If you don't have access to the primary data and need to estimate the standard error from a 95% confidence interval (95% CI), see this blog entry. If you have forgotten how to calculate the standard error of the log odds ratio use this formula:

SE(logOR)=1n1+1n2+1n3+1n4−−−−−−−−−−−−−−−√

To test if two odds ratios are significantly different and get a p-value for the difference follow these steps:

(1) Take the absolute value of the difference between the two log odds ratios. We will call this value δ.

(2) Calculate the standard error for δ, SE(δ), using the formula:

√

(3) Calculate the Z score for the test: z=δ/SE(δ)

(4) Calculate the p-value from the z score. The p-value can be easily calculated in R or Microsoft Excel using the below formulas.

R: P-value=2*(1-pnorm(Z))

MS Excel: P-value=2*(1-(NORMDIST(Z,0,1,TRUE)))

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