Convert between p-values and confidence intervals
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Reporting, confidence-interval, and test-selection templates & worked examples from the Statistical Test Selection Workbook. We’ll email you the download link.
How the conversion works
A confidence interval and a p-value carry the same information about precision — they’re two views of an estimate and its standard error. The Altman–Bland method moves between them:
- CI → p: recover the standard error from the interval width, SE = (upper − lower) / (2·z), then z = estimate / SE and p = 2·(1 − Φ(|z|)).
- p → CI: recover z = Φ⁻¹(1 − p/2), then SE = |estimate| / z and CI = estimate ± zconf·SE.
- Ratios: for odds, risk, and hazard ratios the same steps run on the natural-log scale, then exponentiate back.
Assumes a normal (Wald) approximation and an interval that’s symmetric on the appropriate scale — true of most reported intervals. Not for proportions near 0/1 or very small samples.
Frequently asked questions
How do I get a p-value from a 95% CI?
SE = (upper − lower)/(2 × 1.96), then z = estimate/SE and p = 2 × (1 − Φ(|z|)). For ratios, use the log of each value first.
How do I get a CI from a p-value?
Recover z = Φ⁻¹(1 − p/2), set SE = |estimate|/z, then form estimate ± zconf × SE (or exponentiate for a ratio).
Does it handle odds/hazard ratios?
Yes — pick “Ratio” and the tool works on the log scale, which is correct for OR, RR, and HR.
Why does p → CI need the estimate?
The p-value fixes the ratio estimate/SE but not the scale; the estimate pins down SE so the interval can be placed.
Does it store anything?
No. Everything runs in your browser; nothing is uploaded or saved.