THE NATIONAL REFERENCE SCALE FOR READING: AN APPLICATION OF THE RASCH MODEL1

Abstract

In this paper we will report on the development of the National Reference Scale (NRS) for reading (Rentz and Bashaw, 1975). The NRS is the result of analyses of data from the equating phase of the Anchor Test Study (Loret, et al, 1974), using item analysis and scaling methods of the Rasch model. The larger study on which this paper is based was designed to determine whether the Rasch model could be used to equate tests of the sort used in the Anchor Test Study (ATS). Although the Rentz and Bashaw study attempted to replicate the raw-score-to-raw-score equating tables of the ATS, the preferred equating procedure was to equate each test to a common reference scale. This procedure avoids a major source of error involved in raw-score-to-raw-score equating, that will be delineated later. The particular reference scale used was the log-ability scale of the Rasch model, transformed by a simple linear function to a scale of threedigit integers. Thus, the NRS is the Rasch model's log-ability scale in a disguised form. Consequently, a discussion of the properties and interpretations of the NRS scores will, in principle, generalize to scores on any test that is calibrated using Rasch model procedures. Our primary concern is the practical use and interpretation of the ability scale of the Rasch model. An understanding of the nature of this ability scale should help test developers and users when they are considering application of the Rasch model, since it has some interesting and desirable features. For example, the log-ability scale of the Rasch model has as its units, the same units used for estimating item difficulties. It also has units of equal intervals (in a sense to be discussed in the section on direct odds comparisons).