One of the innovative approaches in the use of hierarchical linear models (HLM) is to use HLM for Slopes as Outcomes models. This implies that the researcher considers that the regression slopes vary from cluster to cluster randomly as well as systematically with certain covariates at the cluster level. Among the covariates, group indicator…

Although analysis of covariance (ANCOVA) is used fairly infrequently in published research, the method is used much more frequently in dissertations and in evaluation research. This paper reviews the assumptions that must be met for ANCOVA to yield useful results, and argues that ANCOVA will yield distorted and inaccurate results when these…

The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

Recent empirical studies of actual research practice demonstrate that general linear models, such as regression, have become increasingly popular. The present paper explores issues related to the interpretation of regression results, with illustrations drawn from studies in the counseling psychology literature. The primary focus of this paper is…

When normality does not hold, nonparametric tests represent an important data-analytic alternative to parametric tests. However, the use of nonparametric tests in educational research has been limited by the absence of easily performed tests for complex experimental designs and analyses, such as factorial designs and multiple regression analyses,…

The analysis of covariance as a procedure for statistical correction of the effects for an extraneous variable, called a "covariate," is presented. An heuristic data set is used to make the discussion of the calculation of ANCOVA partitions easier to follow. A discussion of homogeneity of regression as an essential condition to be met…

Previous research has demonstrated particular inadequacies in conventional methods used to identify outlier cases in bivariate regression models. Only through a combination of methods can one detect all of the deviant points potentially overinfluencing a regression model's parameters. This paper investigates whether a range of data points might…

The purpose of this paper is to illustrate the use of tobit analysis and tobit decomposition in educational research. Tobit estimates of growth rate in the presence of a ceiling effect were compared with ordinary least squares (OLS) and weighted least squares (WLS) estimates. The tobit estimates had the smallest standard error, the smallest bias,…

The usefulness of path analysis as a means of better understanding various linear models is demonstrated. First, two linear models are presented in matrix form using linear structural relations (LISREL) notation. The two models, regression and factor analysis, are shown to be identical although the research question and data matrix to which these…

While it is imperative that attempts be made to assess the predictive accuracy of any prediction model, traditional measures of predictive accuracy have been criticized as suffering from "the base rate problem." The base rate refers to the relative frequency of occurrence of the event being studied in the population of interest, and the…

Methods for assessing collapsibility in regression problems are described, including possible extensions to the class of generalized linear models. These procedures, with terminology borrowed from the contingency table field, can be used in experimental settings or nonexperimental settings where two models viewed as alternative explanations are…

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

This paper explains how commonality analysis (CA) can be conducted using a specific Statistical Analysis System (SAS) procedure and some simple computations. CA is used in educational and social science research to partition the variance of a dependent variable into its constituent predicted parts. CA determines the proportion of explained…

Monte Carlo techniques were used to examine regression approaches to external unfolding. The present analysis examined the technique to determine if various characteristics of the points are recovered (such as ideal points). Generally, monotonic analyses resulted in good recovery. (TJH)

Various realizations have led to less frequent use of the "OVA" methods (analysis of variance--ANOVA--among others) and to more frequent use of general linear model approaches such as regression. However, too few researchers understand all the various coefficients produced in regression. This paper explains these coefficients and their…