Also interesting how sample size only matters sometimes. In that study:
"The autism group had 33 kids total. Of these, 9 of 31 (29%) were given the HepB vaccine. Compare this to 1,258 of 7,455 (17%) of the non-autism group who were given the HepB."
That is well below the threshold necessary to reliably provide statistical significance.
Wow, I didn't realise/remember the sample size was quite that small (we may have talked about this one before, but i don't remember right now).
Standard statistical counting error is the square root of the top number, so that's a 10% error on the fraction of autistic boys who had had hep b (and in fact that's an underestimate of the error in very small samples). So the two fractions differ by only just more than 1 sigma (1 times the statistical error). In normal distributions this will happen 32% of the time even if there is no difference in the two samples.
So yeah, not a very convincing difference.