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Research Methods & Reporting

How to obtain the confidence interval from a P value

BMJ 2011; 343 doi: https://doi.org/10.1136/bmj.d2090 (Published 08 August 2011) Cite this as: BMJ 2011;343:d2090
  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

Confidence intervals (CIs) are widely used in reporting statistical analyses of research data, and are usually considered to be more informative than P values from significance tests.1 2 Some published articles, however, report estimated effects and P values, but do not give CIs (a practice BMJ now strongly discourages). Here we show how to obtain the confidence interval when only the observed effect and the P value were reported.

The method is outlined in the box below in which we have distinguished two cases.

Steps to obtain the confidence interval (CI) for an estimate of effect from the P value and the estimate (Est)

(a) CI for a difference
  • 1 calculate the test statistic for a normal distribution test, z, from P3: z = −0.862 + √[0.743 − 2.404×log(P)]

  • 2 calculate the standard error: SE = Est/z (ignoring minus signs)

  • 3 calculate the 95% CI: Est –1.96×SE to Est + 1.96×SE.

(b) CI for a ratio
  • For a ratio measure, such as a risk ratio, the above formulas should …

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