2.1 Grunderschnauzer disease

You are informed by your doctor that you have tested positive for Grunderschnauzer disease. You may ask one question to help you figure out whether you really have it. What do you want to know (choices are sensitivity, specificity, prevalence, predictive value, etc.)?

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You would want to know the positive predictive value (or posterior probability), because what you want to know is “What is the probability that I actually have Grunderschnauzer disease given that I have a positive test?”

The most common wrong answer to this question is specificity. But unless specificity is 100%, knowing it is not sufficient to know whether your result is a true positive or a false positive. Since you have never heard of this disease, you might guess that it is rare, in which case even if the specificity were 99% you probably would not have it.

(Of course you also want to know what Grunderschnauzer disease is, but that is not the question. For the record, it does not exist. So you have a legitimate beef with your doctor who tested for it!)

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