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Topic: Common sense and NHST
Replies: 1   Last Post: Jun 20, 2013 12:10 PM

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Luis A. Afonso

Posts: 4,617
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Common sense and NHST
Posted: Jun 20, 2013 12:10 PM
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As promised I will show that a sequence of two no-significant tests could very well lead to a significant over all result: two not sufficient evidence to reject H0 --- > reject this hypothesis.
It is used the fact that p-values, p(i), do follow a Uniform Distribution *** and k of them are such that (Ronald Fisher) :
________H = -2 * Sum (1<= j <= k) Log(p(j))
H is distributed like a Chi-square, k degrees of freedom.
*** The conditions:
___1___i.i.d. data,
___2___Testing H0: miu= true Population value (not shifted)

Then for k=2, H = -2*Log(p(1)) - 2*Log(p(2))
5% significance Critical Value H = 5.99146.
Simulating 1000´000 p(2), random numbers, when fixed p(1) successively from 0.05(0.05)0.95 the following Table was calculated:
____________p(1)___prob. to 5% significant
____________0.05________1.000__
____________0.10________0.500__
____________0.15________0.332__
____________0.20________0.251__
____________0.25________0.200__
____________0.30________0.167__
____________0.35________0.143__
____________0.40________0.125__
____________0.45________0.110__
____________0.50________0.098__
____________0.55________0.091__
____________0.60________0.078__
____________0.65________0.076__
____________0.70________0.067__
____________0.75________0.067__
____________0.80________0.064__
____________0.85________0.060__
____________0.90________0.055__
____________0.95________0.051__
The 2nd column is the frequencies to which H was exceeded owing to p(2)=RND. Note that for p(1)=0.95 we almost attain the 5% level, as it must be from construction when p(1)=1.00000.

Luis A. Afonso



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