Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…

A Monte Carlo simulation approach was taken to investigate the effect of sample size on a variety of latent growth models. A fully balanced experimental design was implemented, with samples drawn from multivariate normal populations specified to represent 12 unique growth models. The models varied factorially by crossing number of time points,…

When one wants to set data reliability standards for a class of scientific inquiries or when one needs to compare and select among many different kinds of data with reliabilities that are crucial to a particular research undertaking, then one needs a single reliability coefficient that is adaptable to all or most situations. Work toward this goal…

Use of linear combinations of Fisher's "z" transformations as a combined test for the common correlation parameter based on "k" independent sample correlations has been previously studied. This article considers additional "z" additive properties and methods of combining independent studies when planning the number of…

Tau, Lambda, and Kappa are measures developed for the analysis of discrete multivariate data of the type represented by stimulus response confusion matrices. The accuracy with which they may be estimated from small sample confusion matrices is investigated by Monte Carlo methods. (Author/LMO)

This technical report provides an updated assessment of the problem of optimizing the periodicity of the Schools and Staffing Survey (SASS). Making use of data from three rounds of SASS data collection (for school years 1987-88, 1990-91, and 1993-94), the report extends and updates the preliminary findings and interim assessments that were…

Some approximate formulas are presented for standard errors of estimated regression coefficients in two-level designs. If the researcher can make a reasonable guess as to parameters occurring in the model, this approximation can be a guide to the choice of sample sizes at either level. (SLD)

Induced probabilities have been largely ignored by educational researchers. Simply stated, if a new or random variable is defined in terms of a first random variable, then induced probability is the probability or density of the new random variable that can be found by summation or integration over the appropriate domains of the original random…

Psychology studies often have low statistical power. Sample size tables, as given by J. Cohen (1988), may be used to increase power, but they are based on Monte Carlo studies of relatively "tame" mathematical distributions, as compared to psychology data sets. In this study, Monte Carlo methods were used to investigate Type I and Type II…

This Monte Carlo study examined the validity of the chi-square test for model evaluation in different instances of misspecification and sample size. The usefulness of the chi-square difference statistic to compare competing structures and improvement in fit is also addressed. (Author/BS)

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

Detection of differential item functioning (DIF) is most often done between two groups of examinees under item response theory. It is sometimes important, however, to determine whether DIF is present in more than two groups. A method is presented for the detection of DIF in multiple groups. The method, the Q(sub j) statistic, is closely related to…

Three strategies for augmenting the interpretation of significance test results are illustrated. Determining the most suitable indices to use in evaluating empirical results is a matter of considerable debate among researchers. Researchers increasingly recognize that significance tests are very limited in their potential to inform the…

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…