The authors argue that a parameterization in terms of cell means is a useful conceptual device for resolving problems inherent in the nonorthogonal analysis of variance. They demonstrate their argument by considering two widely-used methods for testing main effects. (Author/BW)

The basic notion of variability is generalized from a univariate context to a multivariate context using two matrix functions, a determinant, and a trace, yielding a number of alternative multivariate indices of shared variation. Some problems in the interpretation of tests of multivariate hypotheses are reviewed. (Author/BW)

The recommendation to use group means when there may be nonindependence among observational units is unduly restrictive. When random factors are properly identified and included in the analysis, the results are identical in balanced analysis of variance designs, irrespective of whether group means or individual observations are employed.…

The value of variance is emphasized, and the element of design, frequently not adequately understood, is clarified to underscore the importance of variance to the researcher. Two analytic methods, analysis of variance (ANOVA) and multiple regression, are discussed in terms of how each uses/applies variance. Advantages and major difficulties with…

When analysis of variance is used, statistically significant differences may or may not be of practical significance to educators. A large part of the problem is due to the fact that a "zero difference" null hypothesis can always be rejected statistically if the sample size is large enough. If, however, a method based on the noncentral F…

ANOVA designs are used for description and/or explanation of developmental phenomena. These consist of taking any two of age, cohort, or time of measurement as independent variables. Employment of ANOVA has led researchers down blind alleys. Regression techniques are more useful. (Author)

The present paper contributes to research methodology as practiced in the field by providing practitioners with a concise statement of the problems in analyzing unbalanced designs, and by clarifying the conditions under which the analysis alternatives are most appropriate. The purposes of the present paper are: (1) to examine the analysis…

With even the simplest bivariate regression, least-squares solutions are inappropriate unless one assumes a priori that reciprocal effects are absent, or at least implausible. While this discussion is limited to bivariate regression, the issues apply equally to multivariate regression, including stepwise regression. (Author/CTM)

The degree to which the chosen units of analysis are likely to produce spurious findings in staged combinations of multiple linear regression procedures are examined. The effects of grouping variables (e.g., classroom, school, and school district) on Procedures such as Coleman's semipartial regression and Mayeske's commonalities, in light of…

In order to examine the possible effects of violation of assumptions using parametric procedures, this study is an exploratory investigation into the use of parametric versus nonparametric procedures using a multiple case study design. The case study investigation guidelines outlined by Yin served as the methodology. The following univariate…

This guide presents many new experimental designs for data analysis and reviews certain standard procedures. It is hoped that the treatment of the material will stimulate new applications since the emphasis of the guide is on the problems encountered in running experiments rather than on an elaboration of mathematical models. Discussed are:…

Three common methodological problems in the analysis of observational data include: (1) failure to base degrees of freedom for the analysis on the appropriate sampling unit; (2) the validity of the design and data are inconsistent with the generalizations reached; (3) the statistic used to calculate coder reliability is often inappropriate and…

When two groups, initially dissimilar, undergo different treatments, can subsequent differences be partitioned in such a way that the difference between the two treatments is unbiased? This is the central problem of this paper, and it is confronted by the examination of two levels of information using a Follow Through Evaluation. The first…