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| == Testing an odds ratio == | |
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| ||||||<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 || |
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| It turns out that ln(OR) has a variance of (1/a) + (1/b) + (1/c) + (1/d) | It turns out that {{{ Variance{ln(OR)} = (1/a) + (1/b) + (1/c) + (1/d) }}} |
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| (ln OR)* ln(OR) ) / variance ( ln(OR) ) | ln(OR)*ln(OR) / variance ( ln(OR) ) |
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| Reference: | 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. |
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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. |
Testing an odds ratio
Suppose we have a 2 x 2 table of frequencies
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Col 1 |
Col 2 |
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Row 1 |
a |
b |
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Row 2 |
c |
d |
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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.