Yet some people are arguing, based on this data, that the HPV vaccine is not effective. So let's see if we can tell whether these results are statistically significant.

I'm terrible at statistics, but BMJ's "Statistics at Square One" has some handy tips about Chi squared tests. Let's try them out.

First, construct a null hypothesis:

Null hypothesis: vaccination does not reduce prevalence of HPV16Then, organize the results as described in section "Fourfold tables":

HPV16+ HPV16- total vaccinated 58 (720-58)=662 720 unvaccinated (428-58)=370 (4914-720-428-58)=5564 4196 total 428 4493 4914Then apply the formula (here, I use Python to do it, but an online chi-squared calculator works great, too),

a = 58.0 b = 662.0 c = 428.0 d = 4493.0 print ((a*d - b*c)**2.0 * (a + b + c + d)) / ((a+b)*(c+d)*(b+d)*(a+c))I get chi^2 is about 0.33.

Plugging chi^2 = 0.33 and degrees-of-freedeom = 1 into a P-value table says

P = 0.5657and thus the results are not statistically significant. (Rather far from it; P has to be under 0.05 before it's barely significant, and below 0.01 for strong significance.)