A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The probability integrals over the partitioned cubes forms a k-dimensional contingency table with ordered categories. A loglinear model with main effects plus two-way interactions provides an approximation for…

Fleiss' popular multirater kappa is known to be influenced by prevalence and bias, which can lead to the paradox of high agreement but low kappa. It also assumes that raters are restricted in how they can distribute cases across categories, which is not a typical feature of many agreement studies. In this article, a free-marginal, multirater…

The frequencies of "m" independent "p-way" contingency tables are analyzed by a model that assumes that the ordinal category data in each of "m" groups are generated from a latent continuous multivariate normal distribution. The model permits analysis of several groups of individuals simultaneously. (TJH)

A class of multivariate exponential distributions is defined as the distributions of occupancy times in upwards skip-free Markov processes in continuous time. These distributions are infinitely divisible, and the multivariate gamma class defined by convolutions and fractions is a substantial generalization of the class defined by N. L. Johnson and…

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

Examination of the stochastics of moderated multiple regression (MMR) reveals that MMR is an appropriate technique when predictors are fixed variables and the distribution of errors is normal but is not appropriate when predictors are random variables and the joint distribution of criterion and predictor variables is multivariate normal. (SLD)

Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality distribution assumption, which may not be realistic for practical data. It is…

Mardia's measure of multivariate kurtosis has been implemented in many statistical packages commonly used by social scientists. It provides important information on whether a commonly used multivariate procedure is appropriate for inference. Many statistical packages also have options for missing data. However, there is no procedure for applying…

Provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and details Monte Carlo simulation results on Type I and Type II error control. Demonstrates through the simulation that robustness and nonrobustness of structure analysis techniques vary as a…

A Monte Carlo study was used to examine the Type I error rates of five multivariate tests for the single-factor repeated measures model. The performance of Hotelling's T-squared and four nonparametric tests, including a chi-square and an "F" test version of a rank-transform procedure, was investigated for different distributions, sample…

New multivariate permutation tests are proposed that may be effectively substituted for Hotelling's T-Square test in situations commonly arising in educational research. The new tests: (1) are distribution-free; (2) provide tests of directional as well as non-directional hypotheses; (3) may be tailored for sensitivity to specific treatment…

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…