This is incorrect. The study does not indicate that 28% of Catholic women have had abortions, it indicates that 28% of the women WHO HAVE had abortion are Catholic. The correct interpretation of this statistic is out of 100 women who have aborted, 28 would be Catholic. Very different.
PMFJIH, but I love statistics, and this is troubling. I’m not sure which is worse.
Here’s what I mean.
Let’s say the chance of an woman with abortion being Catholic is .28
That is, probability of Catholic, given they had an abortion, is .28
Symbolically, I’ll write: p(C g A) = 0.28
Now, what is interesting is how many Catholic women have had an abortion.
That is: p(A g C) = ???
So which is worse, and under what conditions? So to symbolize the question “are there more of the Catholics who had abortions, than the number of abortions that are Catholic?” we ask:
Code:
is: p(A g C) > p(C g A) ??
Dividing both sides by p(C g A) I get:
Code:
p(A g C)
-------- > 1 ???
p(C g A)
Now, using a probability formula we can write:
p(A g C) = p(A AND C) / p(C)
and
p(C g A) = p(A AND C)/p(A)
With a little algebra magic, that gives me:
Code:
p(A g C) / p(C g A) = p(A) / P(C)
Where p(A) is the percentage of all women who have had abortion, and p(C) is the percentage of all women who are Catholic.
CONCLUSION:
If there are more women who have had abortions than there are women who are Catholic, then p(A g C) > p(C g A) which means that P(A g C) > 28%.
If there are more women who are Catholic than have had abortions, then p(A g C) < p(C g A) which means that P(A g C) < 28%.
TRANSLATION:
So to know which is worse, we have to know whether there are more: a) women who are Catholic, or b) women who have had abortions.
If there are more women who have had abortions than there are Catholic women, then the percentage of Catholic women who have abortion is greater than 28%.
If there are more women who are Catholic than women who have had abortions, then the percentage of Catholic women who have abortion is less than 28%.
Alan