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…

A general delta method is described for computing the standard error (SE) of a chain of linear equations. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. Computer simulations demonstrate the method. (SLD)

The power functions of Student t tests performed on initial scores, ordinary ranks, 3 kinds of modular ranks, and dichotomies were investigated for 1 normal and 3 nonnormal distributions using 2 samples of 26 simulated scores each. Advantages of extending the rank transformation concept are discussed. (SLD)

It is argued that outlier-prone distributions reduce the power of nonparametric tests, but power can be restored through procedures usually associated with parametric tests. Computer simulation is used to show how an outlier detection and downweighting procedure augments the power of the t-test and the Wilcoxon-Mann-Whitney test. (SLD)

Examined the degree to which coefficient alpha is affected by including items with different distribution shapes within a unidimensional scale. Computer simulation results indicate that reliability does not increase dramatically as a result of using differentially shaped items within a scale. Discusses implications for test construction. (SLD)

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

This study was designed to derive the distribution of a test statistic based on normal probability plots. The first purpose was to provide an empirical derivation of the critical values for the Line Test (LT) with an extensive computer simulation. The goal was to develop a test that is sensitive to a wide range of alternative distributions,…

Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual's true number-correct score; presents two general interval estimation procedures for an individual's true scale score (i.e., normal approximation and endpoints conversion methods); compares various…

Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…

Previous research examining the effects of reducing the number of score groups used in the matching criterion of the Mantel-Haenszel procedure, when screening for differential item functioning, has produced ambiguous results. The goal of this study was to resolve the ambiguity by examining the problem with a simulated data set. The main results…

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations found that standard errors derived without the normality assumption were more accurate than those derived with the normality assumption in a large sample with moderately skewed score distributions. (SLD)

A complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)

Results of a Monte Carlo study with 4 populations (3,072 conditions) indicate that when distributions depart markedly from normality, nonparametric analysis and parametric analysis of transformed data show superior power to parametric analysis of raw data. Under conditions studied, parametric analysis of transformed data is more powerful than…

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…

Purpose: The aim of this work is to implement bootstrapping methods into software tools, based on Java. Design/methodology/approach: This paper presents a category of software e-tools aimed at simulating laboratory works and experiments. Findings: Both students and teaching staff use traditional statistical methods to infer the truth from sample…