This Monte Carlo study examined strategies for forming the matching variable for the Mantel-Haenszel (MH) differential item functioning (DIF) procedure. Data were generated using a three-parameter logistic item response theory model, with common guessing parameters. The number of subjects and test length were manipulated, as were the difficulty,…

Test data from a large licensure examination were used to investigate the impact of the number of score groups and score group size on the Mantel-Haenszel (MH) alpha statistic. Two kinds of quasi-experimental studies were conducted: (1) baseline MH analyses in which the number of score groups and the ethnicity of each randomly equivalent…

Studies of differential item functioning (DIF) under item response theory require that item parameter estimates be placed on the same metric before comparisons can be made. Evidence that methods for linking metrics may be influenced by the presence of differentially functioning items has been inconsistent. The effects of three methods for linking…

Concern over the validity of statistical tests performed on data that may not satisfy underlying assumptions has prompted methodological researchers to perform Monte Carlo studies for frequently used tests. Unfortunately, these studies appear to have had little impact on methodological practice. One reason is the lack of an overarching framework…

The purpose of this study was to develop a single procedure for comparing population variances which could be used for distribution forms. Bootstrap methodology was used to estimate the variability of the sample variance statistic when the population distribution was normal, platykurtic and leptokurtic. The data for the study were generated and…

Since about 1962, researchers have explored the effectiveness of educational software in the schools under various conditions, and many have concluded that computer assisted instruction (CAI) is effective. Many of the studies reviewed to support this conclusion, however, had design flaws. Reviews of educational software effectiveness studies have…

This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate…

The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as…

A normally distributed data set of 1,000 values--ranging from 50 to 150, with a mean of 50 and a standard deviation of 20--was created in order to evaluate the bootstrap method of repeated random sampling. Nine bootstrap samples of N=10 and nine more bootstrap samples of N=25 were randomly selected. One thousand random samples were selected from…

The American College Testing (ACT) Program offers research services through which colleges can predict the freshman grades of their future students. This paper describes research done to establish a minimum sample size requirement for calculating least-squares prediction equations for college freshman grade average. Prediction equations were…

This paper presents the description and several applications of a model which can be used to determine how long a researcher must wait for the return of completed mail questionnaires to be sure the data collected reflect the true values of the parameters of interest. This model proposes to fit two linear time trend lines to a set of mailed…

In most behavioral science research very little attention is ever given to the probability of committing a Type II error, i.e., the probability of failing to reject a false null hypothesis. Recent publications by Cohen have led to insight on this topic for the fixed-effects analysis of variance and covariance. This paper provides social scientists…

Five-hundred dichotomously scored response patterns were generated with sequentially independent (SI) items and 500 with dependent (SD) items for each of thirty-six combinations of sampling parameters (i.e., three test lengths, three sample sizes, and four item difficulty distributions). KR-20, KR-21, and Split-Half (S-H) reliabilities were…

A program obtained random samples from known populations, some of which violated the homogeneity assumption. Student t tests and Mann-Whitney U Tests were performed on the sample value. Where the t test led to incorrect decisions, the use of Mann-Whitney U test in its place led to poorer results. (JAZ)

This article discusses the circumstances under which unequal sample size in the two-group study can arise and result in an attenuated point-biserial correlation. Formulas are provided for correcting the coefficient either directly or through the mediation of relevant statistics found in studies where the coefficient itself is not reported.…