This is what justified our taking in the data that 90% of sick patients and 30% of healthy patients would get positive test results \(a black tongue depressor\), and summarizing this as the likelihood ratio \(3 : 1\), which would have been the same ratio if 45% of sick patients and 15% of healthy patients got positive test results\. Note that this likelihood ratio, "Sick patients are individually three times as likely as healthy patients to get positive test results", is not the same concept as "There are 3 sick patients with positive test results for each 1 healthy patient with a positive test result\."
Would love to see some kind of footnote or popup that answers the question, "why not?"