
147More on Inferential Statistics
a high value of F. In contrast, the example in Figure 5.4b shows little difference among means and
not exceeding the within variability. In this case, we expect to get a value of F closer to 1.
When sample size varies by sample, we have an unbalanced ANOVA. The overall variance
(within) can be calculated from the pooled sample variances. The pooled sample variance is a
weighted average of the sample variances where the weights are the degrees of freedom
s
ns
n
ns
nm
n
p
ii
i
m
i
i
m
ii
i
m
i
i
m
i
2
2
1
1
2
1
1
1
1
1
=
−
−
=
−
−
=
−
=
=
=
=
()
()
() ( 11
2
1
)s
Nm
p
i
i
m
=
−
(5.17)
where
n
i
is size of the ith sample
=
is the total number of observations ...