Suppose we have an estimate of a risk difference and a respective 95 percent confidence interval of 3.60 (0.70, 6.50). Here are the steps to follow:

(1) Subtract the lower limit from the upper limit to get the difference and divide by 2: (6.50-0.70)/2=2.9

(2) Divide the difference by 1.96 (for a 95% CI) to get the standard error estimate: 2.9/1.96=1.48

(3) Divide the risk difference estimate by the standard error estimate to get a z score: 3.60/1.48=2.43

(4) Look up the z score using Python, R (ex: 2*pnorm(-abs(z))), Excel (ex: 2*1-normsdist(

*z score*)), or an online calculator to get the p-value. Usually the two-sided p-value is reported: p=0.015 (two-sided)

For an odds ratio, things are a bit trickier because we need to first take the natural log of the estimate and 95% confidence interval before we can carry out the back calculation of the standard error for calculating the p-value. Suppose we have an odds ratio and 95 percent confidence interval of 1.28 (1.05, 1.57). Here are the steps to follow:

(1) Take the natural log (ln) of each value in the 95% CI: 0.25 (0.05, 0.45)

(2) Subtract the lower limit from the upper limit and divide by 2: (0.45-0.05)/2=0.2

(3) Divide the difference by 1.96 (for a 95% CI) to get the standard error estimate: 0.2/1.96=0.10

(4) Divide the log odds ratio by the standard error estimate to get a z score: 0.25/0.10=2.50

(5) Look up the z score using Python, R (ex: 2*pnorm(-abs(z))), Excel (ex: 2*1-normsdist(

*z score*)), or an online calculator to get the p-value. Usually the two-sided p-value is reported: p=0.012 (two-sided)

Hopefully these are good examples to get you started. As you can imagine you can also go from a p-value to a 95% confidence interval by extending these methods in the opposite direction, but in practice it is somewhat unlikely an author would report an effect size and p-value while leaving out the 95% confidence interval.

Thanks for the article! Is there a way to calculate the p-value from confidence intervals from a mixed-model regression?

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