It would seem there are some major confounding factors here not detailed in the article.
1) The population doesn't reflect a realistic test--if the overall incidence is 0.3%, but the sample size had 50% (or more given her adamant hit), then we need to know whether she was expecting more.
2) More importantly, the incidence in men is 1.49x that of women [1], and age also plays a factor. So given that the sample is already skewed towards a higher incidence of positives, the gender differences might be factored into her senses--especially since it was her husband who was her training set. With n=12, it would be very easy for the probabilities/priors to be much different than truly random. (E.g., the learning function of her nose might be "men + people over 65" which happened to match up with the test and control group quite well.") Or it could tune into medication used to treat the disease.
If you look at the Bayesian analyses and the frequentist analyses assuming she knew how many AD shirts there would be, you'd see that point 1 doesn't matter. We can statistically test this without the need to make her sniff 1000's of shirts.
Point 2 is interesting though, and the first thoughtful criticism I've seen in the thread. What if she's both a bit lucky, and also picking up on some correlated marker like age/gender?
1) The population doesn't reflect a realistic test--if the overall incidence is 0.3%, but the sample size had 50% (or more given her adamant hit), then we need to know whether she was expecting more. 2) More importantly, the incidence in men is 1.49x that of women [1], and age also plays a factor. So given that the sample is already skewed towards a higher incidence of positives, the gender differences might be factored into her senses--especially since it was her husband who was her training set. With n=12, it would be very easy for the probabilities/priors to be much different than truly random. (E.g., the learning function of her nose might be "men + people over 65" which happened to match up with the test and control group quite well.") Or it could tune into medication used to treat the disease.
Great if true, but I am skeptical.
[1] http://jnnp.bmj.com/content/75/4/637.full