== 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]]. Bonett and Price Jnr (2015) report on an inproved form of standard error for the Odds Ratio. __References__ Agresti A (1996) An Introduction to Categorical Data Analysis. Wiley:New York. Bonett DG and Price Jr RM (2015) Varying coefficient meta-analysis methods for odds ratios and risk ratios. ''Psychological Methods'' '''20(3)''' 394-406. 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.