The nation's generation of "Baby Boomers" is now the grandparents of a new generation of students known as "Gen Y" and "Gen Z," respectively. "Gen X," parents of our current students, have the enormous task of raising their children as "digital natives" in a technological-savvy world. The idea of…

This study investigated the extent that cooperative group members' levels of hopefulness, operationalized as a combination of pathways to meet desired goals and the agentic thinking that motivates an individual to use those pathways, predict (a) group performance, namely, the quality of an article critique assignment and research proposal…

The purpose of this study was to determine the extent to which Collective Teacher Efficacy explained the variance in Black and Hispanic enrollment in Advanced Placement and International Baccalaureate classes. In order to achieve this purpose, survey research methodology was employed with Virginia high schools as the unit of study. Fifty-three…

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Two well known directional (one-tailed) tests of significance, mean difference and correlation coefficient, are presented within the multiple linear regression framework. Adjustments on the computed probability level are indicated. The case for a directional interaction research hypothesis is defended. Conservative adjustments on the computed…

Using a Monte Carlo approach, comparison was made between traditional procedures and a multiple linear regression approach to test for differences between values of r sub 1 and r sub 2 when sample data were dependent and independent. For independent sample data, results from a z-test were compared to results from using multiple linear regression.…

A growing controversy surrounds the strict interpretation of statistical significance tests in social research. Statistical significance tests fail in particular to provide estimates for the stability of research results. Methods that do provide such estimates are known as invariance or cross-validation procedures. Invariance analysis is largely…

The purpose of this paper is to demonstrate how multiple linear regression provides a viable statistical methodology for dealing with meta-analysis in general, and specifically with the issues of nonindependence and design complexity, such as multiple treatments. Since the F-test and t-test are special cases of the general linear model,…

Remarkability is introduced as a quantifiable attribute of given data and as a basis upon which one may rationally judge its scientific value. Applications of remarkability theory to various research and statistical problems and procedures are discussed. (DG)

The effects of violation of the assumption of homogeneity of regression on the Type I error rate and on the power of analysis of covariance (ANCOVA) were investigated. The data situations included in the study involved two groups with one covariate and one criterion, with varying equal and unequal group sizes, and varying degrees of violation of…

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…

This study was concerned with various schemes for reducing the number of variables in a multivariate analysis. Two sets of illustrative data were used; the numbers of criterion groups were 3 and 5. The proportion of correct classifications was employed as an index of discriminatory power of each subset of variables selected. Of the four procedures…

Statistical methods are described for diagnosing and treating three important problems in covariate tests of significance: curvilinearity, covariable effectiveness, and treatment-covariable interaction. Six major assumptions, prerequisites for covariate procedure, are discussed in detail: (1) normal distribution, (2) homogeneity of variances, (3)…

The purpose of this study was to develop the Johnson-Neyman Procedure (JN-Procedure) appropriate to multiple groups and covariables, and demonstrate its use in the analysis of group differences. A sequence of significance tests which makes it possible to identify the most parsimonious analysis of group differences appropriate to a given set of…