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A large number of correlational models for cross-tabular analysis are available for utilization by social scientists for data description. Criteria for selection (such as levels of measurement and proportional reduction in error) do not lead to conclusive model choice. Moreover, such criteria may be irrelevant. More pertinent criteria are operational characteristics of a model. Operational criteria examined in this research include sensitivity to changes in population convariance; and insensitivity to sample size, table dimensions, and variable distributional characteristics. A complete facit or factorial design of 384 elements is generated to include cross-slassification conditions of typical social science utilization. A Monte Carlo computer program is then utilized to generate a cross-tabulation table as specified by the parameters of each of its design elements. Twenty-five correlational models are then applied to each of the tables. Because the tables are generated by design and their characteristics known, a priori, changes in the value of a given correlation coefficient can be explained. Analysis over all the facits lends to a description of the operational characteristics of each of the models. Finally, a factorial analysis leads to a reduction of the 25 models into four types of correlational models. (Author)

When random assignment has been accomplished and an analysis of covariance (ANCOVA) is being used to correct for initial differences among treatment groups, use of unreliable covariables not only decreases the power of ANCOVA, but also causes ANCOVA to test biased treatment effects. Several correction procedures have been suggested for the single fallible covariable design. The purpose of this paper is to extend the earlier work by describing two alternative correction procedures for the multiple fallible covariable design, demonstrate their properties in terms of population parameters, and investigate empirically the sampling distributions of their test statistics, i.e., probability of Type I error and power. (Author)

In this paper problems caused by the existence of errors of measurement are identified for factor analysis, regression analysis, ANOVA, and ANCOVA. At least one detrimental effect is shown to exist for each type of analysis. When a researcher's interest is with infallible variables, he runs the risk of biased results from all of the procedures except ANOVA. The estimates of parameters in all four procedures suffer from inflated error variance. Some partial solutions are indicated, but clearly more work is needed on several of the problems. Most statistical procedures have been developed for models where variables are assumed to be free from errors of measurement. Since almost all educational research involves use of fallible variables, it is important that the effects of errors of measurement for the various models be understood and that the understanding be reflected in current research practice. (Author/GS)

This paper relates educational and psychological statistics to certain "Research Statistical Tools" (RSTs) necessary to accomplish and understand general research in the behavioral sciences. Emphasis is placed on acquiring an effective understanding of the RSTs and to this end they are are ordered to a continuum scale in terms of individual precision, power, and robustness. The Precision-Power-Gradient theory is suggested as a means of structuring an introductory graduate course in statistics. Twelve RSTs are considered, ranging from normative comparisons (at the simplest level), through parametric/non-parametric statistics, analysis of variance and covariance, correlations, factor analysis, to canonical correlation analysis, and, briefly, other advanced techniques. Equally important is a working knowledge of the computer, which enables the RSTs to be used with greater facility and accuracy. Computer orientation should include a basic knowledge of FORTRAN programming, nature and availability of computer-based statistical libraries, the ability to utilize such libraries, with a general understanding of computer output. (Author/AE)

In most behavioral science research very little attention is ever given to the probability of committing a Type II error, i.e., the probability of failing to reject a false null hypothesis. Recent publications by Cohen have led to insight on this topic for the fixed-effects analysis of variance and covariance. This paper provides social scientists with some insight in dealing with Type II error, and optimum sample size and number of levels in the random-effects analysis of variance. (Author)

This experiment was conducted to determine whether preservice teachers taking a combination of Minicourses and student teaching (the experimental group) would develop greater teaching skills than teachers taking only student teaching (the control group). Pre- and post-video tapes of their teaching performances were scored and compared using analysis of covariance. It was found that, compared to the control group, experimental-group teachers repeated pupil answers less often, answered their own questions less often, and used more higher-cognitive questions in discussions. In tutoring sessions, they used more diagnostic questions, verbal praise, demonstration techniques, and evaluation. The overall significance of this experiment is that it serves as a demonstration that microteaching as a specialized technique, and Minicourses as an adaptation of it, can be used effectively, within certain limits, in training preservice teachers. (Author/JA)

