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

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 ∑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?

Data From Example 1:

Listed on the top of the next page are attribute ratings of males by females who participated in speed dating events (from Data Set 18 “Speed Dating” in Appendix B ). In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the three samples.

Data Set 18: Speed Dating

Data are from 199 dates (first five rows shown here). DEC BY FEM is decision (1 = yes) of female to date again, AGE FEM is age of female, LIKE BY FEM is “like” rating by female of male (scale of 1-10), ATTRACT BY FEM is “attractive” rating by female of male (scale of 1-10), ATTRIB BY FEM is sum of ratings of five attributes (sincerity, intelligence, fun, ambitious, shared interests) by female of male. Data for males use corresponding descriptors. Higher scale ratings correspond to more positive impressions.

Based on replication data from Data Analysis Using Regression and Multilevel/Hierarchical Models, by Andrew Gelman and Jennifer Hill, Cambridge University Press.