Exact Probability Levels for Multisample SMIRNOV-TYPE Statistics
Abstract
Let there be given c independent random samples of continuous random variables of size nl, n2, ... , nc; and denote the observations in the i th sample by xi1, xi2, ... , xini. Suppose it is desired to test the null hypothesis that the samples all come from the same population. Birnbaum and Hall proposed for this null hypothesis the test statistic D(n1,n2,...,nc)-Sup / Fi*(x) -Fj*(x) / for i, j - 1,2, ..., c, where Fi* denotes the empirical cumulative distribution function for the i th sample. In their 1960 paper they published the probabilities P/D(n,n,n)<r/ for n - 1(1)20(2)40 where r = k/n, k = 1,2, ..., n. The tables appearing here are an extension of the Birnbaum-Hall tables, resulting from the examination of a larger number of samples and the consideration of unequal sample sizes. In addition, an application of this work to a problem in ballistics is discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1983
- Accession Number
- ADA126104
Entities
People
- Malcolm S. Taylor
- William E. Baker
Organizations
- Ballistic Research Laboratory