Chapter 13.5, Problem 13BB

Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by

$1-\frac{{\displaystyle \sum T}}{N^3-N}$

First combine all of the sample data into one list, and then, in that combined list, identify the different groups of sample values that are tied. For each individual group of tied observations, identify the number of sample values that are tied and designate that number as t, then calculate T = t³ − t. Next, add the T values to get ${\displaystyle \sum T}$. The value of N is the total number of observations in all samples combined. Use this procedure to find the corrected value of H for Example 1 in this section on page 628. Does the corrected value of H differ substantially from the value found in Example 1?