MTB > # Researcher is interested in determining relative effectiveness
MTB > # of two drugs.  Suppose that each drug has possible cure rates
MTB > # of .1, .3, .5, .7, .9.  You believe a priori that two drugs
MTB > # have same cure rates with probabability .5; otherwise you have
MTB > # no knowledge about relative effectiveness of two drugs.
MTB > # Suppose that each drug is tested on 10 people; 3 are cured using
MTB > # first drug and 7 using second drug.  Want to compute prior and
MTB > # posterior odds of two drugs being equivalent and the Bayes factor.
MTB > 
MTB > # Use program 'pp_disct' to display the prior.
MTB > 
MTB > exec 'pp_disct'

 FOR EACH P DISTRIBUTION:
 ------------------------
 INPUT LO AND HI VALUES:
DATA> .1 .9
 
 INPUT NUMBER OF MODELS:
DATA> 5
 
 INPUT PROBABILITY THAT P1=P2:
DATA> .5
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN FIRST SAMPLE:
DATA> 0 0
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN SECOND SAMPLE:
DATA> 0 0
 
Posterior distribution of P1 and P2:

  ROWS: PER_1     COLUMNS: PER_2
 
          10       30       50       70       90
  
 10 0.100000 0.025000 0.025000 0.025000 0.025000
 30 0.025000 0.100000 0.025000 0.025000 0.025000
 50 0.025000 0.025000 0.100000 0.025000 0.025000
 70 0.025000 0.025000 0.025000 0.100000 0.025000
 90 0.025000 0.025000 0.025000 0.025000 0.100000
 
TYPE 'Y' AND RETURN TO SEE A TABLE OF THE POSTERIOR DISTRIBUTION
OF THE DIFFERENCE IN PROBABILITIES P2-P1:
y

 Row   DIFF  P_DIFF

   1   -0.8   0.025
   2   -0.6   0.050
   3   -0.4   0.075
   4   -0.2   0.100
   5    0.0   0.500
   6    0.2   0.100
   7    0.4   0.075
   8    0.6   0.050
   9    0.8   0.025

MTB > # Use program 'pp_disct' again to display the posterior.

MTB > exec 'pp_disct'

 FOR EACH P DISTRIBUTION:
 ------------------------
 INPUT LO AND HI VALUES:
DATA> .1 .9
 
 INPUT NUMBER OF MODELS:
DATA> 5
 
 INPUT PROBABILITY THAT P1=P2:
DATA> .5
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN FIRST SAMPLE:
DATA> 3 7
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN SECOND SAMPLE:
DATA> 7 3
 
Posterior distribution of P1 and P2:
(Rows and columns are expressed in percentage format.)

 ROWS: PER_1     COLUMNS: PER_2
 
          10       30       50       70       90
  
 10  0.00001  0.00200  0.02602  0.05925  0.01274
 30  0.00001  0.03717  0.12097  0.27543  0.05925
 50  0.00000  0.00408  0.21251  0.12097  0.02602
 70  0.00000  0.00031  0.00408  0.03717  0.00200
 90  0.00000  0.00000  0.00000  0.00001  0.00001
 
  CELL CONTENTS --
             POST:DATA

TYPE 'Y' AND RETURN TO SEE A GRAPH OF THE POSTERIOR DISTRIBUTION:
n
 
TYPE 'Y' AND RETURN TO SEE A TABLE OF THE POSTERIOR DISTRIBUTION
OF THE DIFFERENCE IN PROBABILITIES P2-P1:
y

 Row   DIFF     P_DIFF

   1   -0.8   0.000000
   2   -0.6   0.000001
   3   -0.4   0.000321
   4   -0.2   0.008180
   5    0.0   0.286859
   6    0.2   0.245930
   7    0.4   0.327473
   8    0.6   0.118493
   9    0.8   0.012744