Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…

Within the context of moderated multiple regression, mean centering is recommended both to simplify the interpretation of the coefficients and to reduce the problem of multicollinearity. For almost 30 years, theoreticians and applied researchers have advocated for centering as an effective way to reduce the correlation between variables and thus…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The…

Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the…

Most study samples show less variability in key variables than do their source populations due most often to indirect selection into study participation associated with a wide range of personal and circumstantial characteristics. Formulas exist to correct the distortions of population-level correlations created. Formula accuracy has been tested…

It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared…

Classroom observation of teachers is a significant part of educational measurement; measurements of teacher practice are being used in teacher evaluation systems across the country. This research investigated whether observations made live in the classroom and from video recording of the same lessons yielded similar inferences about teaching.…

A typical question in multiple regression analysis is to determine if a set of predictors gives the same degree of predictor power in two different populations. Olkin and Finn (1995) proposed two asymptotic-based methods for testing the equality of two population squared multiple correlations, [rho][superscript 2][subscript 1] and…

This article presents an improved approximation formula for the problem of correcting correlation coefficients that arise from range-restricted distributions on either or both the independent and dependent variable. (BS)

Eight asymptotically robust tests of population correlation coefficient equality are proposed and are studied along with two parametric tests. Monte Carlo simulation is used to compare the small sample performance of these ten procedures. The sampled distributions consist of the normal distribution, two mixed normal distributions and four…

The use of mean inter-item correlation as a technique for examining homogeneity is proposed as a descriptive tool that can orient researchers to salient aspects of their scales. A study of 341 undergraduates who completed the NEO Personality Inventory illustrates the technique. (SLD)

A modification of Horn's parallel analysis is introduced that is based on the Monte Carlo simulation of the null distributions of the eigenvalues generated from a population correlation identity matrix. This modification reduces the tendency of the parallel analysis procedure to overextract or to extract poorly defined factors. (SLD)

This study investigated the validity of Hayes's formula for converting rank-ordered Rokeach Values data to a normal distribution theoretically achieved through the use of rated data. Findings support the validity of Hayes's formula and expand the analytic possibilities of data collected on the Rokeach instrument. (Author/PN)

A comparison is made of the power and actual alpha levels of three tests of homogeneity for independent product-moment correlation coefficients using Monte Carlo methods while selectively studying sample size and varying the number of correlation reliabilities. How robust these are in applied work is discussed. (SLD)