Introductory Biostatistics

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:

1. Data are summarized separately to obtain

sample 1: n 1 ;x 1 ;s 12

sample 2: n 2 ;x 2 ;s 22

2. 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

3. 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