Chi2 test

[Daves Cordova]

I am running a chi2 test in Stata, however I see the degreees of freedom may not be right. The data can be put as:

input str10 gender chocolat vainilla strawberry
"man" 15 10 15
"woman" 10 5 5
end

When running the test, as for example, in chocolat:

. tab gender chocolat, chi2

| chocolat
gender | 10 15 | Total
-----------+----------------------+----------
man | 0 1 | 1
woman | 1 0 | 1
-----------+----------------------+----------
Total | 1 1 | 2

Pearson chi2(1) = 2.0000 Pr = 0.157

The degress of freedom is calculated as 1. However, (rows-1)x(columns-1), is 2. What I am missing here?

[Clyde Schechter]

When you run -tab gender chocolat, chi2-, the variables vainilla [sic] and strawberry are ignored. chocolat itself is a 0/1 variable. So the number of degrees of fredom in this analysis is indeed (#genders - 1) * (#chocolats - 1) = (2-1)*(2-1) = 1*1 = 1.

What I think you have in mind, is an analysis of gender vs flavor, where flavor encompasses all three of chocolat, vainilla, and strawberry. That would indeed provide df = (#genders - 1) * (#flavors - 1) = (2-1) * (3-1) = 1*2 = 2. But your data set, as currently organized, does not have a flavor variable, so you cannot do this analysis. To get to that you need to -reshape- the data and create a flavor variable:

. rename (chocolat vainilla strawberry) n=

. reshape long n, i(gender) j(flavor) string
(j = chocolat strawberry vainilla)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations                2   ->   6           
Number of variables                   4   ->   3           
j variable (3 values)                     ->   flavor
xij variables:
        nchocolat nstrawberry nvainilla   ->   n
-----------------------------------------------------------------------------

.
. tab gender flavor, chi2

           |              flavor
    gender |  chocolat  strawbe..   vainilla |     Total
-----------+---------------------------------+----------
       man |         1          1          1 |         3
     woman |         1          1          1 |         3
-----------+---------------------------------+----------
     Total |         2          2          2 |         6

          Pearson chi2(2) =   0.0000   Pr = 1.000

[Nick Cox]

If #1 were the only prpblem, this is another way to solve it directly:

. tabi 15 10 15 \ 10 5 5, chi2

           |               col
       row |         1          2          3 |     Total
-----------+---------------------------------+----------
         1 |        15         10         15 |        40 
         2 |        10          5          5 |        20 
-----------+---------------------------------+----------
     Total |        25         15         20 |        60 

          Pearson chi2(2) =   1.1250   Pr = 0.570

In #2 Clyde Schechter forgot to apply the frequencies as weights.

. clear 

. input str10 gender chocolate vanilla strawberry

         gender  chocolate    vanilla  strawbe~y
  1. "man" 15 10 15
  2. "woman" 10 5 5
  3. end

. 
. rename (chocolate-strawberry) (n=), string 

. 
. reshape long n, i(gender) j(flavour) string 
(j = chocolate strawberry vanilla)

Data                               Wide   ->   Long
-----------------------------------------------------------------------------
Number of observations                2   ->   6           
Number of variables                   4   ->   3           
j variable (3 values)                     ->   flavour
xij variables:
        nchocolate nstrawberry nvanilla   ->   n
-----------------------------------------------------------------------------

. 
. list, sepby(gender)

     +--------------------------+
     | gender      flavour    n |
     |--------------------------|
  1. |    man    chocolate   15 |
  2. |    man   strawberry   15 |
  3. |    man      vanilla   10 |
     |--------------------------|
  4. |  woman    chocolate   10 |
  5. |  woman   strawberry    5 |
  6. |  woman      vanilla    5 |
     +--------------------------+

. 
. tab gender flavour [fw=n], chi2 

           |             flavour
    gender | chocolate  strawbe..    vanilla |     Total
-----------+---------------------------------+----------
       man |        15         15         10 |        40 
     woman |        10          5          5 |        20 
-----------+---------------------------------+----------
     Total |        25         20         15 |        60 

          Pearson chi2(2) =   1.1250   Pr = 0.570