An Extension of the Rank Transformation Concept
Donald W. Zimmerman · The Journal of Experimental Education · 1992
It is known that the Mann-Whitney-Wilcoxon test is equivalent to an ordinary Student t test performed on scores transformed to ranks in place of the scores themselves. Not as well known is the fact that another widely used nonparametric method, Mood's median test, is equivalent to a t test on scores taking only the values 0 and 1 in place of the initial values. In this study, t tests were performed on ranks obtained by combining two samples of 26 scores each, so that there were 52 possible values, as well as on transformed scores having 26, 13, 4, or 2 possible values. For the normal distribution, power decreased slightly as the number of values decreased, whereas for various nonnormal distributions, power increased as the number of values decreased. Advantages of extending the rank transformation concept to include more general transformations are discussed.