This Brief compares three hypothetical Quality Rating and Improvement Systems (QRIS) that use different rating structures: block, points, and hybrid. Because the quality standards in the hypothetical QRIS are held relatively constant across structures, analyses can be conducted to determine how structure relates to key QRIS outcomes. Three…

The continued accumulation of validity evidence for the intended uses of educational assessment scores is critical to ensure that inferences made using the scores are sound. To that end, the College Board has continued to collect college outcome data to evaluate the relationship between SAT® scores and college success. This report provides updated…

We find the correlation of two jointly distributed random variables connected with a coin tossing experiment. The marginal distributions are binomial and negative binomial.

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

Restricted the range of nonnormal distributions by eliminating scores above a designated cutoff value or eliminating scores above or below the mean by a certain distance. Results of a simulation study show that range restriction sometimes increased the correlation between variables having outlier prone distributions. Discusses practical…

The correlation coefficient is an integral part of many other statistical techniques (analysis of variance, t-tests, etc.), since all analytic methods are actually correlational (G. V. Glass and K. D. Hopkins, 1984). The correlation coefficient is a statistical summary that represents the degree and direction of relationship between two variables.…

Outliers, extreme data values relative to others in a sample, may distort statistics that assume internal levels of measurement and normal distribution. The outlier may be a valid value or an error. Several procedures are available for identifying outliers, and each may be applied to errors of prediction from the regression lines for utility in a…

The posterior distribution of the bivariate correlation is analytically derived given a data set where "X" is completely observed, but "Y" is missing at random for a portion of the sample. Interval estimates of the correlation are constructed from the posterior distribution in terms of the highest density regions. (SLD)

Multivariate normality is required for some statistical tests. This paper explores the implications of violating the assumption of multivariate normality and illustrates a graphical procedure for evaluating multivariate normality. The logic for using the multivariate bootstrap is presented. The multivariate bootstrap can be used when distribution…

This paper discusses the issue of multiple testing and overall Type I error rates in contexts other than multiple comparisons of means. It demonstrates, using a 5 x 5 correlation matrix, the application of 5 recently developed modified Bonferroni procedures developed by the following authors: (1) Y. Hochberg (1988); (2) B. S. Holland and M. D.…

A Monte Carlo evaluation of four test statistics for comparing dependent zero-order correlations was conducted with four sample sizes and three population distributions. Results indicate that choice of optimal test statistic depends on sample size and distribution, and predictor intercorrelation and effect size or magnitude of the…

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)

The adequacy of multidimensional trait and item parameters using multidimensional item response theory analysis was studied through simulation using different degrees of correlation between two trait dimensions and the existence of a restricted trait on the second dimension. Conditions allowing adequate recovery of trait and item parameters are…

Provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and details Monte Carlo simulation results on Type I and Type II error control. Demonstrates through the simulation that robustness and nonrobustness of structure analysis techniques vary as a…