That footnote is an important point. People need to learn to use odds ratios. Though I think that with odds ratios, the equivalent increase is to 1 - ((1/99) x ((1/99) / (10/90))) = 99.908%, not the intuitive-looking 99.9%.
Also, the interpretation of odds ratios is often counter-intuitive when comparing test groups of different sizes. If P(X) >> P(~X) or P(X) << P(~X), the probability ratio P(W|X) / P(W|~X) can be very different from the odds ratio [P(W,X) / P(W,~X)] / [P(~W,X) / P(~W,~X)]. (Hope I’ve done that math right. The odds ratio would normally just use counts, but I used probabilities for both to make them more visually comparable.)
That footnote is an important point. People need to learn to use odds ratios. Though I think that with odds ratios, the equivalent increase is to 1 - ((1/99) x ((1/99) / (10/90))) = 99.908%, not the intuitive-looking 99.9%.
Also, the interpretation of odds ratios is often counter-intuitive when comparing test groups of different sizes. If P(X) >> P(~X) or P(X) << P(~X), the probability ratio P(W|X) / P(W|~X) can be very different from the odds ratio [P(W,X) / P(W,~X)] / [P(~W,X) / P(~W,~X)]. (Hope I’ve done that math right. The odds ratio would normally just use counts, but I used probabilities for both to make them more visually comparable.)