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13.10 THE SPEARMAN RANK CORRELATION COEFFICIENT 733
we can follow the usual procedure of assigning the tied observations the mean of
the ranks for which they are tied and proceed with steps 2 to 6.
EXAMPLE 13.10.1
In a study of the relationship between age and the EEG, data were collected on 20 subjects
between ages 20 and 60 years. Table 13.10.1 shows the age and a particular EEG
output value for each of the 20 subjects. The investigator wishes to know if it can be
concluded that this particular EEG output is inversely correlated with age.
Solution:
1. Data. See Table 13.10.1.
2. Assumptions. We assume that the sample available for analysis is a
simple random sample and that both X and Y are measured on at least
the ordinal scale.
3. Hypotheses.
H 0 : This EEG output and age are mutually independent.
H A : There is a tendency for this EEG output to decrease with age.
Suppose we let a = .05.
TABLE 13.10.1 Age and EEG Output
Value for 20 Subjects
Subject
EEG Output
Number Age (X) Value (Y)
1 20 98
2 21 75
3 22 95
4 24 100
5 27 99
6 30 65
7 31 64
8 33 70
9 35 85
10 38 74
11 40 68
12 42 66
13 44 71
14 46 62
15 48 69
16 51 54
17 53 63
18 55 52
19 58 67
20 60 55