A new and unified approach to test equating is described that is based on log-linear models for smoothing score distributions and on the kernel method of nonparametric density estimation. The new method contains both linear and standard equipercentile methods as special cases and can handle several important equating data collection designs. An…

Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. Alternatives are proposed and discussed. (Author/JKS)

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)

Tests of mean equality proposed by Alexander and Govern (1994) and Tsakok (1978) were compared to the well-known procedures of Brown and Forsythe (1974), James (1951), and Welch (1951) for their ability to limit the number of Type I errors in one-way designs where the underlying distributions were nonnormal, variances were nonhomogeneous, and…

The utility of the three-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. Simulation studies demonstrate that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly…

The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects…

Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…