college students answered similar problems correctly. However, about half of the students who appeared to be reasoning normatively on a question concerning the most likely outcome of five flips of a fair coin gave a logically inconsistent answer on a follow-up question about the least likely outcome. It is hypothesized that these students were reasoning according to an "outcome approach" to probability in which they interpreted their task as predicting what actually would occur if they flipped a fair coin five times. This finding suggests that the percentage correct on corresponding NAEP items are inflated estimates of normative reasoning about independence.
These results support the hypothesis that one major cause of inappropriate closure among young children is the confusion of possibility with probability
In this work teachers' responses to a survey about combinatorics and its teaching are analyzed. Participants were 22 in service teachers and 14 trainee teachers who respond to questions concerning actual teaching methodology, suggestions for change, and students' difficulties and interest in combinatorics. We present information about the following aspects: content being taught, time spend for it and its planning, types of problems proposed to students and their relative difficulty in opinion of those teachers and suggested changes for teaching of the subject.
The foundations of adult reasoning about probabilities are found in children's reasoning about frequencies.