🚀 go-pugleaf

I would recommend Agresti "Categorical Data Analysis" (1990) Wiley, ppg.239-245
for a discussion of the topic.  His result is basically as follows...

The noncentrality parameter for G2 is

         L = 2n sum[ pi_i log (pi_i/pi_i(M))]

where L is the noncentrality parameter, n is the sample size, pi_i is the set
of hypothetical true cell probabilities, and pi_i(M) is the set of cell
probabilities estimated under some model M.  Agresti (p 242) presents a part of
a full table of the power values for variouL and model df.  

For example, suppose you have a 2x3 table with the following "true" cell
probabilities...

                      .15  .20  .15
                      .05  .10  .35

and you wish to test the model of independence.  Then, the cell probabilities
under themodel would be...

                       .10  .15  .25
                       .10  .15  .25

Now, plugging these values in the above equation, we arrive at:

                    L = 2 n (.104575)

where (.104575) is what you get when you plug the "true" and expected
probabilities into the summation.  Now, looking on the table on pg 242, we can
see that for df=2 (the model of independence for a 2x3 table), and a desired
power value of .883 leads us to a value of L=12.0.  Now, plugging this into our
result, we get

                  12 = 2 n (.104575) = .2091515 n
 
so that          
                       n = 12.0 / .20915 = 57.37

and we now know that we need a sample size of at least 58!


I would recommend Agresti's book for any issue in categorical data analysis
(Gee, that might make a GREAT name for the book!!).

Enjoy!!


Raymond V Liedka
Department of Sociology
Cornell University
Ithaca  NY  14850

e-mail:  rjoy@cornellc