This question originates from this question, where my answer tries to clear a purely mathematical misunderstanding that OP seems to have. Now to me the key advantage of this is that you don't need to rely on the reputability of some source to believe this.

I feel this answer would actually become worse if I put some source. As it is, it makes a statement and you can follow the argument yourself and then decide on the truthfulness yourself. If instead I put a source this becomes 'the following is true because math professor X says so'. If you believe him it's true, if you think professor X is not reputable enough you question the result. It degrades from an absolute mathematical truth (which may or may not be applicable to specific real world situations) to a mere proof by authority.


No, basic math does indeed not need such a reference.

But the problem for this answer on main is a different one than presenting just 'basic math'.

It is not just 'basic math'! As the math you present may be trivial for you, or really a number of readers here, it is the interpretation of these numbers and even the basic applicability or validity of these numbers hang in free space here.

There is no 'pure math' in reality that is of any use to anyone. Why is your depiction of pre-test probability important? In such a case as (PCR-) medical testing? Where do you get your formulas? Who says that these should be observed, when interpreting real-world test-results coming back from a lab? Presenting and explaining these parts of fundamentals of test theory are nice and valuable to have on this site.

To really "clear a purely mathematical misunderstanding that OP seems to have", we need to explain the theory behind the formula. Meaning first: to present and explain the formulas… This requires a reference, at least. Is that formula accepted, standard practice? Etc.

For these reasons (and others) such an answer, any answer here, always needs references to drive home the point being made.

That is standard policy for this site as detailed in for example

FAQ: Welcome to New Users

FAQ: What are theoretical answers?

To fix that, I'd suggest at least two changes:

  • Your apodictic statement in bold does read like being from a standard textbook on the subject. If it is, quote it properly. If it is not, find one of many similar ones and quote them.

  • Calculations such as those you present are being made for many tests. Not just corona. You may pick one of those and compare or contrast them. Such calculations are being made for the specific problem of inflated corona-case numbers and overconfidence in ungrounded and unreliable test results. Choose any of those you find and present them in your answer. (Criticise them, if they don't conform to expectations of quality. There are also 'bad critiques' out there…)

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