Kulick and Wright concluded, based on theoretical mathematical simulations of hypothetical student exam scores, that assigning exam grades to students based on the relative position of their exam performance scores within a normal curve may be unfair, given the role that randomness plays in any given student's performance on any given exam.…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

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…

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

Using a Monte Carlo simulation, a bootstrap procedure was evaluated for setting a confidence interval on the unrestricted population correlation (rho) assuming various degrees of incomplete truncation on the predictor. Sample size was the most important factor in determining accuracy and stability. Sample size should be at least 50. (SLD)

The estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS) is discussed. Starting points are the delta method equations. The jackknife and bootstrap methods are compared for providing finite difference approximations to the derivatives. Examining the…

Effects of violating the independence assumption when combining correlation coefficients in a meta-analysis were studied. This Monte-Carlo simulation varied sample size, predictor number, population intercorrelation among predictors, and population correlation between predictors and criterion. Combining statistics from nonindependent data in a…

A mathematical formula is introduced for the effect of integrating data. A method is then derived to eliminate the effect from correlations of variables, including mean composites, thus allowing for a clustering algorithm that requires allocation of variables according to the magnitude of their correlations. Examples illustrate the procedure. (SLD)

The applicability of a mathematical theorem designed to trace causality of a three-variable path that consists of an initial cause variable, an intermediate variable, and a final-effect variable with control over other system variables is evaluated. The formula was used with a horizontal rather than a normal distribution, as had been done in an…

Use of parallel analysis (PA), a selection rule for the number-of-factors problem, is investigated from the viewpoint of permutation assessment through a Monte Carlo simulation. Results reveal advantages and limitations of PA. Tables of sample eigenvalues are included. (SLD)

This study compared three approaches to the two-factor experiment with repeated measures on one factor: (1) the conventional mixed model analysis of variance, (2) the Greenhouse-Geisser conservative analysis of variance, and (3) multivariate extensions of analysis of variance. Computer simulated data were used in a total of 96 sets of covariance…

Meta-analysis is a technique for combining the summary statistics from previously conducted research studies to indicate the direction of results and provide an index of the magnitude of effect size. This paper focuses on the effect of the violation of the assumption of independence (that the value of any included statistic is in no way…

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…

A model and computation procedure based on classical test score theory are presented for determination of a correlation coefficient corrected for attenuation due to unreliability. Delta and Monte Carlo method applications are discussed. A power analysis revealed no serious loss in efficiency resulting from correction for attentuation. (TJH)

A Monte Carlo simulation was used to ascertain the degree of inflation that can occur in regression estimates when samples contain randomly occurring instances of a pattern among correlations called cooperative suppression. Ten thousand samples of scores on three variables were randomly drawn from a population in which the correlations among the…