Suppose we have a 2 x 2 table of frequencies ||||||<33% style="TEXT-ALIGN: center"> ||<33% style="TEXT-ALIGN: center"> '''Col 1''' ||<34% style="TEXT-ALIGN: center"> '''Col 2'''|| ||||||<33% style="VERTICAL-ALIGN: top"> '''Row 1''' ||<33% style="VERTICAL-ALIGN: top"> a ||<34% style="VERTICAL-ALIGN: top"> b || ||||||<33% style="VERTICAL-ALIGN: top"> '''Row 2''' ||<33% style="VERTICAL-ALIGN: top"> c ||<34% style="VERTICAL-ALIGN: top"> 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.