Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating"…

The effect of scale selection on error in calibrating item and ability parameters was investigated, with particular reference to the standardized mean-squared difference (SMSD) statistic. Through simulation, three scaling methods for selecting the common scale were used to demonstrate their effects on SMSD values. (SLD)

A simulation study compared the performance of the Mann-Whitney "U" test, Student's "t" test, and the alternate (separate variance) "t" test for two mutually independent random samples from normal distributions, with both one-tailed and two-tailed alternatives. Type I error probabilities were computed with equal and…

This repeated measures factorial design study compared the results of two procedures for identifying multivariate outliers under varying conditions, the Mahalanobis distance and the Andrews-Pregibon statistic. Results were analyzed for the total number of outliers identified and number of false outliers identified. Simulated data were limited to…

A variety of paired comparison, triple comparison, and ranking experiments are discussed as generalized linear models. All such models can be easily fit by maximum likelihood using the GLIM computer package. Examples are presented for a variety of cases using GLIM. (SLD)

A numerical approach for computing standard errors (SEs) of a linear equating is described in which first partial derivatives of equating functions needed to compute SEs are derived numerically. Numerical and analytical approaches are compared using the Tucker equating method. SEs derived numerically are found indistinguishable from SEs derived…

The challenge of multiple comparisons is to maximize the power for answering specific research questions, while still maintaining control over the rate of Type I error. Several multiple comparison procedures have been suggested to meet this challenge. The stagewise protected procedure (SPP) of A. J. Klockars and G. R. Hancock tests null hypotheses…

Simulation techniques were used to generate conventional test responses and track the proportion of alternatives examinees could classify independently before and after taking the test. Finite-state scores were compared with these actual values and with number-correct and formula scores. Finite-state scores proved useful. (TJH)

The influence of sample size (N) and model parsimony on a set of 22 goodness of fit indices was investigated, including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from 2 known population data structures, values for 6 of 22 fit indices were reasonably independent of N and were…

An investigation of the effects of randomly missing data in two-predictor regression analyses is described. The differences in the effectiveness of five common treatments of missing data on estimates of R-squared values and each of the two standardized regression weights is also investigated. Bootstrap sample sizes of 50, 100, and 200 were drawn…

This paper develops and applies three nonparametric comparisons of the shapes of two item characteristic surfaces: (1) proportional latent odds; (2) uniform relative difficulty; and (3) item sensitivity. A method is presented for comparing the relative shapes of two item characteristic curves in two examinee populations who were administered an…

The present study compares the robustness of two different one way fixed-effects analysis of covariance (ANCOVA) models to investigate whether the model which uses a test statistic incorporating estimates of separate unequal regression slopes is more robust than the conventional model which assumes the slopes are equal. (Author/BW)

The algorithm developed by B. A. Schneider (1980) for analysis of paired comparisons of psychological intervals is replaced by one proposed by R. M. Johnson. Monte Carlo simulations of pairwise dissimilarities and pairwise conjoint effects show that Johnson's algorithm can provide good metric recovery. (SLD)

New methods for comparing the medians corresponding to independent treatment groups are suggested. Procedures are based on the estimator of F. Harrell and C. Davis in conjunction with a modification and extension of the bootstrap calibration technique suggested by W. Loh. Data from two groups provide an illustration. (SLD)

Performance of the logistic regression (LR) procedure was compared to that of the Mantel Haenszel (MH) procedure in the detection of uniform and nonuniform differential item functioning on a simulation examining distributional properties of the LR and MH test statistics and the relative power of the two procedures. (SLD)