Impact of Rank-Based Normalizing Transformations on the Accuracy of Test Scores

The purpose of this article is to provide an empirical comparison of rank-based normalization methods for standardized test scores. A series of Monte Carlo simulations were performed to compare the Blom, Tukey, Van der Waerden and Rankit approximations in terms of achieving the T score's specified mean and standard deviation and unit normal skewness and kurtosis. All four normalization methods were accurate on the mean but were variably inaccurate on the standard deviation. Overall, deviation from the target moments was pronounced for the even moments but slight for the odd moments. Rankit emerged as the most accurate method among all sample sizes and distributions, thus it should be the default selection for score normalization in the social and behavioral sciences. However, small samples and skewed distributions degrade the performance of all methods, and practitioners should take these conditions into account when making decisions based on standardized test scores. Introduction Standardization and normalization are two ways of defining the frame of reference for a distribution of test scores. Both types of score conversions, or transformations, mathematically modify raw score values (Osborne, 2002). The defining feature of standard scores is that they use standard deviations to describe scores' distance from the mean, thereby creating equal units of measure within a given score distribution. Standard scores may be modified to change the scale's number system (Angoff, 1984), but unless distributions of standard scores are normalized, they will retain the shape of the original score distribution. Therefore, standardization may enable effective analysis of individual scores within a single test, but normalization is needed for meaningful comparisons between tests.