Testing a point null hypothesis
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Example: Does Joe have an average IQ?

Let M denote Joe's true IQ.  He will take a test with result y which is
normal with mean M and standard deviation 15.  We wish to test H: M = 100
against K: M<>100.  We assign a prior probability q to H and under the
alternative hypothesis, we assign M a normal distribution with mean 100
and standard deviation t.  Suppose Joe gets a score of 130 -- is this
strong evidence that he does not have an "average" IQ?

The Minitab program 'm_norm_t' accepts as input 
 - the value M0 to be tested
 - the prior probability of H
 - a set of alternative values for the prior standard deviation t
  (assuming that M is distributed N(M0, t) under K)
 - the data -- here we input the sample mean (130) and the sample size (1)
The program outputs the Bayes factors and the posterior probabilities of
the H for each value of t.

MTB > exec 'm_norm_t'
 
ENTER THE NULL HYPOTHESIS MEAN M0:
DATA> 100
 
ENTER THE PRIOR PROBABILITY OF M0:
DATA> .5
 
FOR THE ALTERNATIVE HYPOTHESIS THAT M = M0,
ENTER STANDARD DEVIATION(S) OF THE NORMAL PRIOR DISTRIBUTION:
DATA> 1 2 4 8 16 32 64 128
DATA> end
 
ENTER THE STANDARD DEVIATION OF THE POPULATION:
DATA> 15
 
OBSERVED DATA IN WORKSHEET? (TYPE 'y' OR 'n'.)
  IF YES, INPUT NUMBER OF COLUMN.
  IF NO, INPUT OBSERVED SAMPLE MEAN AND SAMPLE SIZE:
n

DATA> 130 1

The Bayes factor in favor of the null hypothesis is:
BF_HK   
  0.99339  0.97421  0.90626  0.72779  0.50431  0.45716  0.65817  1.19470

The posterior probability of the null hypothesis is:
prob_H  
  0.498342  0.493469  0.475412  0.421226  0.335243  0.313735  0.396927  0.544356