[R] Pearson's Chi-squared Test

[Jorge Magalhães]

 How i can perform a Pearson's Chi-squared Test  in this data set:
                                   |          Outcome

    -----------------+-----------+----------------------------------+
    Treatment   |  Sex     | None |Some | Marked  |  Total
    -----------------+------------+--------+--------+-------------+
    Active        |  Female |      6 |      5 |     16      |     27

                     |  Male     |      7 |      2 |      5       |     14

    ----------------+-------------+--------+--------+-------------+
    Placebo     |  Female |     19 |      7 |      6       |     32

                    |  Male     |     10 |      0 |      1       |     11

    ---------------+-------------+---------+--------+-------------+
        Total                       42       14       28              84

 if i do:
 y<- matrix(c(5,6,16, 19,7,6,7,2,5,10,0,1), nc=3)

 and

 chisq.test(y) i found that X-squared=20.3176 but the true value is 15.075
 (http://www.math.yorku.ca/SCS/Courses/grcat/grc2.html#H2_43:Sample)

 Now i tried:

 the Cochran-Mantel-Haenszel Chi-Squared Test for Count Data:

 x <- array(c(6, 19, 7, 10,
         	5, 7, 2, 0,
 		16, 6, 5, 1),
       dim = c(2, 2, 3),
       dimnames = list(
           Active = c("Female", "Male"),
           Placebo = c("Female", "Male"),
           Outcome.Level = c("None", "Some", "Marked")))

 mantelhaen.test(x)

 and now X-squared=2.0863

 What is wrong?

 Best regards
 Many thanks in advance

 Jorge M.