Testing an odds ratio

Suppose we have a 2 x 2 table of frequencies

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.

Hosmer DW and Lemeshow S (1995) Applied Logistic Regression. 2nd Edition. Wiley:New York. In CBSU library. A 3rd edition is due to be published in 2013.