Testing random

[Steven D'Aprano]

On Wed, 17 Jun 2015 08:33 pm, Laura Creighton wrote:

> Stick to dice.  Stay away from children.  One thing we know of, for sure,
> is that certain breeding pairs are more likely to produce males, and
> others are more likely to produce females.  We will ignore  those born who
> are of indeterminate sex, for this discussion.
[...]
> All we know is that notion that every human birth has a 50/50
> chance of being male or female is wrong.


This is certainly true. In human beings, certain families tend to run with
all girls or all boys, more often than you would expect from just chance.
This suggests that at least some people are predisposed to have boys, or
girls, rather than equal chance of both.

Oh, and those intersex children? Surprisingly common: Wikipedia suggests
that according to some definition, as many as 1.7% (about one in sixty)
newborns may have ambiguous genitalia, or something other than XY/XX
chromosomes. The frequency of non-XX, non-XY children alone is 3 in 5000.

While it is important to know these facts, to understand that human beings
(like other mammals) do not divide neatly into two distinct sexes, I think
that's a complication not really necessary for basic statistics classes. As
a first approximation, the idea that the proportion of boys and girls are
both roughly equal at 1/2 isn't too far off the truth.

After all, we make other simplifying assumptions about probability too.
There are magicians who are capable of forcing coins to land the required
way up, and somebody once built a machine capable of tossing a coin with
the precise equal force and velocity every single time. Dice are rarely
unbiased, and neither are roulette wheels. Nevertheless, we ignore those
factual biases for the sake of simplicity.


> In human beings, as well as a whole lot of animal species, infant-and-
> chidhood mortality is not sex neutral.  More baby boys die than baby
> girls.

Correct. And more Y sperm die than X sperm. Together, these two factors lead
to a small but real bias towards girl children, at least on countries that
don't practice wide-spread sex-specific abortion.


> But when you look at breeding age men and women you will find 
> that the ratio is a lot closer to 50/50 than the birth age ratio.
> Human beings, as a population currently produce more males than
> females.

Surely that depends on where (and when) you are?

I know that, today, both India and China both abort far more female fetuses
than male ones, leading to a large excess of men. But in countries that
don't practice selective abortions, my understanding is that there is a
small excess of women at virtually all ages, especially among the elderly.
Men tend to die earlier than women in every age bracket.



-- 
Steven