A comparison of methods of normalizing a discrete distribution

Abstract

Normal distributions are the foundation of modern statistical procedures, which differ in their sensitivity to violation of the assumption of normality. This paper reports on the effectiveness of two different methods of normalizing distributions of discrete test score data. The scores of 971 Ontario high school students on the 22 scales of PRF-E (Jackson, 1974) were normalized using two variants of the cumulative proportions method and by a rank method. Neither cumulative procedure appreciably altered the modality or skewness of the distributions. The rank method succeeded in normalizing all the distributions, except for an occasional case of platykurtosis. It was concluded that normalization by ranks is to be preferred over cumulative methods for use in situations in which a statistical procedure is sensitive to violations of normality.