Computer programs for analysis of covariance use classical experimental, regression, or hierarchical methods of least squares. In a 3 X 3 factorial experiment with equal cell frequencies, three solutions yielded different sums of squares for main effects although correlation between variables was negligible and cell frequencies were equal.…

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. It is shown that previously proposed ad hoc tests are, in fact, likelihood ratio tests. (Author/JKS)

A process is described for multiple comparisons when covariates are involved in the analysis. The method can be accomplished with considerable ease whenever pairwise comparisons are involved. More complex contrasts require the use of full and restricted models of variance. (CTM)

Repeated measures designs often involve dichotomization of a continuous variable in order to be amenable to the analysis of variance nature of such designs. An alternative to that approach wherein the independent variable is kept continuous is presented. (JKS)

The multiple regression or general linear model (GLM) is a parameter estimation and hypothesis testing model which encompasses and approaches the more familiar fixed effects analysis of variance (ANOVA). The transition from ANOVA to GLM is accomplished, roughly, by coding treatment level or group membership to produce a set of predictor or…

Repeated measures designs often involve dichotomization of a continuous variable in order to be amenable to the analysis of variance nature of such designs. An alternative to that approach wherein the independent variable is kept continuous is presented. (JKS)

The problems inherent in analyzing data in which subjects are "nested" within hierarchical units (such as classrooms or schools), and thus are not independent of one another, are addressed through the use of Joreskog's LISREL model for analyzing covariance matrices. A solution to the problem is proposed and illustrated using data from…

It is shown how partial covariance, part and partial correlation, and regression weights can be estimated and tested for significance by means of a factor analytic model. Comparable partial covariance, correlations, and regression weights have identical significance tests. (Author)

The unbiased estimate of a "treatment effect" reached by analysis of covariance in a nonrandomized experiment would often require that a different covariate be used in each treatment. A sufficient but unlikely condition for an unbiased estimate is that the covariate for each treatment is (1) the complete covariate that predicts the outcome as…

A method for the estimation of covariance structure models under polynomial constraints (such as quadratic constraints) is presented. Estimation is on maximum likelihood principles, and the test statistics, parameter estimates, and standard errors are based on a statistical theory which takes the constraints into account. (Author/JKS)

A variety of algorithms for analyzing covariance structures are considered. Additionally, two methods of estimation, maximum likelihood, and weighted least squares are considered. Comparisons are made between these algorithms and factor analysis. (Author/JKS)

A study was conducted to assess the possible effects of headings on the search and recall performance of high- and low-knowledge subjects, 153 college students in an introductory psychology course. Seventy-five of the subjects read a 1,760-word adaptation of the passage on organizational processes in memory--the low-knowledge passage. The other 78…

Multiple linear regression is a versatile model for encompassing analysis of variance, analysis of covariance, and aptitude-by-treatment interaction designs. The questions of how to teach the coding of levels of a qualitative variable is addressed in this paper. (Author/LMO)

The utility of several longitudinal data analysis models for use with educational attainment are discussed and illustrated on a large data set. Assumptions of the models, choice of scale units, and data transformations, as well as real-life implications are emphasized. (Author/JKS)

The use of a path analysis model to obtain unique, substantively meaningful decomposition of variance among endogenous (independent) variables in the model is argued. This reasoning runs counter to more traditional path analytic work. An example is provided. (Author/JKS)