Intended for healthcare professionals

Research Methods & Reporting Statistics Notes

How to obtain the P value from a confidence interval

BMJ 2011; 343 doi: https://doi.org/10.1136/bmj.d2304 (Published 08 August 2011) Cite this as: BMJ 2011;343:d2304
  1. Douglas G Altman, professor of statistics in medicine 1,
  2. J Martin Bland, professor of health statistics2
  1. 1Centre for Statistics in Medicine, University of Oxford, Oxford OX2 6UD
  2. 2Department of Health Sciences, University of York, Heslington, York YO10 5DD
  1. Correspondence to: D G Altman doug.altman{at}csm.ox.ac.uk

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: …

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