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narkee

So P(jobless|PhD) = 0.017, whereas P(jobless) = 0.066

According to Baye's Theorem, the P(PhD|jobless) = P(jobless|PhD)*P(PhD)/P(jobless)

Where according to [1], P(PhD) = 0.01 (for all PhDs) so assuming roughly half are science, P(PhD) = 0.005, and we get

P(PhD|jobless) = 0.0013, or 0.13%, which means that roughly 1 out of every 1000 jobless people has a PhD.

[1]http://factfinder.census.gov/servlet/QTTable?_bm=y&-geo_...

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But who cares about P(PhD|jobless)? P(jobless|PhD) is important; it's a measure of how much job security a PhD leads to. But P(PhD|jobless) is only important if you're a jobless PhD and you want to know what your chances of finding someone else who's survived grad school in the unemployment line. I wouldn't know how to interpret "1 out of every n jobless people has a PhD"; the first thing I'd ask is "what proportion of all people have a PhD", and then essentially run things through a crude mental version of Bayes' theorem.

(I have a PhD. In probability.)

P(jobless|PhD) is important; it's a measure of how much job security a PhD leads to.

No, it is a measure of how much job security a PhD is correlated with. I believe that the qualities that lead to one being able to complete a PhD are positively correlated with being able to get and hold a job. Therefore you need to restrict to just those people you think could get a PhD to figure out how much the PhD helps or hurts you.

I stand corrected. This is exactly what I'd tell my students if they had made the mistake I made.

But then you wouldn't get to use Bayes' theorem in a public setting.

Despite it's practicality, I for one enjoyed the statistic.

Bayes' theorem states that P(A|B) = P(B|A) * P(A) / P(B), so in this case it says P(PhD|jobless) = P(jobless|PhD) * P(PhD) / P(jobless). It seems that you stated it incorrectly but used the correct version in the computation (the incorrect gives 0.2244).

Right, good catch there - it was a sloppy typo.

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