How to obtain the P value from a confidence intervalBMJ 2011; 343 doi: https://doi.org/10.1136/bmj.d2304 (Published 08 August 2011) Cite this as: BMJ 2011;343:d2304
- Douglas G Altman, professor of statistics in medicine 1,
- J Martin Bland, professor of health statistics2
- 1Centre for Statistics in Medicine, University of Oxford, Oxford OX2 6UD
- 2Department of Health Sciences, University of York, Heslington, York YO10 5DD
- Correspondence to: D G Altman
We have shown in a previous Statistics Note1 how we can calculate a confidence interval (CI) from a P value. Some published articles report confidence intervals, but do not give corresponding P values. Here we show how a confidence interval can be used to calculate a P value, should this be required. This might also be useful when the P value is given only imprecisely (eg, as P<0.05). Wherever they can be calculated, we are advocates of confidence intervals as much more useful than P values, but we like to be helpful.
The method is outlined in the box below in which we have distinguished two cases.
Steps to obtain the P value from the CI for an estimate of effect (Est)
(a) P from CI for a difference
If the upper and lower limits of a 95% CI are u and l respectively:
1 calculate the standard error: SE = (u − l)/(2×1.96)
2 calculate the test statistic: …