
Replicated Poin t Patterns and Designed Experiments 681
and n
2
people, respectively, had average heights of h
1
and h
2
, respectively, then the pooled average
height is (n
1
h
1
+ n
2
h
2
)/(n
1
+ n
2
), the weighted average of th e group averages with w eights p ropor-
tional to size of group. This is the corre ct calculation because n
i
h
i
is the total he ight in group i, so
the numerator n
1
h
1
+ n
2
h
2
is the total height of all p eople in the two grou ps, while the de nominator
n
1
+ n
2
is the total numbe r of people.
In general if the e stimator of our desired quantity R is a ratio
b
R =
b
Y/
b
X, and we ca lculate esti-
mates
b
R
1
,...,
b
R
m
from m different datasets, the natural ...