Small (Expected) Frequencies in a 2 x 2 Contingency Table

Dear Dr Wuensch,
I should be so grateful if you please look at this question:
I have a contingency table with an actual zero cell (not the expected). This table is 2*2 and for a sample of 90. Is actual zero is a problem? I know that Yates' correction is suggested to fix a problem of small expected frequencies.  But what about the actual ones? No one is mentioning them!
 Imad Alsuwaih

Hello Imad:

    It is not troublesome to have a cell with a zero frequency.  Yates correction should NEVER be used with data from a contingency table, unless both of the pairs of marginals are fixed rather than random, and that is very highly unlikely (see Howell, 2002, 151-152).  Low expected frequencies result in low power, but no other problem (although this is commonly misunderstood).  If your chi-square is significant, there is no problem with low expected frequencies.  If your chi-square is not significant, there is a big problem, a high probability of a Type II error even if the association between the categorical variables is nontrivial in size.  Again, see Howell (2002, 158-158).
Imagine that there was a perfect association between your categorical variables.  You would expect to get sample data like this:
            col 1    col 2
row 1    45        0
row 2    0          45
and that would speak to the large size of the effect, not to any statistical problem. 
Reference:  Howell, D. C. (2002). Statistical methods for psychology (5th ed.). Belmont, CA: Wadsworth. 


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This page most recently revised on 13. November 2004.