Ascertainment
Bias in a determination of the Primary
Sex Ratio:
a classroom demonstration
The Primary Sex Ratio
is the ratio of males to females in a
population: from first principles, it is expected to be 1:1.
One possible way to count this is to ask a group of people how
many brothers and sisters are in their families (including
themselves). For example, n=57 women in Biol2250 were asked to
give the counts for their families, with the results as
reported above. Note that the ratio of male : female
is heavily skewed towards women, almost 2:1 [to be
precise, 1.88:1] instead of the expected 1:1.
Why is this? Notice first that a census limited to women is
guaranteed to include a large number of women (n = 11 out of
57 respondents) that are "only children" (no boys, one
girl), and also a number of women from larger all-girl
families (a further 22 respondents). Such a census also
excludes the reciprocal family types, those with single or
all-boy makeup. The result is an ascertainment bias, a
miss-measurement of a phenomenon by an error in which the
measurement is made. A partial correction is to exclude
all respondents with no brothers [first four lines], which in
these data would give a male : female ratio of 50:56.
A bias in the other direction is expected from a census
limited to men.
[Homework:
Suppose the classroom measurement of primary sex ratio were
done for all undergraduates in the Department of Biology,
irrespective of sex. Would you expect a 1:1 ratio? Why or why
not? Hint: suppose you did this at the Royal Military
College.]