Discusses relationships between a mathematical measurement model and its real-world applications. Makes a distinction between large-scale data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Also evaluates nonparametric methods for estimating item response functions and…

It is unrealistic to suppose that standard item response theory (IRT) models will be appropriate for all the new and currently considered computer-based tests. In addition to developing new models, we also need to give attention to the possibility of constructing and analyzing new tests without the aid of strong models. Computerized adaptive…

It is well known that the two-sample Student t test fails to maintain its significance level when the variances of treatment groups are unequal, and, at the same time, sample sizes are unequal. However, introductory textbooks in psychology and education often maintain that the test is robust to variance heterogeneity when sample sizes are equal.…

Recently, nonparametric methods have been proposed that provide a dimensionally based description of test structure for tests with dichotomous items. Because such methods are based on different notions of dimensionality than are assumed when using a psychometric model, it remains unclear whether these procedures might lead to a different…

This paper investigates urban-rural and size effects on public upper secondary school efficiency in Northern Thailand. Efficiency is assessed by a nonparametric technique, namely data envelopment analysis. Urban-rural and size effects are examined through a Mann-Whitney nonparametric statistical test and by Tobit regression analysis, respectively.…

Inspection of differential item functioning (DIF) in translated test items can be informed by graphical comparisons of item response functions (IRFs) across translated forms. Due to the many forms of DIF that can emerge in such analyses, it is important to develop statistical tests that can confirm various characteristics of DIF when present.…

Statistics such as chi-square, phi, and Cramer's V are related to the R squared statistic of regression analysis. It is shown that the proportion of variance accounted for can be computed from many contingency table situations. (JKS)

A randomization model appropriate for evaluating priority effects in free recall (i.e., whether "new" items are recalled prior to "old" items) is discussed and related to well-known nonparametric significance tests. Since the bases for the measures that have been suggested in the psychological literature may be interpreted…

The Cochran Q and the Minimum X sub one squared statistics are two ways to test a hypothesis of equivalent correlated proportions. This study investigated the small sample properties of Q and X sub one squared by Monte Carlo methods. The observed distributions were compared for their rates of covergence to the limiting theoretical X sub one…

A distribution-free test for trend in one-way experimental designs is described. Critical values are derived, and a schematic diagram is given so that a computer package can be implemented. (Author/JKS)

The Cartesian theory of dimensionality (defined in terms of geometric distances between points in the test space) and Leibnitzian theory (defined in terms of order-generative connected, transitive, and asymmetric relations) are contrasted in terms of the difference between a factor analysis and an order analysis of the same data. (Author/CTM)

Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

The validity of five methods of estimating the reliability of criterion-referenced tests was evaluated across nine conditions of variability among item means. The results were analyzed by analysis of variance, the Newman-Keuls test, and a nonparametric procedure. There was a tendency for all of the methods to be conservative. (Author/JKS)

Three dimensional contingency tables in which one variable is considered to be a factor and the other two variables have a natural relationship (such as left and right eye vision) are analyzed. Models involving symmetry and proportional symmetry between the related variables are also presented. (Author/JKS)

Many methodologists are aware that parametric tests associated with the analysis of variance and the analysis of covariance can be computed using regression procedures. It is shown that multiple linear regression can also be employed to compute the Kruskal-Wallis nonparametric analysis of variance. (Author)