The Rasch model, objective measurement, equating, and robustness

Abstract

This study investigated the adequacy of the Rasch model in providing objective measurement when equating existing standardized reading achievement tests with groups of examinees not widely separated in ability. To provide the context for the assessment of objectivity with the Rasch model, information relevant to several assumptions of the model was provided. An anchor test procedure was used to equate the various pairs of existing achievement tests. Despite the considerable lack of fit of the data to the model found for all tests used, the Rasch difficulty estimates were reasonably invariant for replications with random samples as well as samples that differed in ability by one grade level. Furthermore, with the exception of the data for one test pair and one grade level, the Rasch model using the anchor test procedure provided a reasonably satisfactory means of equating three test pairs on the log ability scale for the examinees at two grade levels.