This Monte Carlo study examined the impact of misspecifying the [big sum] matrix in longitudinal data analysis under both the multilevel model and mixed model frameworks. Under the multilevel model approach, under-specification and general-misspecification of the [big sum] matrix usually resulted in overestimation of the variances of the random…

This study aimed at estimating the correlation between true scores (true consistency) of vocational interest over a short time span in a sample of 1089 adults. Participants were administered 54 items assessing vocational, family, and leisure interests twice over a 1-month period. Responses were analyzed with a multitrait (MT) model, which supposes…

The present study compared item and ability invariance as well as model-data fit between the one-parameter (1PL) and three-parameter (3PL) Item Response Theory (IRT) models utilizing real data across five grades; second through sixth as well as simulated data at second, fourth and sixth grade. At each grade, the 1PL and 3PL IRT models were run…

The major aim of educational effectiveness research is to examine and explain school, class, and teacher differences with respect to relevant educational criteria. Until now, in the large majority of studies, language and mathematics scores were used as a criterion. In the present study, the educational track students choose at the start of…

A procedure for checking the score equivalence of nearly identical editions of a test is described. The procedure employs the standard error of equating (SEE) and utilizes graphical representation of score conversion deviation from the identity function in standard error units. Two illustrations of the procedure involving Scholastic Aptitude Test…

The purpose of this study was to examine the effect of test dimensionality on the stability of examinee ability estimates and item response theory (IRT) based score reports. A simulation procedure based on W. F. Stout's Essential Unidimensionality was used to generate test data with one dominant trait for the whole test and three minor traits…

The use of a covariate for randomized response (RRT) research has been shown to reduce standard errors of sensitive trait proportion estimates. At the same time, the model has been shown to be subject to serious misspecification when the relationship between the covariate and the sensitive trait is non-monotonic. The RRT covariate model is adapted…

Logistic regression was used for modeling the observation-to-indicator ratio needed for the standard error scree procedure (SEscree) to correctly identify the number of factors existing in generated sample correlation matrices. The created correlation matrices were manipulated along the number of factors (4,6), sample size (250, 500), magnitude of…

Educational researchers often use multiple statistical tests in their research studies and program evaluations. When multiple statistical tests are conducted, the chance that Type I errors may be committed increases. Thus, the researchers are faced with the task of adjusting the alpha levels for their individual statistical tests in order to keep…

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…

Simulations were performed to verify the accuracy with which the Mantel-Haenszel (MH) and Rasch PROX procedures recover simulated item bias. Several standard error estimators for the MH procedure were evaluated. Item bias is recovered satisfactorily by both techniques under all simulated conditions. The proposed MH standard error estimators have…

A recurring problem in educational research is how to account for non-random selection that has restricted the range of the variables of interest in correlational analyses. Several expressions due to H. Pearson (1903) and presented in matrix notation by D. N. Lawley (1943-44) are commonly used in selection settings to adjust for samples chosen on…

An approximation formula for the standard error of measurement was recently proposed by Garvin. The properties of this approximation to the standard error of measurement are described in this paper and illustrated with hypothetical data. It is concluded that the approximation is a systematic overestimate of the standard error of measurement…

In the light of research by Epstein (1979) (which reported that error of measurement in the analysis of behavior stability may be reduced by examining the behavior of aggregate stability coefficients computed for measurements with known stability characteristics), this study examines stability coefficients for computer-generated data sets…

Classical test theory has been rejected for application to criterion-referenced (CR) tests by most psychometricians due to an expected lack of variance in scores and other difficulties. The present study was conceived to resolve the variance problem and explore the possibility that classical test theory is both appropriate and desirable for some…