Ben Shapiro and others often cite a UCLA study which claimed
that 45% of transwomen try to commit suicide to “prove” that transgender people
are mentally ill and that we should not reinforce their “delusion”.   A big problem with their line of reasoning is
that  they generalize a single survey
based on a self-selected convenience sample to a whole population.  One could dismiss that as some kind of pseudo
intellectual argument based on feelings and facts don’t care about
feelings. 

Math is a fact.  If
45% of transgender people, try to commit suicide at some point in our lives
then on average in any given year about that many will make the attempt.  Assuming we are as good at killing ourselves
as anyone else, and that 0.01% of births will result in a person who will grow
up to come out as trans this is a plot of how transgender population would vary
with time if that number was naively generalizeable.

As you can see it leads to a halving of the transgender
population every 50 years.  Clearly that
does not happen! Ergo, naively generalizing the finding of that study and using
it to argue on how a whole group of people will behave is not valid. 

He can argue other facts.  Chromosomes,
etc… but Ben Shapiro and his minions need to retire this one or stop claiming
to be unbiased.

I wrote this all up as a paper which will have a DOI after a period of days being open for comments.