The problem addressed by this worksheet is:  Given two samples of data, which may contain ties, how may one test the hypothesis that they are drawn from the same distribution?

The worksheet demonstrates the use of a MAPLE implementation of an algorithm to perform two-sample homogeneity tests, based on any one of three Kolmogorov-Smirnov (K-S) test statistics.

The MAPLE package KSNstat, which is introduced in this worksheet, contains the MAPLE procedure gsmirn which implements the GSMIRN algorithm given in 1994 by Nikiforov [1] to calculate exact p-values for generalised (conditionally distribution-free) two-sample homogeneity tests based on two-sided and one-sided Kolomogorov-Smirnov statistics.  Notably, the Nikiforov algorithm covers the range from discrete to continuous distributions; specifically, it handles tied data points.

[1] Exact Smirnov two-sample tests for arbitrary distributions, A. Nikiforov, Appl.Stat., vol.43, No. 1. pp.265-270, 1994.