WIREs Computational Statistics

The rank transformation—an easy and intuitive way to connect many nonparametric methods to their parametric counterparts for seamless teaching introductory statistics courses

Journal Article


The rank transformation refers to replacing the data by their ranks, or average ranks in case of ties, prior to performing standard statistical procedures on the ranks. There are several forms of transforming the data to ranks. RT‐1 refers to ranking all of the data together, and giving the smallest observation the rank 1, the second smallest the rank 2, and so on. RT‐2 involves ranking data within subgroups only, and not comparing data across subgroups. RT‐3 involves re‐expressing the data prior to ranking, such as subtracting a sample mean or median from the data and taking an absolute value of the difference prior to ranking. RT‐4 describes situations where data are re‐expressed within subgroups, and then ranked within subgroups.

The rank transformation is a convenient way to bridge the pedagogical gap between parametric and nonparametric methods in statistics. First present the classical statistical procedure, such as a t test or a correlation coefficient, and then perform the same operation on the ranks of the data instead of the data themselves. The resulting method is equivalent to the standard presentation of nonparametric methods, and is amenable to convenient use in computer software. Limitations of this method are also described. WIREs Comput Stat 2012 doi: 10.1002/wics.1216

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