== Testing an odds ratio ==

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)*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.

An odds ratio test is carried out by this [attachment:oratio.xls spreadsheet].

'''References'''

Agresti A (1996) An Introduction to Categorical Data Analysis. Wiley:New York.

Everitt BS (1996) Making Sense of Statistics in Psychology A Second Level Course. OUP:Oxford.