### Stata Textbook Examples Introduction to the Practice of Statistics by Moore and McCabe Chapter 8: Inference for Proportions

Example 8.1, page 587 can be solved with the cii command. We supply the sample size (N) and the number of successes (X) and we get the confidence interval for p as shown in the book.
cii 17096 3314

-- Binomial Exact --
Variable |     Obs         Mean    Std. Err.       [95% Conf. Interval]
---------+-------------------------------------------------------------
|   17096     .1938465    .0030234        .1879441    .1998532
Example 8.2, page 589-590 shows how to test whether the probability of getting a head was really .5 given 2048 heads in 4040 flips. We compute the observed probability of a head as 2048/4040=.5069 and use prtesti as shown below.
prtesti 4040 .5069 .5

One-sample test of proportion                      x: Number of obs =     4040

------------------------------------------------------------------------------
Variable |      Mean    Std. Err.       z     P>|z|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
x |     .5069    .0078657   64.4443   0.0000       .4914835    .5223165
------------------------------------------------------------------------------

Ho: proportion(x) = .5

Ha: x < .5              Ha: x ~= .5               Ha: x > .5
z =  0.877               z =  0.877               z =  0.877
P < z = 0.8098         P > |z| = 0.3804           P > z = 0.1902
Example 8.3, page 591 is illustrated below, and it is much like example 8.2.
prtesti 4040 .4931 .5

One-sample test of proportion                      x: Number of obs =     4040

------------------------------------------------------------------------------
Variable |      Mean    Std. Err.       z     P>|z|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
x |     .4931    .0078657   62.6898   0.0000       .4776835    .5085165
------------------------------------------------------------------------------

Ho: proportion(x) = .5

Ha: x < .5              Ha: x ~= .5               Ha: x > .5
z = -0.877               z = -0.877               z = -0.877
P < z = 0.1902         P > |z| = 0.3804           P > z = 0.8098
Example 8.4, page 591 shows how to get a confidence interval for the proportion of heads.
cii 4040 2048, level(99)

-- Binomial Exact --
Variable |     Obs         Mean    Std. Err.       [99% Conf. Interval]
---------+-------------------------------------------------------------
|    4040     .5069307    .0078657        .4865486    .5272972
We skip examples 8.5-8.7.

Example 8.8 and 8.9, page 603 and 606 are illustrated below. This shows how to get a confidence interval for the difference of 2 proportions, illustrated below in Stata. Note that you supply N1 then p1 then N2 then p2. This also tests whether the two proportions are equal (as shown in example 8.9). (Note that our copy of the book shows the Z=9.34, but we obtain Z=9.304, so this appears to be a misprint).

prtesti 7180 .227 9916 .17

Two-sample test of proportion                      x: Number of obs =     7180
y: Number of obs =     9916

------------------------------------------------------------------------------
Variable |      Mean    Std. Err.       z     P>|z|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
x |      .227    .0049436   45.9183   0.0000       .2173108    .2366892
y |       .17    .0037722   45.0665   0.0000       .1626066    .1773934
---------+--------------------------------------------------------------------
diff |      .057    .0062184                          .0448122    .0691878
|  under Ho:   .0061268    9.3034   0.0000
------------------------------------------------------------------------------

Ho: proportion(x) - proportion(y) = diff = 0

Ha: diff < 0            Ha: diff ~= 0             Ha: diff > 0
z =  9.303               z =  9.303               z =  9.303
P < z = 1.0000          P > |z| = 0.0000          P > z = 0.0000
Example 8.10, page 607 can be solved with the iri (incidence rate, immediate) command. Note that we supply the # male binge drinkers then # female binge drinkers then # males then # females.
iri 1630 1684 7180 9916

|   Exposed   Unexposed  |     Total
-----------------+------------------------+----------
Cases |      1630        1684  |      3314
Person-time |      7180        9916  |     17096
-----------------+------------------------+----------
|                        |
Incidence Rate |  .2270195    .1698265  |  .1938465
|                        |
|      Point estimate    |  [95% Conf. Interval]
|------------------------+----------------------
Inc. rate diff. |          .057193       |   .043509    .0708769
Inc. rate ratio |         1.336773       |  1.247998    1.431833  (exact)
Attr. frac. ex. |         .2519297       |  .1987167    .3015944  (exact)
Attr. frac. pop |         .1239123       |
+-----------------------------------------------
(midp)   Pr(k>=1630) =                  0.0000  (exact)
(midp) 2*Pr(k>=1630) =                  0.0000  (exact)
Example 8.11, page 608 can also be solved with the iri command as illustrated below. The confidence interval is slightly different from the book, probably due to rounding.
iri 55 21 3338 2676

|   Exposed   Unexposed  |     Total
-----------------+------------------------+----------
Cases |        55          21  |        76
Person-time |      3338        2676  |      6014
-----------------+------------------------+----------
|                        |
Incidence Rate |  .0164769    .0078475  |  .0126372
|                        |
|      Point estimate    |  [95% Conf. Interval]
|------------------------+----------------------
Inc. rate diff. |         .0086294       |  .0031315    .0141273
Inc. rate ratio |         2.099632       |  1.249441    3.655221  (exact)
Attr. frac. ex. |          .523726       |  .1996418    .7264188  (exact)
Attr. frac. pop |         .3790123       |
+-----------------------------------------------
(midp)   Pr(k>=55) =                    0.0014  (exact)
(midp) 2*Pr(k>=55) =                    0.0027  (exact)

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