Accuracy of Individual Scores Expressed in Percentile Ranks: 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 accuracy of the individual percentile rank score. Here, accuracy follows the common-sense interpretation of how close you come to the target. Calculations are presented for: (i) percentile discrepancy (the difference between the percentile rank of the obtained test score compared to perfectly accurate measurement); (ii) comparisons of a student score to a standard (e.g., national norm 50 th percentile); (iii) test-retest consistency (difference between the percentile rank of the obtained test score in two repeated administrations); and (iv) comparison of two students (difference between the percentile rank of the obtained test scores for two students of different achievement levels). One important theme is to compare the results of these calculations with the traditional interpretations of the test reliability coefficient: e.g., Does high reliability imply good accuracy?