Introductory Biostatistics

ln 8: 4 
 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

30

þ

1

10

þ

1

30

þ

1

84

r

¼ 1 : 30

to

ln 8: 4 þ 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

30

þ

1

10

þ

1

30

þ

1

84

r

¼ 2 : 96

and hence the corresponding 95% confidence interval for the population odds
ratio is (3: 67 ; 19 :30), indicating a very high risk elevation for Rely users.

4.5 ESTIMATION OF CORRELATION COEFFICIENTS

Similar to the case of the odds ratio, the sampling distribution of Pearson’s
coe‰cient of correlation is also positively skewed. After completing our
descriptive analysis (Section 2.4), information about a possible relationship
between two continuous factors are su‰ciently contained in two statistics: the
number of pairs of datan(sample size) and Pearson’s coe‰cient of correlation
r(which is a number between 0 and 1). Confidence intervals are then derived
from the normal approximation to the sampling distribution of

z¼

1

2

ln

1 þr

1 
r

with variance of approximately

VarðzÞ¼

1

n
 3

Consequently, an approximate 95% confidence for the correlation coe‰cient
interval, on this newly transformed scale, for Pearson’s correlation coe‰cient is
given by

zG 1 : 96

ffiffiffiffiffiffiffiffiffiffiffi

1

n
 3

r

TABLE 4.9

Brand Cases Controls

Rely 30 30

Others 10 84

Total 40 114

168 ESTIMATION OF PARAMETERS