Wilson interval with zero trials I'm calculating Wilson score interval for

Pelizzolaf40

Pelizzolaf40

Answered question

2022-03-08

Wilson interval with zero trials
I'm calculating Wilson score interval for some number of trials, so I have a question:
is it correct to assume this interval as [0 , 1] when you have zero trials?

Answer & Explanation

Jamiya Shah

Jamiya Shah

Beginner2022-03-09Added 2 answers

What is the value of p^=Xn when there are no trials? I don't see how the formula for the Wilson interval can be applied if there is no data.
In the Wikipedia link the word "equivalently," between the first and second formulas for the interval, tacitly assumes n is a positive integer. However, if you use the second form anyway for n=0 then you do get, formally, 12±12 or (0,1) for a CI of any desired level of confidence. (If you're playing out this fantasy to the end, you could say (0,1) is an 'all purpose CI' for p which is assumed from the start to lie in (0,1).)
In a Bayesian framework, one might choose the 'flat' prior Unif(0,1)Bη(1,1). With no data, the posterior could be taken to be the same as the prior and one Bayesian 95% probability interval would be (0.025, 0.975).

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