In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.

The problem of objectively comparing two independently determined partitions of N objects or variables is discussed. A similarity measure based on the simple matching coefficient is defined and related to previously suggested measures. The problem of merging groups in one partition to maximize this similarity measure is discussed and formulated as a mathematical programming problem; such an approach is useful for determining to what extent the groups in one partition merely represent a finer subdivision of the groups in the other partition. By exploiting the structure of the similarity measure, an efficient algorithm is developed to determine which groups (if any) should be merged to maximize partition similarity.

A model of the utility of gambling is presented in a modified von Neumann-Morgenstern format. Axioms imply a utility function that preserves preferences between sure things and between gambles. The addition of a utility of gambling term to the expected utility of a gamble preserves preference comparisons between gambles and sure things. Aspects of the utility of gambling are noted, and comparisons are made to standard concepts of risk attitudes.

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of K dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0-1 response pattern vectors to form the subset of the total possible 2k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.

The proposed method handles the classical method of reciprocal averages (MRA) in a piecewise (item-by-item) mode, whereby one can deal with smaller matrices and attain faster convergence to a solution than the MRA. A new concept “the principle of constant proportionality” is introduced to provide an interesting interpretation for scaling multiple-choice data á la Guttman. A small example is presented for discussion of the technique.

A major research direction for ability measurement has been to identify the information-processes that are involved in solving test items through mathematical modeling of item difficulty. However, this research has had limited impact on ability measurement, since person parameters are not included in the process models. The current paper presents some multicomponent latent trait models for reproducing test performance from both item and person parameters on processing components. Components are identified from item subtasks, in which performance is a logistic function (i.e., Rasch model) of person and item parameters, and then are combined according to a mathematical model of processing on the composite item.

The paper obtains a maximum likelihood criterion test for multisample sphericity. The test contains Mauchly’s sphericity test as a special case.