• This article presents a critique of the concept of randomness as it occurs in the psychological literature. The first section of our article outlines the significance of a concept of randomness to the process of induction; we need to distinguish random and non-random events in order to perceive lawful regularities and formulate theories concerning events in the world. Next we evaluate the psychological research that has suggested that human concepts of randomness are not normative. We argue that, because the tasks set to experimental subjects are logically problematic, observed biases may be an artifact of the experimental situations and that even if such biases do generalise they may not have pejorative implications for induction in the real world. Thirdly we investigate the statistical methodology utilised in tests for randomness and find it riddled with paradox. In a fourth section we find various branches of scientific endeavour that are stymied by the problems posed by randomness. Finally we briefly mention the social significance of randomness and conclude by arguing that such a fundamental concept merits and requires more serious considerations.

  • In their article Ayton, Hunt and Wright (1989) address a number of issues that impinge on the concept of randomness. They appear to question not only the methodological soundness and general implications of research on "misconceptions" in statistics, but also the soundness of aspects of statistical inference. We concentrate here on a few key issues about which we are in disagreement (we think) with the authors.

  • This paper develops some ideas from the point of view of students moving on to tertiary education and the statistical needs they will have regardless of their mathematical background.

  • This paper explores some of the underlying conceptions and heuristics students bring to the study of statistics, and makes some initial hypotheses as to how these approaches might complicate students' learning the foundations of statistical inference.

  • There seems to be an irrevocable link between intuitions (intuitive ideas, intuitive conceptions) and theory (abstract models, concepts). It is not possible to separate these two aspects, each of which is necessary to understand the other. For such aspects, not really separable without loss of genuine meaning, it has become popular to say they are complementary.

  • It is certainly true for some developing nations the immediate task is to put in place an independent and efficient system of national economic and social statistics and to train professionals, planners, and managers to operate this system and use its products. Statistics for all, with its emphasis on the wider public, may appear to be a luxury for the developed world. If a greatly increased numerical competence on the part of ordinary citizens seems utopian, consider that even in Western Europe programmes to achieve near-universal literacy were established only in the latter half of the nineteenth century. Developed nations may soon be giving numeracy the same emphasis that they placed a century ago on literacy. Developing societies may wish to telescope the process by simultaneously emphasising literacy and numeracy . Statistics for all may move from the reveries of ICOTS to national policy.

  • Statistics is the collection, arrangement and interpretation of numerical facts or data. Here we have the ideal vehicle for this transformation, the means by which we can demonstrate the relevance of numeracy skills instead of just calling for them. Note here that I am not talking about theoretical statistics, but about the sensible use of numbers, the use of display techniques such as graphs and charts, and the extraction of information from numbers. These ideas can and should be applied in all subject areas.

  • A controversy has arisen concerning the relative merits of conceptually-oriented teaching versus calculation-centered teaching. Marks (1989) maintains that concepts are far more important than computations, and that they can be successfully taught without the related computations. In contrast, Khamis (1989) claims that students cannot truly understand statistical information until they have had experience doing calculations by hand. Both authors present persuasive arguments, but no empirical evidence to support their conclusions. The present paper outlines a study which aimed to fill this gap. First, however, we try to place the controversy into the context of wider cognitive issues.

  • This paper provides a conceptual framework for generating assessment tasks which provide an instructor with a richer description of students' thinking and reasoning than is possible by just giving students problems to solve. Although the framework is general, its application is illustrated with material from college and beginning graduate level pre-calculus introductory statistics courses which focuses on the following topics: sampling, interval estimation, point estimation, and hypothesis testing.

  • In professional fields such as education, psychology, sociology, etc., applied statistics courses emphasise developing skills in planning quantitative research studies, properly analysing data, and correctly interpreting the results of analysis. In general, students lack the background which would be required to deal with mathematical derivations. Furthermore, it is doubtful that this background would materially benefit these students in the professional roles for which they are preparing. The vast majority of researchers in the behavioural sciences are able to conduct their data analyses using the sophisticated statistical packages that are readily available. Thus, it becomes critical that applied statistics courses realistically prepare them for their role as data analysts. Each academic year, our department enrolls about 1000 students in undergraduate and graduate applied statistics courses. Approximately 50% of these students are enrolled in an undergraduate elementary statistics course and the other 50% of the students are enrolled in a series of four graduate courses offered, primarily, for students in the College of Education.