This article describes two methods for obtaining the standard errors of two commonly used population invariance measures of equating functions: the root mean square difference of the subpopulation equating functions from the overall equating function and the root expected mean square difference. The delta method relies on an analytical…

This exploratory study was built on research spanning three decades. Petersen, Marco, and Stewart (1982) conducted a major empirical investigation of the efficacy of different equating methods. The studies reported in Dorans (1990) examined how different equating methods performed across samples selected in different ways. Recent population…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

The discussion here covers five articles that are linked in the sense that they all treat population invariance. This discussion of population invariance is a somewhat broader treatment of the subject than simply a discussion of these five articles. In particular, occasional reference is made to publications other than those in this issue. The…

This article discusses the five studies included in this issue. Each article addressed the same topic, population invariance of equating. They all used data from major standardized testing programs, and they all used essentially the same statistics to evaluate their results, namely, the root mean square difference and root expected mean square…

Using the characteristic curve method for dichotomously scored test items, the sampling distributions of equating coefficients were examined. Simulations indicate that for the equating conditions studied, the sampling distributions of the equating coefficients appear to have acceptable characteristics, suggesting confidence in the values obtained…

The delta method was used to derive standard errors (SES) of the Levine observed score and Levine true score linear test equating methods using data from two test forms. SES derived without the normality assumption and bootstrap SES were very close. The situation with skewed score distributions is also discussed. (SLD)

This study investigated the adequacy of the Rasch model in equating existing standardized tests with groups of examinees not widely separated in ability. With the exception of one test pair and one grade level, the Rasch model using the anchor test procedure provided a reasonably satisfactory means of equating. (Author/CTM)