Four computer programs using the general purpose multiple linear regression program have been developed. Setwise regression analysis is a stepwise procedure for sets of variables; there will be as many steps as there are sets. Covarmlt allows a solution to the analysis of covariance design with multiple covariates. A third program has three solutions to the two-way disproportionate analysis of variance: (a) the method of fitting constants, (b) the hierarchical model and (c) the unadjusted main effects solution. The fourth program yields three solutions to the two-way analysis of covariance, with or without proportionality, and with multiple covariates. The three solutions are similar to those described for a two-way analysis of variance with disproportionate cell frequencies. (Author)

This paper discusses the use of contrast coefficients in multiple linear regression models, and shows how they can provide for a logical method of analysis in both the analysis of variance and the analysis of covariance. (CK)

In many circumstances it is appropriate to use the school as the unit of analysis. The variables measured on students must be aggregated to form a mean for each school. However, the means derived from the students sampled in a school will tend to fluctuate around the true mean for the school in a way determined by the within-school correlations among student variables rather than by the between-school correlations. A model is presented which circumvents this problem by obtaining replicate measures for each variable. The model permits estimation of the true between-schools covariance matrix and measurement error variances. An example employing real data is presented. (Author)

This paper concerns situations in which a p x p covariance matrix is a function of an unknown q x 1 parameter vector y-sub-o. Notation is defined in the second section, and some algebraic results used in subsequent sections are given. Section 3 deals with asymptotic properties of generalized least squares (G.L.S.) estimators of y-sub-o. Section 4 concerns methods for obtaining estimates of parameters in certain linear covariance structures. (Author/KM)

Use of the usual bivariate correction for attenuation with more than two variables presents two statistical problems. This pairwise method may produce a covariance matrix which is not at least positive semi-definite, and the bivariate procedure does not consider the possible influences of correlated errors among the variables. The method described here, a generalized correction for attentuation, is a multivariate method which accommodates both the negative variance component problem and the collinearity problem. (Author/KM)

An exact multivariate analysis for troublesome repeated measures designs has been described by Bock and programmed by Finn. The method is applied to digit span from an actual experiment involving first-grade pupils in an inner-city school and a suburban school in Canada. The repeated measures are first transformed by an orthogonal matrix derived from the design on the measures; the resulting new variables are treated as dependent variables in the multivariate analysis of variance employing the design on the subjects. In this example, Bock's method yielded more significant results compared to conventional approximate analyses. Covariates may be used. (Author)

Joreskog's general method for analysis of covariance structures was developed for estimating a model involving structures of a very general form on means, variances, and covariances of multivariate observations. This method achieves a great deal of generality and flexibility, in that it is capable of handling most standard statistical models as well as many nonstandard and complicated ones. This paper describes a computer program for the method. When the variance-covariance matrix of the observed variables is unconstrained, the method may be used to estimate location parameters and to test linear hypotheses about them. For example, the program may be used to handle such standard problems as multivariate regression, ANOVA, and MANOVA. A unique feature of the method is that it can also be used when the variance-covariance matrix is constrained to be of a certain form. Various other models involving correlated errors or errors of measurement can also be handled. An illustration of how input data is set up, and what the printout looks like for two small sets of data, are included. (Author/CK)

Guttman's "rank-reduction" theorem is employed to demonstrate how most of the algebra and computational work for standard correlational and analysis of variance methods can be examined within a single matrix system. Analyses of both correlational and experimental data are illustrated with an easy-to-use computer program. This application and the corresponding discussion emphasize distinctions and qualifications needed for appropriate interpretations of both types of data. Since this theorem was initially presented within the framework of factor analysis, it is intended that this paper will contribute to a better understanding of relationships among factor analytic, general correlational, and experimental design methods. (Author/CK)

Methods exist for testing the homogeneity of group regression for the case in which there is only one predictor. Studies which have investigated aptitude-treatment interactions have adopted the homogeneity of regressions test as standard methodology for assessing the difference in regression slopes across treatments. Additional statistical methodology is suggested by which the homogeneity of group regressions can be tested when two or more predictors are present. Before covariate analysis can be used, the homogeneity of group regression must be tested. To test the hypothesis that the slopes are equal for the homogeneity of group regressions for a single covariate, one can follow the standard linear prediction model. For the case in which there are multiple covariates, a test for homogeneity of regressions provides an overall estimate of the difference between treatments, taking into account the effect of the multiple covariates upon each treatment, simultaneously. Partial hypotheses for a multiple covariate model are presented in order to isolate the cause of overall interaction when treatment slopes with multiple covariates are not equal. Data from two aptitude-treatment investigations are used to illustrate the equations. (CK)

