Comparing two proportions using a discrete prior.
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Example (from Berry):  Three Duke students were interested in whether basketball
players are more effective when under less pressure. They considered the 
three-point shots attempted by Duke's 1992-3 basketball team in the First 
half vs Second half of games, thinking there would be more pressure in the 
second half. Regard the following as random samples from larger populations: 
Of the 211 three-point shots attempted in the first half 71, or 33.6%, were 
successful; of the 255 attempted in the second half, 90 (35.3%) were successful.

We illustrate the discrete approach.  Suppose each proportion can be .3, 
.35, .4, .45, or .5 and each ordered pair (p1, p2) has the same probability
The program 'pp_disc'  finds the posterior probability matrix and computes 
the marginal distribution of the difference p2-p1.

MTB > exec 'pp_disc'

 FOR EACH P DISTRIBUTION:
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 INPUT LO AND HI VALUES:
DATA> .3 .5
 
 INPUT NUMBER OF MODELS:
DATA> 5
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN FIRST SAMPLE:
DATA> 71 140
 
INPUT OBSERVED NUMBER OF SUCCESSES AND FAILURES IN SECOND SAMPLE:
DATA> 90 165
 
Posterior distribution of P1 and P2:

 ROWS: PER_1     COLUMNS: PER_2
 
          30       35       40       45       50
 30  0.04150  0.21516  0.06551  0.00153  0.00000
 35  0.07335  0.38030  0.11579  0.00271  0.00001
 40  0.01307  0.06774  0.02063  0.00048  0.00000
 45  0.00029  0.00149  0.00045  0.00001  0.00000
 50  0.00000  0.00000  0.00000  0.00000  0.00000


 Row   DIFF     P_DIFF

   1  -0.20   0.000001
   2  -0.15   0.000291
   3  -0.10   0.014554
   4  -0.05   0.141544
   5   0.00   0.442431
   6   0.05   0.331427
   7   0.10   0.068214
   8   0.15   0.001536
   9   0.20   0.000003