## How not to do statistics

Good Math, Bad Math lampoons some moonbat statistics from an HIV denier who either has the mathematical aptitude of a tree or is lying in order to advance a pernicious agenda, take your pick.

Most, if not all, of these adolescents must have acquired HIV from perinatal infection for the following reasons: sexual transmission of HIV depends on an average of 1000 sexual contacts, and only 1in 250 Americans carries HIV (Table 1). Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission. It follows that probably all of the healthy adolescent HIV carriers were perinatally infected, as for example the 22-year-old Kimberly Bergalis (Section 3.5.16).

Both of these numbers are a bit too high: the UNDP puts the USA’s 15-49 HIV prevalence at 0.6%, or 1/167, and a significant number of HIV cases are transmitted via anal sex, for which the probability of infection is 1 in 200, and needle sharing, for which it’s 1 in 150 (link).

But either way, it’s a classic example of the Argumentatum ad Numeros (I’d add an adjective, if I knew the Latin 1st/2nd declension plural accusative adjective for “Large” or “Huge”): concoct fantastic large numbers, multiply them together, and assert that the probability of something happening is 1 in that number.

In fact, going by the denier’s statistics, for Americans to get HIV, only 1 in 250 needs to get infected, so in fact the average American needs to have sex 1,000 times with people of unknown status. Which isn’t out of the ordinary, given that shockingly low numbers of Americans regularly use condoms or even insist that their SOs be tested.

In the context of the original assertion, the military, it’s even easier: about 1 in 4,000 American military recruits aged 17-19 are HIV+, reducing the number of sexual contacts necessary per American teenager to 64. Which, again, is perfectly possible, especially if anal sex is involved, reducing the number of contacts necessary to 13.