Basic Statistics

196 NONPARAMETRIC STATISTICS

Table 13.2 Cholesterol Levels and Ranks for a Combined Sample

Chol. Group Rank

126

138

148

152

158

158

165

171

175

176

177

180

188

189

195

197

200

204

213

HPP

HPP

No

HHP

HPP

No

HPP

HHP

No

HPP

HPP

HPP

HPP

No

HPP

No

No

No

No

1

2

3

4

5.5

5.5

I

8

9

10

11

12

13

14

15

16

17

18

19

To compare the two independent samples, we rank the combined samples together
from 1 to 19. The sum of the ranks in the smaller group of 8 employees is W = 101.5.
Note that we have a tie in the HPP and No groups and the ties were given the rank of
5.5. Here ti = 2 since two observations were tied.
The formulas for the E(W) and the Var(W) are

E(W) = (m(m + n + 1))/2

or

E(W) = 8(8 + 11 + 1)/2 = 80

If we had no ties, the variance of W would be

Var (W) = mn(m + n + 1)/12

or

Var (W) = 8 x 11(8 + 11 + l)/l2 = 88(20)/12 = 146.67