Literature Index

In 1974, one of the authors (GAFS) introduced a terminating first year service course in statistics, paper 26.181, for non-mathematics students. In the following years we observed that the service course 26.181 catered not only for students majoring in other subjects, but also for a substantial number of mathematics students who preferred a more practical approach than the traditional one. The numbers were also steadily growing (about 1500 in 1990). At that stage we realised that 26.181 provided a potential source of advancing statistics students who might be interested in taking a second year follow-up course. In the 1980s Alan Lee (and probably most of us that vintage) had been strongly influenced by works on exploratory data analysis by such people as Tukey , McNeil, Velleman and Hoaglin. Under Lee's direction a second year data analysis course 26.281 was launched in 1981. His aim was to provide further training in practical statistics and data analysis without requiring too much mathematical knowledge or statistical theory. He realised that the students needed easy computer access for a realistic approach to data analysis. Suitable access to a mainframe was out of the question at the time, but micros seemed a viable alternative. A suitable statistical package was therefore developed called STATCALC (Lee et al., 1984) which had partly evolved from several programs on exploratory data analysis adapted from McNeil (1977) by Ross Ihaka. The package runs on IBM and Macintosh personal computers, the latter being currently used in our department. Lee and Peter Mullins also wrote a manual to go with the package. The manual, with its extensive tutorial section, also serves as the text for the course.

Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization and sampling processes. We explicate the role of probability in this approach and draw upon a models and modeling perspective to support the development of teachers’ models for using a repeated sampling approach for inference. We explicate the model development task sequence and examine the teachers’ representations of their conceptualizations of a repeated sampling approach for inference. We propose key conceptualizations that can guide instruction when using simulations and repeated sampling for drawing inferences.

Statistical analysis for social scientists very often means statistical analysis of some questionnaire data. The meaning of the numbers obtained in such analyses depends very much on the kind of scales used. In this paper it is shown that the meaning of numbers can also depend on how exactly the scales are constructed. First, some background information about how scales of the same type (e.g., interval scales) can considerably differ in meaning is given and then a series of study results with interval, ordinal, and nominal scales that demonstrate these differential effects are reported. It is argued that such results can easily be replicated in statistics classes. It is further argued that due to the preponderance of scales in social science research, statistics courses should put an emphasis on teaching the correct use and interpretation of scales. Here, demonstrations such as the ones described in this paper can play a helpful role.

This paper defines statistical reasoning, provides a model of statistical reasoning, and discusses the assessment of statistical reasoning.