Introductory Biostatistics

SEðx 1 
x 2 Þ¼ 4 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

25

þ

1

26

r

¼ 1 : 39

It follows that

t¼

47 : 5
37 : 5

1 : 39

¼ 7 : 19

indicating a significant di¤erence between joggers and nonjoggers (at 49 de-
grees of freedom anda¼ 0 :01, the tabulatedtvalue, with an upper tail area of
0.025, is about 2.0).

Example 7.6 Vision, or more especially visual acuity, depends on a number of
factors. A study was undertaken in Australia to determine the e¤ect of one of
these factors: racial variation. Visual acuity of recognition as assessed in clini-
cal practice has a defined normal value of 20/20 (or zero in log scale). The fol-
lowing summarized data on monocular visual acuity (expressed in log scale)
were obtained from two groups:

1. Australian males of European origin

n 1 ¼ 89

x 1 ¼
 0 : 20

s 1 ¼ 0 : 18

2. Australian males of Aboriginal origin

n 2 ¼ 107

x 2 ¼
 0 : 26

s 2 ¼ 0 : 13

To proceed with a two-samplettest, we have

s^2 p¼

ð 88 Þð 0 : 18 Þ^2 þð 106 Þð 0 : 13 Þ^2

194

¼ð 0 : 155 Þ^2

SEðx 1 
x 2 Þ¼ð 0 : 155 Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

89

þ

1

107

r

¼ 0 : 022

COMPARISON OF TWO MEANS 255