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Apprentice comments on I love zebras - Less Wrong Discussion
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Comments (25)
I agree with Apprentice: this is not a comparison of two independently obtained samples but an observed sample vs a predicted state of affairs.
The problem with this situation is another flavour of 0 and 1 are not probabilities. Here, treating the expected population of zebras as literally P(zebra)=0 in which case inferential statistical methods related to possible variation around observed values break down. Under the null hypothesis: observed data come from the expected distribution, and if P(zebra)=0) the variance in this distribution = 0.
Or put a different way, the "expected" distribution is not a distribution as we typically consider them - because 0 is not a probability.
"Here, treating the expected population of zebras as literally P(zebra)=0"
That phrase lacks a finite verb.
I don't see that inferential statistical methods break down. On the contrary, they give exactly the correct answer that one would expect. The variance under the null is zero, so the z value is infinity, so the p value is zero. Whether you do a z-test, a t-test, or a Poisson test, you're going to get p = 0, and therefore reject the null. Your trying to link this to the claim that 0 is not a probability is begging the question.