Introductory Biostatistics

A 95% confidence intervalðrl;ruÞfor the coe‰cient of correlation under inves-
tigation is obtained by transforming the two endpoints,

zl¼z
 1 : 96

ffiffiffiffiffiffiffiffiffiffiffi

1

n
 3

r

and

zu¼zþ 1 : 96

ffiffiffiffiffiffiffiffiffiffiffi

1

n
 3

r

as follows to obtain the lower endpoint,

rl¼

expð 2 zlÞ
 1

expð 2 zlÞþ 1

and the upper endpoint of the confidence interval for the population coe‰cient
of correlation,

ru¼

expð 2 zuÞ
 1

expð 2 zuÞþ 1

(In these formulas, ‘‘exp’’ is the exponentiation, or antinatural log, operation.)

Example 4.13 The data shown in Table 4.10 represent systolic blood pressure
readings on 15 women. The descriptive analysis in Example 2.9 yieldsr¼ 0 : 566
and we have

z¼

1

2

ln

1 þ 0 : 566

1 
 0 : 566

¼ 0 : 642

zl¼ 0 : 642 
 1 : 96

ffiffiffiffiffi

1

12

r

¼ 0 : 076

TABLE 4.10

Age (x) SBP (y) Age (x) SBP (y)

42 130 80 156

46 115 74 162

42 148 70 151

71 100 80 156

80 156 41 125

74 162 61 150

70 151 75 165

80 156

ESTIMATION OF CORRELATION COEFFICIENTS 169