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| == Testing an odds ratio == |
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| ||||||<33% style="TEXT-ALIGN: center"> ||<33% style="TEXT-ALIGN: center"> '''Time 1''' ||<34% style="TEXT-ALIGN: center"> '''Time 2'''|| ||||||<33% style="VERTICAL-ALIGN: top"> Correct ||<33% style="VERTICAL-ALIGN: top"> a ||<34% style="VERTICAL-ALIGN: top"> b || ||||||<33% style="VERTICAL-ALIGN: top"> Correct ||<33% style="VERTICAL-ALIGN: top"> c ||<34% style="VERTICAL-ALIGN: top"> d || |
||||||<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]]. 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. |
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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 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.