How do you figure an alleged/anecdotal 50% contraception failure rate is not a huge difference when compared with an empirically verified >95% success rate ???
Because the 50% is not "failure rate". It is the share of women who used contraception among all the women who had abortions. These two proportions measure two very different things, so I do not understand why it is a surprise that there would be a "huge difference" between the two.
First, >95% is on a yearly basis, so for a month it's more like 0.5% failure rate.
WUT?
Wouldnt it be
harder to hit the jackpot failure in just 1 month as opposed to having 12 attempts to fail over an entire year.
"Wut" yourself. That's why I set the monthly failure rate (0.5%) at 1/10 of the annual failure rate (~5%). I did not bother with 1/12 or binomial distribution or anything because this is just a proof of concept, so rough calculations are ok.
We aren't talking about ALL sexually active women whose contraception failed. We're only talking about the ones who decided to have an abortion.
Sure. But the latter is a subset of the former.
...and who decided to answer a survey.
I do not care about the survey part. Sampling and surveying doesn't enter into my argument, because I am doing a (rough) population modelling to show that there is no contradiction between saying that contraception has e.g. a 95% success rate while 50% of women who chose to have an abortion had used contraceptives. In fact, for the purposes of this discussion, I do not even care if the 50% figure is anywhere near true. I just care to show you that it is feasible that it would be true and that there is no contradiction between these two proportions that are measuring very different things.
...asking whether they (think they) used contraception (correctly) sometime in the month before they (amazingly) got pregnant despite their (diligent) efforts not to get pregnant
Nothing amazing about that.
This is vastly different to the empirical evidence based clinical studies into 95%+ effectiveness of contraceptives.
Because they measure vastly different things. Duh!
Women on birth control are MORE likely to get pregnant and seek an abortion? Since when?
A woman on birth control is more likely to seek abortion
IF she gets pregnant.
What do you mean?
l'm asking how these outlier women managed to hit the statistically improbable pregnancy jackpot that other women on (95% effective birth control) somehow avoided by using the exact same birth control.
They may be different reasons for failure. User error (the old "perfect use" vs. "typical use"). Rhea already mentioned antibiotics, but there can also be intrinsic variances in how different bodies respond to things like exogenous hormones. There is the mechanical failure of barrier methods, and lastly, sheer luck of the draw.
But the point is, that if many women use contraception, there will be many women, on aggregate, whose contraception fails. 0.5% of a million is still 5,000 women. If 40% of them choose to abort, that's 2,000 abortions. If, at the same time, 200,000 sexually active women do not use contraception, maybe 10,000 will get pregnant. If 20% of them choose to abort, that's also 2,000 abortions. 50-50 ratio, despite very effective birth control.
These numbers are just examples, of course.
Those aren't 'variables' those are irrelevant red herrings.
They are not red herrings, they are highly relevant, as I shall show.
How do you reconcile the (Baysean) gap between such a small number of survey respondents and such a large number of deliberate abortions each year?
Oh, you've heard of Bayes. Good. Then let me elaborate.
B = birth control
A = abortion
G = pregnant for "gravida"
P(B|A) - this is the probability the woman was on birth control, given that she had an abortion. This is the 50% figure.
P(G|B) - this is the probability the woman gets pregnant if she is on birth control, in this case over the course of a month. This is the 0.5% figure.
As you see, these are very different variables, and so it should not be surprising that they have very different values. So much is trivial.
These variables are connected though. What connects them are other variables (not red herrings) such as prevalence of birth control P(B), the likelihood a woman would abort if pregnant P(A|G) or even the likelihood that a woman will get pregnant in a given month P(G).
The way all these variables are related is Bayes' Theorem.
P(B|A) = P(A|B) * P(A) / P(B)
As you can see right away, the higher the prevalence of birth control use in a population, the higher P(B|A) will be.
Probability of abortion P(A) can be calculated by P(A)=P(A|G) * P(G) / (P(G|A). But since P(G|A)=1, it simplifies to P(A)=P(A|G)*P(G)
So our variables are nicely connected.
P(B|A) = P(A|B) * P(A|G) * P(G) / P(B)
You can continue going. For example, P(G) = P(G|B) * P(B) + P(G|¬B)*P(¬B). I.e. likelihood of a woman getting pregnant is dependent on prevalence of birth control use, birth control failure rate P(G|B) and also the likelihood of pregnancy if no birth control is used P(G|¬B).
You can do the same analysis for P(A|G) and P(A|B). This is left for you as a homework exercise.