Confidence interval from an estimate and its P value
When a paper gives an effect and a P value but no interval, recover the standard error and the confidence interval.
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- z value of this P
- Standard error
- Confidence interval
How it is calculated
The P value gives the z value of the test; the standard error is the estimate divided by that z value, and the interval is the estimate plus and minus 1.96 standard errors for 95 %.
For ratios the calculation is done on the logarithm and converted back, so the interval is not symmetric.
z = Φ⁻¹(1 − P / 2)SE = |estimate| / z (ratios: estimate = ln(ratio))CI = estimate ± z₁₋α/₂ × SE
Worked example: Difference 10 with P = 0.05: standard error 5.10, 95 % interval 0.00 to 20.00.
Sources
These calculators support research; they do not replace the advice of a statistician or a clinician.
Questions
Is the recovered interval exact?
It is exact only if the P value comes from a normal (z) test. For small samples that used a t test the true interval is a little wider, so treat the result as an approximation.