Phi Coefficient (fourfold correlation)
--------------------------------------

         ^phi^ categorical_var categorical_var [^if^ exp] [^in^ range], options

You can enter any tabulate option ^except chi^; the chi option is built into
the command since the statistic is needed to calculate ^phi^.  You can use the
^all^ option, however.

^phi^ calculates the phi, or correlation coefficient, for a 2 X 2 table, along
with the chi-squared statistic.  This is also Cohen's effect size, ^w^, for
those using J. Cohen (1988), Statistical Power Analysis for the Behavioral
Sciences, 2nd edition, Hillsdale, NJ:  Lawrence Erlbaum Associates,
Publishers.  You might also need this if you are using software to calculate
power that requires that you know ^w^.

The ^phi^ coefficient is equal to sqrt(chi-square/N).  If you have a 2 X 2
table this is equal to the correlation coefficient for these variables (see
the example below).  Since this is a correlation coefficient, its square is
meaningful and is provided in the output.  If either the rows or the columns
are greater than 2, then this program supplies ^Cramer's phi-prime^, as well
as Cohen's ^w^.  Note that if either rows or columns is greater than 2, then
^w^ does not equal ^phi-prime^ and ^phi-prime^ is not the correlation
coefficient either; also, its square is not meaningful and is not provided.

Examples:

A 2 X 2 table, followed by the correlation:

. phi female ra if staff==0

           | Returned Admin.
     female|        no        yes |     Total
-----------+----------------------+----------
      Male |        27         16 |        43
    Female |        31          3 |        34
-----------+----------------------+----------
      Total|        58         19 |        77

          Pearson chi2(1) =   8.2311   Pr = 0.004
phi = Cohen's w = fourfold point correlation = 0.3270   phi-squared = 0.1069

. corr female ra if staff==0
(obs=77)
        |   female       ra
--------+------------------
  female|   1.0000
      ra|  -0.3270   1.0000

A 2 X 4 table followed by its correlation:

. phi female srank if staff==0

           | srank
     female|         0          1          2          3 |     Total
-----------+--------------------------------------------+----------
      Male |        17         14          9          3 |        43
    Female |        17         17          0          0 |        34
-----------+--------------------------------------------+----------
      Total|        34         31          9          3 |        77

          Pearson chi2(3) =  11.3940   Pr = 0.010
Cramer's phi-prime =  0.3847     Cohen's w = 0.3847

. corr female srank if staff==0
(obs=77)
        |   female    srank
--------+------------------
  female|   1.0000
   srank|  -0.2786   1.0000