Lecture, Chapter 13

13.5 Differences Among Samples: The H-Test (Kruskal-Wallis Test)

This is a "non-parametric test." Advantages of non-parametric tests:

Don't require same conditions of many previously discussed tests

that the population have roughly the shape of a normal distribution, or

that variations of samples be the same, or

that samples be independent

Easily computed, typically

H-Test (Kruskal-Wallis Test) is a test of the differences among means

It is a "rank-sum" test, based on

1. Arranging the data values in order

2. Assigning a rank to each value

3. Adding all the ranks for a set of values. Call the sums R₁, R₂, R₃...

1. H₀: populations are identical; H_A: populations are not identical

2. α = .05 or .01

3. Criterion: Reject H₀ if H > critical value = χ² for df = n-1

4. Calculation of H:

H-statistic is

where

n = total samples for all data sets

n_i = total samples for data set i. n_i should be at least 5 for each data set

R_i = sum of ranks for data set i

5. Decision: Compare the calculated H with χ² for df = n-1 and apply the rejection criterion

Minitab example for:

Kruskal-Wallis non-parametric test

Tests whether the difference among several means is significant

All data goes into column 1; column 2 tells which data set the entry comes from.

In this example, the first 4 items are from set 1, the next 4 from set 2, and the last 4 from set 3.