The Distributions of Smirnov Type Two-Sample Rank Tests for Discontinuous Distribution Functions
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1982 · Volume 44 · Issue 3
DOI: 10.1111/j.2517-6161.1982.tb01214.x
Abstract
An important area of application for rank tests occurs when there are ties in the data which may happen when the observations are drawn from a discrete population or are grouped. The standard theory for the two-sample Smirnov test as to whether two samples have been drawn from the same population assumes continuous distributions in which case ties only arise with probability zero. The null distribution of the test statistic for large sample sizes is obtained here for discontinuous distributions. Since this depends upon the (unknown) population distribution a procedure for estimating the null probabilities is discussed. One application of the resulting test is for testing association in a 2 ×Ccontingency table for ordinal data when there is a large total entry, but several cells have small entries. The distribution of a competitor to the Smirnov test introduced by the author is also discussed in the case of discontinuous distribution functions.
Keywords
discontinuous distribution functions, smirnov two-sample rank test, limiting distribution, mann-whitney type tests
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