Literature Index

In reflecting upon the possible components of a course of study for students doing doctoral work in the field called statistics education, it seemed that the preparation should contain most of the components of a model preparation program for doctoral students in mathematics education. In fact, except for the particulars of the discipline, I see very little difference in what I would recommend as the core of either doctoral program. There may be great benefit in having a major overlap in the coursework, seminar work, research practicum, and any work in the fields of education, psychology, and foreign languages in mathematics and statistics education programs. I would even advocate for a consideration of combined prgrams in Mathematics and Statistics Education at the doctoral level. In many universities in my country, from the practical point of view. Below I briefly discuss Core components of a statistics education doctoral program, and factors that are necessary for institutions to support quality doctoral work in statistics education.

An important topic presented in introductory statistics courses is the estimation of population parameters using samples. Students learn that when estimating population variances using sample data, we always get an underestimate of the population variance if we divide by n rather than n-1. One implication of this correction is that the degree of bias gets smaller as the sample gets larger and larger. This paper explains the nature of bias and correction in the estimated variance and discusses the properties of a good estimator (unbiasedness, consistency, efficiency, and sufficiency). A BASIC computer program that is based on Monte Carlo methods is introduced, which can be used to teach students the concept of bias in estimating variance. The program is included in this paper. This type of treatment is needed because surprisingly few students or researchers understand this bias and why a correction for bias is needed. One table and three graphs summarize the analyses. A 10-item list of references is included, and two appendices present the computer program and five examples of its use. (Author/SLD)

We highlight one interpretation of Pearson's r (largely unknown to behavioral scientists), inspired by the genetic measurement of inbreeding. The coefficient of inbreeding, defined as the probability that two paired alleles originate from common descent, equals the correlation between the uniting gametes. We specify the statistical conditions under which r can be interpreted as probability of identity by descent and explore the possibility of generalizing that meaning of correlation beyond the inbreeding context. Extensions to the framework of agreement between judges and to that of sequential dependencies are considered. Viewing correlation as probability is heuristically promising. We examine the implications of this approach in the case of three types of bivariate distributions and discuss potential insights and risks.

The theoretical basis of this paper is the modeling of students' knowledge about a specific subject as a qualitative and systemic construct. Following therefrom, a discussion about the role of multivariate analysis for studying the structure of this knowledge and for building explanatory models relating its structure to task, cognitive and instructional variables. Correspondence analysis in an empirical study referring to statistical association is used as an example.