Presents a summary report of the Algebra Working Group's discussion subgroup on secondary algebra at the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Three appendixes include the reactions to the keynote addresses in this issue. (MKR)

Biases and models usually offered by cognitive and social psychology and by philosophy to explain causal induction are evaluated with respect to focal sets (contextually determined sets of events over which covariation is computed). A probabilistic contrast model is proposed as underlying covariation computation in natural causal induction. (SLD)

Presents an allegory to illustrate the problem of testing an axiomatic system. A fictitious discussion begins by examining an axiomatic system underlying the intercom system of an association. The discussion continues to examine an unusual model of Euclidean geometry and a model of the noneuclidean geometry discovered by Lobachevsky. (MDH)

The one-sided problem of comparing treatments with a standard on the basis of data available in the context of a one-way analysis of variance is examined, and the methodology of S. Chakraborti and J. D. Gibbons (1991) is extended to the case of unequal sample sizes. (SLD)

The concept of item discrimination is generalized to the case in which more than one ability is required to determine the correct response to an item, using the conceptual framework of item response theory and the definition of multidimensional item difficulty previously developed by M. Reckase (1985). (SLD)

Two versions of a decision rule for determining the most appropriate number of clusters on the basis of a correlation matrix are presented, applied, and compared with three other decision rules. The new rule is efficient for determining the number of clusters on the surface level for multilevel data. (SLD)

Adaptive forms of weighted structural regression are developed and discussed. Bootstrapping studies indicate that the new methods have potential to recover known population regression weights and predict criterion score values routinely better than do ordinary least squares methods. The new methods are scale free and simple to compute. (SLD)

Discusses language comprehension and describes a technology for computer-aided text analysis called READWARE and software from the READWARE family called the Research Assistant that measures the relatedness of words or phrases by examining their letters. The theory of Letter Semantics is explained, and paradigms for text processing in information…

A method of comparing one-step M-estimates of location for heavy tailed distributions is proposed and investigated. Simulations indicate that the new procedure provides good control over Type I errors and has more power than do some other methods for dealing with heavy tailed distributions. (SLD)

E.J. Bedrick recently derived the asymptotic distribution of the modified sample biserial correlation estimator of F.M. Lord and studied its efficacy for bivariate normal populations. A more detailed examination of the properties of Lord's estimator is provided, and the small sample bias and variance are studied. (SLD)

Several methods for the analysis of three-way data (data classified three ways) are described and shown to be variants of principal components analysis of the two-way supermatrix in which each two-way slice is strung out into a column vector. Direct fitting and fitting derived data are considered. (SLD)

A stochastic multidimensional scaling procedure is presented for analysis of three-mode, three-way pick any/"J" data. The procedure fits both vector and ideal-point models and characterizes the effect of situations by a set of dimension weights. An application in the area of consumer psychology is discussed. (SLD)

Smallest exact confidence intervals for the ability parameter of the Rasch model are derived and compared to the traditional asymptotically valid intervals based on Fisher information. Tables of exact confidence intervals, termed Clopper-Pearson intervals, can be drawn up with a computer program developed by K. Klauer. (SLD)

A rational model of human categorization behavior is presented that assumes that categorization reflects the derivation of optimal estimates of the probability of unseen features of objects. A case is made that categorization behavior can be predicted from the structure of the environment. (SLD)

The routine epsilon approximate test in repeated measures designs when the condition of circularity is unfulfilled uses an erroneous formula in the case of two or more groups. Because this may lead to underestimation of the deviation from circularity when the subject number is small, a correction is proposed. (Author/SLD)