Nonparametric and robust statistics (those using trimmed means and Winsorized variances) were compared for their ability to detect treatment effects in the two-sample case. The use of two specialized tests, designed to be sensitive to treatment effects when data distributions are skewed to the right, is not supported by the analyses. (SLD)

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)

Empirical data analysis using the Mokken models of monotone homogeneity and double monotonicity is discussed. Results from the Mokken approach with 3 data sets (for a total of 425 elementary school students) pertaining to transitive interference items are compared to Rasch analysis. (SLD)

Person-fit statistics test whether the likelihood of a respondent's complete vector of item scores on a test is low given the hypothesized item response theory model. This binary information may be insufficient for diagnosing the cause of a misfitting item-score vector. The authors propose a comprehensive methodology for person-fit analysis in the…

In this article, an overview of nonparametric item response theory methods for determining the dimensionality of item response data is provided. Four methods were considered: MSP, DETECT, HCA/CCPROX, and DIMTEST. First, the methods were compared theoretically. Second, a simulation study was done to compare the effectiveness of MSP, DETECT, and…

It is believed by some that most tests are multidimensional, meaning that they measure more than one underlying construct. The primary objective of this study is to illustrate how variations in the secondary ability distribution affect the statistical detection of dimensionality and to demonstrate the difference between substantive and statistical…

A smoothed version of standardization, which merges kernel smoothing with the traditional standardization differential item functioning (DIF) approach, was used to examine DIF for student-produced response (SPR) items on the Scholastic Assessment Test (SAT) I mathematics test at both the item and testlet levels. This nonparametric technique avoids…

A class of closely related hierarchical grouping methods are discussed and a procedure which implements them in an integrated fashion is presented. These methods avoid some theoretical anomalies inherent in clustering and provide a framework for viewing partitioning and nonpartitioning grouping. Significant relationships between these methods and…

The debate still continues regarding Stevens' paper on the relationship between scales of measurement and appropriate statistics. The central issue is the nature of the relationship between ordinal and interval scales and parametric and nonparametric statistics. This article presents some of arguments regarding these issues. (Author/DEP)

When examining a repeated measures design with independent groups for a significant group by trial interaction, classical analysis of variance or multivariate procedures can be used if the assumptions underlying the tests are met. Neither procedure may be justified for designs with small sample sizes and dichotomous dependent variables. An omnibus…

The present study examined three different methods of data collection in which subjects judged proximity between object pairs. One method required subjects to partition objects into homogeneous subsets; the second entailed rating object pairs on a similarity-dissimilarity continuum; and the third involved comparing inter-object proximities to a…

The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950's, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers. ( Author/JKS)

Given a set of dichotomously scored items, ordering theory attempts to identify a hierarchy among those items. A graphic representation is presented for an empirically obtained hierarchy and a testing procedure to evaluate hypothesized hierarchical relationships. (Author/JKS)

Using computer simulation, parametric analysis of covariance (ANCOVA) was compared to ANCOVA with data transformed using ranks, in terms of proportion of Type I errors and statistical power. Results indicated that parametric ANCOVA was robust to violations of either normality or homoscedasticity, but practiced significant power differences favored…

The use of Bayesian theory to connect ordinal data and ordered scale points with the theory of order statistics is presented. Exact and approximate multivariate and marginal densities for the scale points are derived. (Author/JKS)