Statistical Methods for Psychology

was a well-known economist. This test is closely related to a standard repeated-measures

analysis of variance applied to ranks instead of raw scores. It is a test on the null hypothe-

sis that the scores for each treatment were drawn from identical populations, and it is espe-

cially sensitive to population differences in central tendency.

Assume that we want to test the hypothesis that the judged quality of a lecture is re-

lated to the number of visual aids used. The experimenter obtains 17 people who frequently

give lectures to local business groups on a variety of topics. Each lecturer delivers the same

lecture to three different, but equivalent, audiences—once with no visual aids, once with a

few transparencies to illustrate major points, and once with transparencies and flip charts

to illustrate every point made. At the end of each lecture, the audience is asked to rate the

lecture on a 75-point scale, and the mean rating across all members of the audience is taken

as the dependent variable. Since the same lecturers serve under all three conditions, we

would expect the data to be correlated. Terrible lecturers are terrible no matter how many

visual aids they use. Hypothetical data are presented in Table 18.9, in which a higher score

represents a more favorable rating. The ranking of the raw scores within each participant

are shown in parentheses.

Section 18.10 Friedman’s Rank Test for kCorrelated Samples 685

Table 18.9 Hypothetical data on rated quality of lectures

Number of Visual Aids

Lecturer None Few Many

1 50 (1) 58 (3) 54 (2)

2 32 (2) 37 (3) 25 (1)

3 60 (1) 70 (3) 63 (2)

4 58 (2) 60 (3) 55 (1)

5 41 (1) 66 (3) 59 (2)

6 36 (2) 40 (3) 28 (1)

7 26 (3) 25 (2) 20 (1)

8 49 (1) 60 (3) 50 (2)

9 72 (1) 73 (2) 75 (3)

10 49 (2) 54 (3) 42 (1)

11 52 (2) 57 (3) 47 (1)

12 36 (2) 42 (3) 29 (1)

13 37 (3) 34 (2) 31 (1)

14 58 (3) 50 (1) 56 (2)

15 39 (1) 48 (3) 44 (2)

16 25 (2) 29 (3) 18 (1)

17 51 (1) 63 (2) 68 (3)

30 45 27

=10.94

=

12

204

1365422204

=

12

17132142

1302145212722231172142

x^2 F=

12

Nk 1 k 112 a

k

i= 1

R^2 i 23 N 1 K 112