A Generalization of the Rank Transform in the Two-Sample Location Problem

Ravinder Nath, B. S. Duran

Research output: Contribution to journalArticle


The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.

Original languageEnglish
Pages (from-to)1437-1455
Number of pages19
JournalCommunications in Statistics - Theory and Methods
Issue number14
Publication statusPublished - Jan 1 1981
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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