Some myths concerning statistical hypothesis testing
Sturla Molden
sturla at molden_dot_net.invalid
Sat Nov 9 12:12:01 EST 2002
On Fri, 08 Nov 2002 20:04:27 +0100, Glen M. Sizemore wrote:
> Sorry, but the p-value IS the conditional probability of observing
> the data given that the null hypothesis
The p-value is not the conditional probability of getting the observed
data under the null hypothesis. Let me provide a simple proof for this:
Assume that you want to test if a dice is fair. Then you have:
H0: Prob of getting 6 is 1/6
HA: Prob of getting 6 is not 1/6
Now you throw the dice 10 times and observe a 6 on five of the trials.
Then the conditional probability of getting the observed result under
given that the nullhypotheis is true is:
Prob(data | H0) = Likelihood of H0
= Prob(x = 5) with x ~ binom(10, 1/6)
= 0.0130
However, the p-value is:
p-value = Prob(x = 5) + Prob(x = 6) + Prob(x = 7) + Prob(x = 8)
+ Prob(x = 9) + Prob(x = 9) + Prob(x = 10) with x ~ binom(10, 1/6)
= 0.0155
Thus in this case
p-value is not equal to Prob(data | H0),
which proves you wrong.
You can present this to any statistican you choose for verification.
Sturla Molden
(crossposted to sci.stat.math)
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