Accuracy of Year-1, Year-2 Comparisons Using Individual Percentile Rank Scores: Classical Test Theory Calculations

In the reporting of individual student results from standardized tests in educational assessments, the percentile rank of the individual student is a major, if not the most prominent, numerical indicator. For example, in the 1998 and 1999 California Standardized Testing and Reporting (STAR) program using the Stanford Achievement Test Series, Ninth Edition, Form T (Stanford 9), the 1998 Home Report and 1999 Parent Report feature solely the National Grade Percentile Ranks. (These percentile rank scores also featured in the more extensive Student Report.) This paper develops a formulation and presents calculations to examine the properties of year-1, year-2 comparisons using these individual percentile rank scores. The approach and formulation follows the previous investigations of the accuracy of the individual percentile rank score in Rogosa (1999a). A typical question that this paper addresses is: What are the chances that a student who really improved 10 percentile points from year-1 (1998) to year-2 (1999) obtains a lower percentile rank in year-2 than year-1? Such questions are addressed using the test reliability coefficient in classical test theory to represent quality of measurement. Thus, we can investigate the question: What level of test reliability is needed to obtain good accuracy in year-1, year-2 comparisons?