a. Exercise 4—Kruskall-Wallis Test

A large corporation has been sending many of its first-level managers to an off-site supervisory skills course. Four different management development centers offer this

course, and the corporation wants to determine whether they differ in the quality of training provided. A sample of 20 employees who have attended these programs has been chosen and the employees ranked in terms of supervisory skills. The results follow.

Note that the top-ranked supervisor attended course 2 and the lowest-ranked supervisor attended course 4. Use α = .05 and test to see whether there is a significant difference in the training provided by the four programs.

Solution to Exercise d.

For the Kruskall-Wallis test we need a table with the respective ranks, which is already provided. With this table, we need to compute the following statistics:

where

BG (Ranks) = Between Groups sum of squares

= unbiased variance of all ranks

We have the following table:

Using this table we obtain

which means

With this information, we compute finally the KW statistics:

The calculation of comes directly from the table. We have to find now the respective p-value for a Chi-squared distribution with 3 degrees of freedom (4 groups minus 1). At the 0.05 level of significance, the cutoff value for acceptance is c=7.81, but since KW=8.02857>7.81, we reject the null hypothesis of no difference between the groups, and we conclude, at the 0.05 level of significance that there is a difference between the training provided by the different courses.