Suppose we have a 2 x 2 table of frequencies
c1 |
c2 |
r1 ||a||b|| r1 ||c||d||
The Odds Ratio is defined as ad/bc
It turns out that ln(OR) has a variance of (1/a) + (1/b) + (1/c) + (1/d)
so it follows
(ln OR)* ln(OR) ) / variance ( ln(OR) )
is chi-square on 1 degree of freedom.
If you have a zero cell then adding one half to all the frequencies enables an estimate of the odds ratio to be made.
Reference:
Everitt BS (1996) Making Sense of Statistics in Psychology A Second Level Course. OUP:Oxford.