Recover a confidence interval from a p-value — or the reverse
One paper gives you p = 0.03 and no interval. The next gives an interval and no p-value. Convert between them with the Altman–Bland method so every study in your review sits on the same footing.
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Filling the gaps in the papers you are synthesising
A confidence interval and a p-value are two views of the same underlying quantity: an estimate and its standard error. That is what makes the conversion possible, and it is why reporting only one of them is a reporting failure rather than a real choice.
For a doctoral literature review this is a practical unblocker. Older papers in particular report bare p-values, and you cannot build a comparative table — let alone a meta-analysis — from a column of asterisks. The Altman–Bland method recovers what is missing:
- Interval to p — recover the standard error from the width, SE = (upper − lower) / (2z), then z = estimate / SE and p = 2(1 − Φ(|z|)).
- p to interval — recover z = Φ⁻¹(1 − p/2), set SE = |estimate| / z, then form estimate ± zconf × SE.
- Ratio measures — for odds, risk and hazard ratios the same steps run on the natural-log scale, then exponentiate back.
It is also worth knowing for your own results chapter. Where you have a choice, report the interval: it carries the p-value's information plus the effect's magnitude and precision, which is what a reader actually needs.
Assumes a normal (Wald) approximation and an interval symmetric on the appropriate scale — true of most published intervals. Not reliable for very small samples, or for proportions close to 0 or 1.
Frequently asked questions
Why would I need this for my literature review?
Because you cannot compare studies that report different things. If half your included papers give confidence intervals and half give bare p-values, converting brings them onto one footing so your synthesis table means something — and it is a prerequisite if you intend to pool results.
Does it work for odds ratios and hazard ratios?
Yes. Select the ratio option and the calculation runs on the log scale, which is the correct treatment for odds ratios, risk ratios and hazard ratios. The result is exponentiated back for you.
Why does converting a p-value to an interval need the point estimate?
The p-value only fixes the ratio of the estimate to its standard error, not the scale of either. Supplying the point estimate pins down the standard error, which is what lets the interval be positioned rather than merely sized.
A reviewer asked me to report intervals instead of p-values. Can I use this on my own data?
Only as a last resort. If you still hold your raw data or your model output, compute the intervals directly in your statistics package — that is exact and this is an approximation. Use the conversion when the underlying data are genuinely out of reach, such as for figures extracted from published papers.
When does the method break down?
When the normal approximation does not hold: very small samples, proportions near 0 or 1, and intervals that are asymmetric on the scale being used. If a published interval is visibly lopsided around its point estimate on the appropriate scale, treat the conversion with caution.
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