Supplementary exercise 9.52 of IPS7e
------------------------------------

(a)

MTB > PTwo 82 28 78 30;
SUBC>   Confidence 95.0;
SUBC>   Test 0.0;
SUBC>   Alternative 0;
SUBC>   Pooled.

Test and Confidence Interval for Two Proportions

Sample      X      N  Sample p
1          28     82  0.341463
2          30     78  0.384615

Estimate for p(1) - p(2):  -0.0431520
95% CI for p(1) - p(2):  (-0.192118; 0.105814)
Test for p(1) - p(2) = 0 (vs not = 0):  Z = -0.57  P-Value = 0.570
Fisher’s exact test: P-Value = 0.623

Comments:
---------

Model: X - the number of patients who improved in the treatment group
           (subjected to gastric freezing) - follows B(82,p1),
       Y - the number of patients who improved in the control group
           - follows B(78,p2).
Estimation: see sample proportions above.
Hypotheses:   H0: p1=p2
              Ha: p1<>p2
Test: z=-0.57, P=0.57 (based on normal approximation, 
                       the conditions are satisfied)

(b)
MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 9\ex09_052.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
9\ex09_052.mtw'
Worksheet was saved on 24/10/2014

MTB > XTabs 'improv' 'tx';
SUBC>   Layout 1 1;
SUBC>   Frequencies 'count';
SUBC>   Counts;
SUBC>   ColPercents;
SUBC>   ChiSquare;
SUBC>   Expected;
SUBC>   DMissing 'improv' 'tx'.
Tabulated Statistics: improv, tx 
Using frequencies in count

Rows: improv   Columns: tx

            0       1     All

0          48      54     102
        61.54   65.85   63.75
        49.73   52.27

1          30      28      58
        38.46   34.15   36.25
        28.27   29.73

All        78      82     160
       100.00  100.00  100.00

Cell Contents:      Count
                    % of Column
                    Expected count

Pearson Chi-Square = 0.322, DF = 1, P-Value = 0.570
(Likelihood Ratio Chi-Square = 0.322, DF = 1, P-Value = 0.570)

Comments:
---------
Model, estimation and hypotheses are the same - comparing two
proportions. P-value = 0.570 - the same. Chi-square statistic 
X^2 = 0.322 = (-0.57)^2 (except for rounding errors).

(c)
Conclusion: We cannot reject H0. Considering the large P-value
and the almost equal sample proportions, there is no substantial indication 
and certainly no evidence that the treatment does better than control.