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The Red Cross, AIDS, and LSAT Practice

I've been having a bit of an argument about statistics with guest blogger Beth Plocharczyk over at Crescat Sententia. The argument reminds me of one of those fancy reasoning questions on the LSAT, so I'll go into it here.

She's arguing that because it's easy to test for HIV-infected blood six-months post-infection, only the number of new HIV infections matters. She then states:

"According to the CDC, a full 33% of new HIV infections are in men and women engaging in heterosexual intercourse. (42% are from men sleeping with men, 10% from IV drug users). 54% of new HIV infections in the U.S. are in African-Americans. I don't see them stricken from the bone marrow donation eligibility list."

As you can see, her argument is that it is irrational for the Red Cross to pre-screen applicants by asking if they have had male homosexual contact, and to allow heterosexuals to donate blood or bone marrow while rejecting male homosexuals. (Or indeed, while allowing African Americans to donate.)

This may be so on other grounds--it's a policy debate I don't want to touch, frankly--but you cannot reach that conclusion based upon the statistics above. Indeed, doing so would be fundamentally 'irrational.'

I'll explain why tomorrow in the unlikely event that no one gets it, but in the meantime any of you studying for the LSAT are welcome to take a crack at it in the comments section.

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Well, the obvious problem with this is that the two sample populations are different. Yes, maybe 1/3 of the population "new HIV cases" are heterosexual... But what we care about in this case is the probability that a randomly selected heterosexual has HIV. So we're looking at the population "all heterosexuals". The fact that "all homosexuals" (or more accurately "all male homosexuals who are open about having had male-male intercourse) is a much smaller population means that the estimated risk of a randomly selected man in that category being an undiagnosed HIV case is very much higher. Then again, stats is a sufficiently poorly understood thing amongst the electorate that one has to remember even a false argument based on bogus statistical reasoning is likely to have a big impact. There's very little one can do about it.
Give the man a gold star. ;)
Played around with the statistics a bit Here.
Ok .... First, the Black community HIV is almost all transmitted by people with open genital lesions -- and constitutes a significant part of the heterosexual transmission, all by a group that is screened out by other questions and that, for the most part, does not donate blood. (I assume, without foundation, that one should only screen donors, not the population at large). Second, guess we really don't need a second part. Yes, the other various arguments do apply, and the analysis is ok, but observational data, to follow up statistical gathering, is important (assuming you don't have enough data for cluster analysis to explain it to you without the observations). So ... Should you screen a group that does not have other markers? (i.e. heterosexual HIV transmitters usually have open genital lesions -- screened for under active infections, etc.)(homsexual HIV transmitters that have them are screened out, those who do not remain). Should you be concerned about screening groups who otherwise do not donate blood (the open genital lesion group tends to be of the lowest social-economic group and tends not to ever have donated blood)? Probably not. But, I wouldn't doubt that people will use the numbers to attack public health.
Anthony- I saw the same thing, and I was appalled by the lack of statistical understanding...What, homosexual men compromise 2-5% of the entire population and are 42% of the total population, while heterosexual men comprise the other 43-46% an yet are 33% of the cases? If the two groups were "just as likely" heterosexual men should be getting about 10 times the number of new infections instead they are getting LESS! Using some very amatuer numbers the statistics she sites shows homosexual men to be at about 16 times greater risk. Then, the other blogger complains about donating with her body because she might faint...UH WELL YEAH...It's not a your body issue, it's a liability issue...if you pass out (and die or not) the likelyhood of suit has just skyrocketed.

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