Kruskal Wallis Test

The Kruskal-Wallis test (also called the H test) uses ranks of simple random samples from three or more independent populations

test the null hypothesis that the independent samples come from populations with the equal medians. • H0: • H1:

The samples come from populations with equal medians.

The samples come from populations with medians that are not all equal.

At least three independent random samples • Each sample has at least 5 observations

• Are requirements met?

• Each of the three samples is a simple random independent and sample.

• Each sample size at least 5.

• H0: The populations of chest deceleration measurements from the three categories have the same median.

• H1: The populations of chest deceleration measurements from the three categories have medians that are not all the same.

• The following statistics come from Table 13-6:

• n1 = 10,

n2 = 10,

n3 = 10

• N = 30

• R1 = 203.5,

R2 = 152.5,

R3 = 109

 R12 R22 Rk2  12 H   ...     3( N  1) N ( N  1)  n1 n2 nk   203.52 152.52 1092  12     3(30  1)   30(30  1)  10 10 10   5.774

Find the critical value. .

• Because each sample has at least five observations, the distribution of H is approximately a chi-square distribution.

• df = k – 1 = 3 – 1 = 2 • α = 0.05 (right-tail) • From Table A-4 the critical value = 5.991.

• The test statistic 5.774 is NOT in the critical region bounded by 5.991, so we fail to reject the null hypothesis of equal medians. • There is not sufficient evidence to reject the claim that chest deceleration measurements from small cars, medium cars, and large cars all have equal medians. The medians do not appear to be different.