**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** (5^{th} ed.). Belmont, CA:
Wadsworth.

Contact Information for the Webmaster,

Dr. Karl L. Wuensch

This page most recently revised on
13. November 2004.