• Three experiments were conducted with college age beginning statistics students to assess the validity of six popular beliefs about factors related to statistics achievement. Mathematics background and ability, logical reasoning ability, attitude toward statistics, and anxiety were all found to have some relationship to statistics achievement. Differences between graduates and undergraduates, and men and women, were also explored. No significant differences were found between the groups on any single factor related to statistics achievement. There were, however, differences in how those factors combined to affect achievement for the different groups. It was concluded that no one variable explored here is singularly necessary for achievement in beginning statistics.

  • The objectives of this research were to determine if there were patterns to elementary teachers' development of statistical ideas. Center of the data and typical of the data were the two concepts studied. Comparisons of teacher's responses before and after instruction were made to determine areas of fixation and ideas about measures of center. Before instruction teachers tended to fixate on large graphical features. After instruction teachers focused on measures of center, particularly the median, to explain their ideas of center, rather than graphical features. More teachers focused on data intervals after instruction to explain typical in the histogram, but these ideas were not stable over the two graphs. We conjecture that fixations and stability are two factors in determining the statistical conceptual development of elementary teachers.

  • This study examine 56 elementary school teachers' knowledge of statistics before and after a three-week statistics workshop. Content knowledge was assessed through a paper-and-pencil instrument of twelve, open-ended statistics questions; responses were scored holistically.

  • Research literatures offer discrepant views concerning what understanding of chance entails, its relation to thinking probabilistically, and the nature of alternative interpretations. This study capitalized on the technology of videotapes to closely examine children's interpretations within tasks involving randomness and a qualitative level of differential probabilities.

  • Subjects were asked to select from among four possible sequences the "most likely" to result from flipping a coin five times. Contrary to the results of Kahneman and Tversky(1972), the majority of subjects (72%) correctly answered that the sequences are equally likely to occur. This result suggests, as does performance on similar NAEP items, that most secondary school and college-age students view successive outcomes of a random process as independent.

  • Children (preschoolers and third-, and sixth-grade pupils) were asked to choose out of 2 sets of marbles of 2 colors the set which they believed offered more chances of drawing a marble of a given color. It was found that a short instruction enabled the third-grade Ss to make their correct decisions, as did the sixth-graders, through a comparison of quantitative ratios. Reprinted from Child Development 41 (1970), 377 - 389.

  • Novices and experts rated 18 phenomena as random or non-random and gave justifications for their decisions. Experts rated more of the situations as random than novices. Roughly 90% of the novice justifications were based on reasoning via a) equal likelihood, b) possibility, c) uncertainty, and d) causality.

  • This analysis extends to the problem of the definition of the statistical experiment and the sample-space enumerating its outcomes.

  • This study presents a series of experiments showing that it is possible to elicit judgments indicating that perceived sample accuracy increases with sample size.

  • Statistical power is defined as the likelihood that a particular test will correctly determine a false null hypothesis. This paper describes an ongoing research program focused on the teaching, learning, and understanding of ideas related to statistical power. The research described includes investigations of the effectiveness of instruction using a specially designed interactive software program (the Power Simulator), and the development and use of assessment instruments to measure students' informal understandings of power prior to instruction.