Statistical Methods for Psychology

where

His then evaluated against the distribution k 21 df.

As an example, assume that the data in Table 18.8 represent the number of simple arith-

metic problems (out of 85) solved (correctly or incorrectly) in 1 hour by participants given a

depressant drug, a stimulant drug, or a placebo. Notice that in the Depressant group three of

the participants were too depressed to do much of anything, and in the Stimulant group three

of the participants ran up against the limit of 85 available problems. These data are decidedly

nonnormal, and we will use the Kruskal–Wallis test. The calculations are shown in the lower

part of the table. The obtained value of His 10.36, which can be treated as on 3 21 52 df.

The critical value of is found in Appendix to be 5.99. Since 10.36 .5.99, we can

reject and conclude that the three drugs lead to different rates of performance.

18.10 Friedman’s Rank Test for kCorrelated Samples

The last test to be discussed in this chapter is the nonparametric analogue of the one-way

repeated-measures analysis of variance, Friedman’s rank test for kcorrelated samples.

It was developed by the well-known economist Milton Friedman—in the days before he

H 0

x^2 .05 122 x^2

x^2

x^2

N= ani=total sample size

Ri=the sum of the ranks in groupi

ni=the number of observations in groupi

k=the number of groups

684 Chapter 18 Resampling and Nonparametric Approaches to Data

Table 18.8 Kruskal–Wallis test applied to data on problem solving

Depressant Stimulant Placebo

Score Rank Score Rank Score Rank

55 9 73 15 61 11

0 1.5 85 18 54 8

1 3 51 7 80 16

0 1.5 63 12 47 5

50 6 85 18

60 10 85 18

44 4 66 13

69 14

Ri 35 115 40

x^2 0.05(2)=5.99

=10.36

=70.36 260

=

12

380

(2228.125) 260

=

12

19(20)

¢

352

7

1

1152

8

1

402

4

≤ 2 3(19 1 1)

H=

12

N(N 1 1)a

k

i= 1

R^2 i

ni

2 3(N 1 1)

Friedman’s rank
test fork
correlated
samples