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.
Daniel Skoog
John Ogilvie
Maplesoft
Igor Hlivka
Dr. Robert Lopez
Yumi Mizuno
Dr. Giuseppe Guarino
I. Hlivka
José Luis Gómez Pardo
Wayne Allen