Suppose we have a 2 x 2 table of frequencies
|
Col 1 |
Col 2 |
||
Row 1 |
a |
b |
||
Row 2 |
c |
d |
||
The Odds Ratio is defined as ad/bc
It turns out that
Variance{ln(OR)} = (1/a) + (1/b) + (1/c) + (1/d)so it follows
ln (OR)2 / 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.