A definition of essential independence is proposed for sequences of polytomous items. For items which satisfy the assumption that the expected amount of credit awarded increases with examinee ability, a theory of essential unidimensionality is developed that closely parallels that of W. F. Stout (1987, 1990). Essentially unidimensional item…

The assessment of dimensionality of data is important to item response theory (IRT) modelling and other multidimensional data analysis techniques. The fact that the parameters from the factor analysis formulation for dichotomous data can be expressed in terms of the parameters in the multidimensional IRT model suggests that the assessment of the…

An investigation of the effects of randomly missing data in two-predictor regression analyses is described. The differences in the effectiveness of five common treatments of missing data on estimates of R-squared values and each of the two standardized regression weights is also investigated. Bootstrap sample sizes of 50, 100, and 200 were drawn…

The extent to which properties of the ability scale and the form of the latent trait distribution influence the estimated item parameters of item response theory (IRT) was investigated using real and simulated data. Simulated data included 5,000 ability values randomly drawn from the standard normal distribution. Real data included the results for…

A rating scale can be expressed as a chain of dichotomous items. The relationship between the dichotomies depends on the manner in which the rating scale is presented to the test taker. Three models for ordered scales are discussed. In the success model, which represents growth, the lowest or easiest category is presented first. If the test taker…

During the past 15 years, considerable attention has been given to a conspicuous longitudinal change in grading patterns in higher education. Commonly referred to as "grade inflation," the phenomenon has been perceived by some as seriously weakening the meaning of grades but by others as reflecting a positive tendency for students to…

Draws attention to an existing methodology for handling decision-making in a typical planning situation of interrelated alternatives and data deficiency, and describes several important extensions that have recently been made to it. (Oriel Press Limited, 32 Ridley Place, Newcastle upon Tyne, NE1 8LH, Great Britain, $7.00 yearly.) (Author)

Illustrated is the power of multidimensional scaling in reducing a complex set of proximity measures to a simple geometric picture that shows the relationship among data objects. Methods are discussed for determining the number of dimensions needed to represent a set. (Author/DEP)

Suggestions are provided for activities involving the construction of mathematical models to solve "real-life" problems. (SD)

Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)

Presents a method of solving decision problems in conditions of incomplete knowledge of the probabilities of the states of nature. It uses all available information in order to delimit the region of ignorance as closely as possible. (Author)