Obscure statistics question for flight safety research

rv8ch said:

I've recently read two books that talk about this, "thinking fast and slow" and "nudge" - I think this might be what you are talking about:

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Ed_Wischmeyer said:

So I'm doing research for the 2019 Founder's Innovation Prize and I know that there's a theorem in sampling theory that says that if you hypothesize that a phenomenon is rare but that phenomenon shows up repeatedly in the first, small sample, you can reject the hypothesis of it being rare without further testing.

Anybody know the name of that theorem, and have a link to it on line? My google skills are apparently not up to the task.

Thanks!

Ed

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BillL said:

I am not sure of a name, Ed, but from my statistics in product reliability and testing (fading rapidly with age) if something shows up repeatedly in small (valid and representative) samples that is (in itself) objective evidence that the occurrence is not rare.

You aren't talking about a null hypothesis or Pearson's Chi-squared test are you?

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aturner said:

Ed, are you thinking of the binomial distribution, or Bernoulli trail?

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See here: https://www.google.com/url?sa=t&sou...FjAAegQIAhAB&usg=AOvVaw0up5_VaJpRdWwf_m3hNfIb

Slide mentions a "rare event rule" but it is basically setting up the foundation of hypothesis testing

Many many different ways to test hypotheses

But the base method is due to Neyman and Pearson and is generally referred to as neyman-pearson hypothesis testing. *Set up null hypothesis (event is rare, in this case) and gather evidence ce for alternative. *If observed data would be unlikely to happen under null, reject null.

It's the probability of obtaining the extreme result under null hypothesis that is the "rare" they are talking about. *I think

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Google "rare event rule". *It is broader than what the commenters suggest on the thread. *They are all giving examples of different ways to set up a hypothesis test; the rare event rule is the assumption under which any hypothesis test gives you information about the world. Basis of a lot of statistical inference

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