A family of integrals over infinite intervals appears frequently in the statistical literature on non-parametric regression. This note presents two simple transform methods, based on beta function and Parseval identity, to explicitly evaluate these integrals. These methods will benefit researchers and practitioners working in non-parametric…

This article considers the problem of educational placement. Several discriminant techniques are applied to a data set from a survey project of science ability. A profile vector for each student consists of five science-educational indicators. The students are intended to be placed into three reference groups: advanced, regular, and remedial.…

Treats the problem of testing an ordered hypothesis based on the ranks of the data. Statistical procedures for the randomized block design with more than one observation per cell are derived. Multiple comparisions and estimation procedures are included. (Author/RC)

This paper illustrates the relevance and utility of non-parametric statistical tests, such as the Kolmogorov-Smirnov two sample test, for analysis of developmental phenomena. This statistic tests the null hypothesis that two samples have been drawn from the same population by comparing their whole distributions, rather than specific parameters and…

The power of the t, expected normal scores, Mann-Whitney U, Tukey, a modified Mann-Whitney U, and an adaptive procedure were investigated when sampling from population models empirically developed from test score distributions. The models used were selected members of the beta family. This investigation was unique in that not only did the means of…

Multivariate models are demonstrated to analyze repeated measures profile and growth curve data when univariate or multivariate mixed model assumptions are not tenable. Standard mixed model tests are recovered from certain multivariate hypotheses. The procedures are illustrated using numerical examples. (Author/RC)

The basic assumption of Cooper's nonparametric test for trend (EJ 125 069) is questioned. It is contended that the proper assumption alters the distribution of the statistic and reduces its usefulness. (JKS)

The normal scores test for scale (variance) is presented as an alternative for evaluating the equality of dispersion for two independent populations. Test development is indicated as well as examples illustrating large and small sample situations. Reference is made to comparisons with the F, Mood, and Siegel-Tukey tests. (Author/JKS)

Ordinal measurement is the rank ordering of individuals in a population. For ordinal measurement, the concept of an individual propensity distribution is his or her true score. Estimation of, as well as other aspects of the distribution, are discussed. (Author/JKS)

A monotone invariant method of hierarchical clustering based on the Mann-Whitney U-statistic is presented. The effectiveness of the complete-link, single-link, and U-statistic methods are evaluated. The U-statistic method is found to be consistently more effective in recovering the original tree structures than the alternative methods. (Author/JKS)

Use of the coefficient of concordance is explained to be a simple technique for estimating reliability in small scale situation and is advocated as a valuable method for physical educators. (GW)

A description of a Mokken test program to test the robustness of nonparametric Stochastic scales is presented. For each sample and the whole population, different scale statistics (both on scale and on item level) are computed recursively. A statistic T is presented for testing the robustness of the scales in the samples. (Author)

Three exact probability tests, counterparts of t tests for single sample, independent samples, and dependent samples, are described for data obtained from ratings on "m" scales by a single rater or on a single scale by "n" raters. (LMO)

New tests for comparing the strength of association between a variable and each of two potential predictor variables are proposed and compared to an existing test in a simulation study. Recommendations for use are made. (Author/JKS)

This paper advocates the use of nonparametric statistics. First, the consequence of using parametric inferential techniques under nonnormality is described. Second, the advantages of using nonparametric techniques are presented. The third purpose is to demonstrate empirically how infrequently nonparametric statistics appear in studies, even those…