OK, I think I might be getting it. You can tell me if this sounds right. This is the example I was thinking of (from the wiki you linked on alpha errors). The false positives are higher in the US than in Northern Europe, not because of the equipment or procedure used, but because of the stringency of the test. Because of that, false positives might be high for a certain set of data where fMRI technology is used but not for all data where fMRI technology is used.Perhaps the most widely discussed false positives in medical screening come from the breast cancer screening procedure mammography. The US rate of false positive mammograms is up to 15%, the highest in world. One consequence of the high false positive rate in the US is that, in any 10-year period, half of the American women screened receive a false positive mammogram. False positive mammograms are costly, with over $100 million spent annually in the U.S. on follow-up testing and treatment. They also cause women unneeded anxiety. As a result of the high false positive rate in the US, as many as 90–95% of women who get a positive mammogram do not have the condition. The lowest rate in the world is in the Netherlands, 1%. The lowest rates are generally in Northern Europe where mammography films are read twice and a high threshold for additional testing is set (the high threshold decreases the power of the test)
It could be that, but there are also procedural factors as in the one where you have cited. For example, to my knowledge (at least in Poland) when you are tested for HIV or other infections that can linger undetected they take two samples. That way you need a follow-up only if both of them show different results, since this is how you can usually catch false-positive. There is still a fraction of people with both samples being false-positives, but it is order(s) of magnitude less than with one sample. This actually a great example of Bayesian Process, one of the more important concepts in probability and applied sciences. I can try and write an example, but I think that it will save both of us some time if I'll just link this: and here is some extra footage that is also relevant: I can explain it further if you would have follow-up question after video, so don't take it as me brushing you off ;).