The relative power of three possible experimental designs under the condition that data is to be analyzed by nonparametric techniques; the comparison of the power of each nonparametric technique to its parametric analogue; and the comparison of relative powers using nonparametric and parametric techniques are discussed. The three nonparametric techniques concerned are the Kruskal-Wallis test on data where experimental units have been randomly assigned to levels of the independent variable, Friedman's rank analysis of variance (ANOVA) on data in a randomized blocks design, and a nonparametric analysis of covariance (ANCOVA). The parametric counterparts are respectively; one way analysis of variance (ANOVA), two-way ANOVA, and parametric ANCOVA. Since the nonparametric tests are based on large sample approximations, the goodness of fit for small samples is also of concern. Statements of asymptotic relative efficiency and imprecision are reviewed as suggestive of small sample powers of the designs and statistics investigated. Results of a Monte Carlo investigation are provided to further illustrate small sample power and to provide data on goodness of fit. (Author/CK)

Change Group Analysis is suggested as a technique for examining the correlates of the differential effects of a compensatory education program within the group of enrolled pupils. It is based on using pretest-posttest relative changes for forming criterion groups and then using multiple disciminant analysis to uncover patterns of predictor variables among relevant demographic, cognitive, and affective measures. The technique's potential for avoiding reliance on the artifactual properties of both regression phenomena and gain scores is discussed. It is suggested that the technique would be useful when post hoc matching or covariance analysis might produce misleading or even erroneous conclusions about the overall effectiveness of an intervention program. A confirmatory empirical study is proposed. (Author)

Two theorems concerning F in analysis of covariance with two groups (experimental and control) and one covariable (pretest score) are presented. The first shows explicitly that F is a direct function of the ratio of the variance about the regression line for the total sample to the variance about the within-group regression line. The second demonstrates the relationship between F and the corresponding F, which would result from analysis of variance using the appropriate pretest-posttest gain scores in the same situation. (Author)

The purpose of the present study was to investigate empirically the effects of violations of the assumption of homogeneity of within-group regression slopes on levels of significance in the F test of fixed-effects ANCOVA (analysis of covariance). The study used a Monte Carlo computer simulation procedure to generate data under the following conditions: (1) the covariate was a random variable; (2) the number of treatment groups was three; (3) treatment group n's were small to medium and were unequal as well as equal; (4) error variances were equal as well as unequal; and (5) covariate means were both equal and unequal. For each simulation, the proportion of F values exceeding certain critical values was compared to the nominal alpha corresponding to the critical values. (Author)

Focus of this paper is on the logic of the model rather than the estimation of parameters or testing the fit of the model to data. (Authors/MB)

Paper develops a model which expresses pair comparisons as a function of (a) affective values which form a perfect simplex, (b) systematic (constant over replications) deviations from the simplex-structured affective values, and (c) errors of measurement for the pair comparisons. (Author)

Paper reviews the test for regression lines and provides equations for expanding this test to regression planes. (Author)

This paper discusses the Lens Model' approach to the analysis of subject performance in multiple-cue judgment tasks embedded in probabilistic environments. (Author/RK)

The conventional analysis of variance applied to designs in which each subject is measured repeatedly requires stringent assumptions regarding the variance-covariance structure of the data. This paper considers alternatives when heterogeneity of covariance exists, including nonparametric tests, randomization and matching procedures, Box and Greenhouse-Geisser corrections, and multivariate analysis. (ST)

This paper is devoted to the study of a certain statistic, u, defined on samples from a bivariate population with two variances and correlation p. (Author)

A principal purpose of this paper is to report systematic data in support of an hypothesized association between noise stress and subsequent behavior. Penetration of traffic sounds into the home was considered as it impaired the child's ability to learn verbal skills. (Author/RK)

It is the intention of this paper to review the purpose, underlying assumptions, and calculation procedures and to arrive at a means of handling analysis of covariance when the classical assumptions are not met. (Author)

The present authors argued that the covariance analysis is completely valid even if there is a true main effect for pretesting and a second point of the paper involved a recommendation for data analysis if the interaction from ANOVA was significant. (Editor/RK)