# [R] Pearson's Chi-squared Test

Mitsuo Igarashi mitsu5 at ruby.famille.ne.jp
Sun Apr 13 05:23:53 CEST 2003

```HI Jorge.

Jorge Magalh??s <jmagalhaes at oninetspeed.pt> wrote:

>
>  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)

I have read these sentences of the URL.
If you combine the data you cited of female and male, you get
the following table.

Active   |     13 |      7 |     21 |
Placebo  |     29 |      7 |      7 |
This is expressed as x<-matrix(c(13,7,21,29,7,7),2,3,byrow=TRUE).
> x
[,1] [,2] [,3]
[1,]   13    7   21
[2,]   29    7    7
> chisq.test(x)  : This runs in R.
Pearson's Chi-squared test
data:  x
X-squared = 13.055, df = 2, p-value = 0.001463

You can see the following sentennces in the URL you cited which
is the same calculation just as I write above.
STATISTICS FOR TABLE OF TREAT BY IMPROVE               |
|                                                                   |
|     Statistic                     DF     Value        Prob        |
|     ------------------------------------------------------        |
|     Chi-Square                     2    13.055       0.001        |
Chi-squared value is completely same.

I like to add a note that this section you cited is "Tests of
Association for Two-Way Tables". And  Cochran-Mantel-Haenszel
Chi-Squared Test is different from chisq.test in R.

You can find a very good basic lectures:"Data Analysis With Epi
Info" at http://www.sjsu.edu/faculty/gerstman/EpiInfo/ .

Good luck!
-------========--------
mitsu5
mitsu5 at ruby.famille.ne.jp

>  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