Statistical modeling of school effectiveness data was originally motivated by the dissatisfaction with the analysis of (school-leaving) examination results that took no account of the background of the students or regarded each school as an isolated unit of analysis. The application of multilevel analysis was generally regarded as a breakthrough,…

In educational effectiveness research, multilevel data analyses are often used because research units (most frequently, pupils or teachers) are studied that are nested in groups (schools and classes). This hierarchical data structure complicates designing the study because the structure has to be taken into account when approximating the accuracy…

A variety of problems associated with the interpretation of traditional canonical correlation are discussed. A response surface approach is developed which allows for investigation of changes in the coefficients while maintaining an optimum canonical correlation value. Also, a discrete or constrained canonical correlation method is presented. (JKS)

The shape of the response surface associated with a discriminant analysis provides insight into the value of the derived optimal discriminant variates. A procedure for the determination of "indifference regions," presented in this article, allows the assessment of the degree of flatness of the response surface for any analysis.…

The use of generalized discriminant analysis as a descriptive technique which can be employed outside of the traditional analysis of variance studies is discussed. Examples based on real data are provided. (Author/JKS)

The triangular decomposition method is suggested as a general technique for obtaining the various measures of an ill-conditioned matrix. The advantages of using triangular decomposition are computing nicety, cost, and parsimony. (Author/PN)

A procedure is presented to transform an n-dimensional scatter diagram into a two-dimensional scatter diagram while preserving proximity relationships between points. This procedure can help in the presentation and interpretation of multivariate results. (Author/SLD)

Canonical correlation analysis is illustrated and three common fallacious interpretation practices are described. Simply, canonical correlation is an example of the bivariate case. Like all parametric methods, it involves the creation of synthetic scores for each person. It presumes at least two predictor variables and at least two criterion…

A new approach to partialling components is used. Like conventional partialling, this approach orthogonalizes variables by partitioning the scores or observations. Unlike conventional partialling, it yields a common component and two unique components. (Author/GDC)

Examination of the stochastics of moderated multiple regression (MMR) reveals that MMR is an appropriate technique when predictors are fixed variables and the distribution of errors is normal but is not appropriate when predictors are random variables and the joint distribution of criterion and predictor variables is multivariate normal. (SLD)

Methods of regression commonality analysis are generalized for use in canonical correlation analysis. An actual data set (involving educators' attitudes toward death and age, locus of control, religion, and occupational role in working with terminally ill children) is employed to illustrate the extension. The method can be applied with respect to…

In the present study Monte Carlo methods were employed to evaluate the degree to which canonical function and structure coefficients may be differentially sensitive to sampling error. Sampling error influences were investigated across variations in variable and sample (n) sizes, and across variations in average within-set correlation sizes and in…

Multiple regression analysis is frequently being employed in experimental and non-experimental research. However, when data include predictor variables that are correlated, some regression results can become difficult to interpret. This paper presents a study to provide a demonstration that structure coefficients may be useful in these cases.…

Each of the four classic multivariate analysis of variance (MANOVA) tests of statistical significance may lead a researcher to different decisions as to whether a null hypothesis should be rejected: (1) Wilks' lambda; (2) Lawley-Hotelling trace criterion; (3) Roy's greatest characteristic root criterion; and (4) Pillai's trace criterion. These…

In the educational research literature alpha, the a priori level of significance, and p, the a posteriori probability of obtaining a test statistic of at least a certain value when the null hypothesis is true, are often confused. Explanations for this confusion are offered. Paradoxically, alpha retains a prominent place in textbook discussions of…