The question you are asking here is more complicated than it first
appears. For this comment I will refer to a working paper by the Max
Planck Institute for Demographic Research (MPIDR) published in May
2002, which considered the gender preferences of German parents. The
link is:
http://www.demogr.mpg.de/papers/working/wp-2002-017.pdf
Firstly to correct an error in your question. If you assume that the
events are independent, the chance of having a boy is 51%. This is
simply because there are 51 male babies born for every 49 female ones.
This small difference becomes statistically insignificant, however,
when you consider more than one baby.
Now we must look at the two babies that are already born.
Statistically, the chances of having two boys are 25%, as demonstrated
by the MPIDR study. This matches the theory because:
Chance of baby A being male: 50%
Chance of baby B being male: 50%
Chance of both being male = Chance A x Chance B = 50% x 50% = 25%.
So we can see that there is no statistical evidence for the second
child's gender to depend at all on the first.
Now we encounter another problem. There are simply no studies (or at
least none that I can find with much searching) that give proper
statistics for the gender of 3 or more successive babies. And we have
to consider the basis of the demographic data that could be collected
for such a study.
Take your example. The parents have two babies (both boys) and are
looking for another. Why? Either because they want to increase the
size of their family further, or because they want a little girl!
Let's say they have a third boy. Will this increase the chances that
they will try for a fourth child? And if the fourth is a boy too,
then when will they stop trying?
If this is true then the results of such a study would be skewed
because in some cases the sample data would be families that have
deliberately continued having children in order to have at least one
child of each gender.
So the question is, do parents continue trying for more babies (after
the second child) in order to have one of each gender? The MPIDR
study suggests that in Germany they do not. In the summary on pages
15-16, we read:
"There is no such manifested gender preference when the progression
from the second to the third child is considered. Both results
corroborate the findings for (West) Germany reported in Hank and
Kohler (2000). The general preference for an ultimate sex mix ? which
parents exhibit when being asked about their favoured sex composition
? is obviously not sufficiently strong to induce an actual revision of
family size goals and higher fertility, even if all previous children
are of the same sex (either boys or girls)."
The Hank & Kohler (2000) paper referenced concerns only parents'
preferences and not the statistical outcomes of the ensuing
pregnancies. However Hank & Kohler do note important and
statistically significant differences in parents gender preferences
(i.e. whether they want a mixed family or not) across different
countries in western Europe, and so this calls into question the
validity of the MPIDR study's conclusion when countries other than
Germany are considered.
The Hank & Kohler paper can be found at:
http://www.demographic-research.org/volumes/vol2/1/2-1.pdf
So we can see that research, should anyone take it on, would need to
address two questions:
1. Did the parents conceive another child in order to attempt to
balance their family with a mix of both sexes?
2. Is the ratio of genders of the third and fourth child different
where both previous children are of the same sex?
Of course, as you hint in your clarification, theories abound, but
with there being no statistically significant difference for the
gender of the second child based on the first, I find it unlikely that
a statistically significant difference will be found with the third.
However, if there is a difference we would expect it to by magnified
with the fourth child, perhaps to a level where it becomes
significant!
Notes:
Quick "definition" of statistical significance. This is normally
taken to mean a result whose statistical likelihood of occurring falls
outside the centre 90-percentile of a normal distribution of possible
results. This is the standard measure of statistical significance.
One good place to get this data would be from a population census,
though that would not include data regarding the parents' basis of
their decision to have a further child. The UK Office of National
Statistics (www.statistics.gov.uk) holds the census data for the UK
and there are counterparts in other countries. Currently the ONS has
not done published any research of this nature. The bulk of their
child research is contained within this report:
http://www.statistics.gov.uk/Children/downloads/child_pop.pdf
Another thing that has not been considered here is multiple births.
With 12 in every 1000 births being of more than one baby, this will
make a difference too.
Canters. |
