This paper gives concise descriptions of a robust location statistic, the remedian of P. Rousseeuw and G. Bassett (1990) and a robust measure of dispersion, the "Sn" of P. Rousseeuw and C. Croux (1993). The use of Sn in least absolute errors regression (L1) is discussed, and BASIC programs for both statistics are provided. The remedian…

Problems of estimation and interpretation are discussed that arise when a statistical package, which does not incorporate a dedicated weighted least-squares (WLS) routine, performs WLS regression by misapplication of a case-weighting strategy. A strategy is offered for adjusting WLS regression estimates after a case weighting strategy has been…

A reparameterization of the general Euclidean model for the external analysis of preference data and a simple least squares method for fitting the model to metric single stimulus data are discussed. The reformulated model is less general than is the earlier formulation by J. D. Carroll (1972). (SLD)

Langmuir's model is studied for the situation where epsilon is independently and identically normally distributed. The "Y/x" versus "Y" plot had a 90% mid-range that did not contain the true curve in a vast portion of the range of "x". The "1/Y" versus "1/chi" plot had undefined expected values,…

Simultaneous estimation of many parameters can often be improved, sometimes dramatically so, if it is reasonable to consider one or more subsets of parameters as exchangeable members of corresponding populations. While each observation may provide limited information about the parameters it is modeled directly in terms of, it also contributes…

The purpose of this study was to examine the effect that large within-examinee item difficulty variability had on estimates of the proportion of consistent classification of examinees into mastery categories over two test administrations. The classification consistency estimate was based on a single test administration from an estimation procedure…

The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

Estimated Type I error rates and power are reported for six tests of variance. Normal and non-normal distributions of a two-group design were investigated. Tests developed by M. B. Brown and A. B. Forsythe and by R. G. O'Brien were considered most useful. Implications are discussed. (SLD)

A maximum test in which the test statistic is the more extreme of the Brown-Forsythe and in which O'Brien's test statistics are developed, with estimated Type I error rates and power for all three tests. For study conditions, Type I error rates for the maximum test are near the nominal level. (SLD)

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977). It is shown that the minimization problem…

Estimation theory in educational statistics and the application of hierarchical linear models are reviewed. Observations within each group vary as a function of microparameters. Microparameters vary across the population of groups as a function of macroparameters. Bayes and empirical Bayes viewpoints review examples with two levels of hierarchy.…

The accuracy of three analytical formulas for shrinkage estimation and four empirical techniques were investigated in a Monte Carlo study of the coefficient of cross-validity in multiple regression. Substantial statistical bias was evident for all techniques except the formula of M. W. Brown (1975) and multicross-validation. (SLD)

Misspecification of mean and covariance structures for metric endogenous variables is considered. Maximum likelihood estimation of model parameters and the asymptotic covariance matrix of the estimates are discussed. A Haussman test for misspecification is developed, which is sensitive to misspecification not detected by the test statistics…

The equivalence between non-parametric marginal logistic models (NMLMs) and a class of discrete marginal logistic models is examined. Parametric models offer some of the advantages of the NMLMs approach, but there are more restrictions on the manifest probabilities. (SLD)