leading to
d¼average di¤erence
¼
31
12
¼ 2 :58 mmHg
s^2 ¼
185 ð 31 Þ^2 = 12
11
¼ 9 : 54
s¼ 3 : 09
SEðdÞ¼
3 : 09
ffiffiffiffiffi
12
p
¼ 0 : 89
With a degree of confidence of 0.95 thetcoe‰cient from Appendix C is 2.201,
for 11 degrees of freedom, so that a 95% confidence interval for the mean dif-
ference is
2 : 58 Gð 2 : 201 Þð 0 : 89 Þ¼ð 0 : 62 ; 4 : 54 Þ
This means that the ‘‘after’’ mean is larger than the ‘‘before’’ mean, an increase
of between 0.62 and 4.54.
In many other interventions, or in studies to determine possible e¤ects of a
risk factor, it may not be possible to employ matched design. The comparison
of means is based on data from two independent samples. The process of esti-
mating thedi¤erence of meansis summarized briefly as follows:
- Data are summarized separately to obtain
sample 1: n 1 ;x 1 ;s 12
sample 2: n 2 ;x 2 ;s 22
- The standard error of the di¤erence of means is given by
SEðx 1 x 2 Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s^21
n 1
þ
s 22
n 2
s
- Finally, a 95% confidence interval for the di¤erence of population means,
m 1 m 2 , can be calculated from the formula
ðx 1 x 2 ÞGðcoe‰cientÞSEðx 1 x 2 Þ
ESTIMATION OF MEANS 159