Introductory Biostatistics

4. Australian females of Aboriginal origin

n 4 ¼ 54

x 4 ¼
 0 : 24

s 4 ¼ 0 : 18

To proceed with a one-way analysis of variance, we calculate the mean of
the combined sample:

x¼

ð 89 Þð
 0 : 20 Þþð 107 Þð
 0 : 26 Þþð 63 Þð
 0 : 13 Þþð 54 Þð
 0 : 24 Þ

89 þ 107 þ 63 þ 54

¼
 0 : 213

and

SSB¼ð 89 Þð
 0 : 20 þ 0 : 213 Þ^2 þð 107 Þð
 0 : 26 þ 0 : 213 Þ^2

þð 63 Þð
 0 : 13 þ 0 : 213 Þ^2 þð 54 Þð
 0 : 24 þ 0 : 213 Þ^2

¼ 0 : 7248

MSB¼

0 : 7248

3

¼ 0 : 2416

SSW¼ð 88 Þð 0 : 18 Þ^2 þð 106 Þð 0 : 13 Þ^2 þð 62 Þð 0 : 17 Þ^2 þð 53 Þð 0 : 18 Þ^2

¼ 8 : 1516

MSW¼

8 : 1516

309

¼ 0 : 0264

F¼

0 : 2416

0 : 0264

¼ 9 : 152

The results are summarized in an ANOVA table (Table 7.7). The resultingF
test inducates that the overall di¤erences between the four population means is
highly significantðp< 0 : 00001 Þ.

Example 7.12 A study was conducted to test the question as to whether ciga-
rette smoking is associated with reduced serum-testosterone levels in men aged
35 to 45. The study involved the following four groups:

ONE-WAY ANALYSIS OF VARIANCE 267