How do I interpret and report P values and 95% confidence intervals in a medical paper?

What does a 95% confidence interval actually mean?

A confidence interval is the range of effect sizes that are reasonably compatible with your data, given the model and its assumptions. The "95%" describes the method, not your particular interval: if the same study were repeated many times and an interval calculated each time, about 95% of those intervals would contain the true effect.

What it does not mean, according to Greenland and colleagues' guide to common misinterpretations:

• It is not a 95% probability that the true effect lies inside this interval.
• Values just outside the interval are not ruled out, and values near the centre are not "proven".
• An interval that includes the null (0 for a difference, 1 for a ratio) does not show that there is no effect.

The practical reading has two parts. Location: does the interval sit on the side of benefit, harm, or straddle the null? Width: a narrow interval means a precise estimate; a wide one means the study cannot distinguish a large effect from a trivial one. A risk difference of −10 percentage points with a 95% CI of −19 to −1 is compatible with a large benefit and with an almost negligible one.

Gardner and Altman argued in the BMJ in 1986 that medical papers should lead with estimates and confidence intervals rather than P values, and the ICMJE Recommendations still ask authors to quantify findings with measures of uncertainty such as confidence intervals and not to rely only on hypothesis tests.

What does a P value of 0.05 mean?

A P value is the probability of seeing data at least as extreme as yours if the null model (including "no difference" and every assumption of the test) were true. A P value of 0.05 says the observed difference would be fairly unusual under that model. It does not say how likely the hypothesis is.

In 2016 the American Statistical Association issued a formal statement with six principles. In plain terms:

1. A P value can show how incompatible the data are with a specified statistical model.
2. It does not measure the probability that the hypothesis is true, or that the result arose by chance alone.
3. Conclusions and decisions should not rest only on whether P crosses a threshold.
4. Proper inference needs full reporting and transparency (every analysis run, not only the significant ones).
5. A P value does not measure the size of an effect or how important it is.
6. On its own, a P value is not a good measure of evidence for a model or hypothesis.

Is P = 0.0001 significant? Is P = 0.1? Against a prespecified alpha of 0.05, the first is below the threshold and the second is not. But a very small P value can come from a clinically trivial effect in a large sample, and P = 0.1 in a small study can accompany a clinically important estimate with a wide interval. Report both as exact values and let the estimate and CI carry the interpretation.

Is 0.05 or 0.01 better? Neither is a law of nature. Choose and state the significance level in the methods before analysing, justify a stricter level when you test many hypotheses or need strong confirmation (for example, genetic association studies), and do not change it after seeing the results.

What is the difference between statistical and clinical significance?

Statistical significance concerns compatibility with a null model. Clinical significance concerns whether the effect is large enough to change care. They answer different questions, and a reviewer will expect you to discuss both.

Illustrative synthetic numbers. Define the minimal clinically important difference in your methods, ideally with a citation, so readers can compare the CI with it. Altman and Bland's reminder that absence of evidence is not evidence of absence applies to every non-significant result: an equivalence or non-inferiority claim needs its own prespecified margin.

How do I report P values in a manuscript?

Follow the target journal first. Without a house rule, these conventions satisfy most editors:

Other points editors expect:

• Name the test that produced each P value in the methods (and in table footnotes).
• Write P = .03, not P = .030 or P = 0.0312 (false precision).
• Do not report P = 0.000 or P = 1.000 from software output; write P < .001 or P > .99.
• Give the effect size and its CI next to every P value. SAMPL recommends giving the estimate and a measure of precision, because a P value alone tells the reader neither.

How do I report confidence intervals?

1. Report the point estimate first, then the interval: "mean difference, 4.2 mm Hg (95% CI, 1.1 to 7.3)".
2. State the confidence level (95% unless prespecified otherwise).
3. Use "to" instead of a hyphen when either limit can be negative: "−3.3 (95% CI, −9.3 to 2.7)" is unambiguous; "−9.3-2.7" is not.
4. Use the same number of decimals for the estimate and both limits.
5. For ratios, the interval is asymmetric around the estimate (it is symmetric on the log scale). That is expected, not an error.
6. Give CIs for every primary and secondary effect estimate, not only significant ones.
7. Name the method in the methods section (for example, Wald, Wilson, exact, bootstrap, or the model that produced it).

How should I word results with P values and CIs?

Worked example: reporting a two-arm trial

Synthetic data, for illustration only. A two-arm randomized trial with 150 participants per arm. Numbers were recomputed with a script: risk differences with Wald 95% CIs, risk ratios with log-method 95% CIs, and P values from the chi-square test (Fisher exact test where expected counts are small).

How to write it up:

• Primary outcome: "The primary outcome occurred in 24 of 150 participants (16.0%) in the intervention group and 39 of 150 (26.0%) in the control group (risk difference, −10.0 percentage points; 95% CI, −19.2 to −0.9; P = .03), corresponding to a number needed to treat of 10 (95% CI, 5.2 to 117.4)."
• Readmission: the interval runs from a meaningful benefit to a small harm, so the trial is inconclusive for this outcome. Do not write "no effect on readmission".
• Serious adverse events: the counts are too small for any conclusion; the very wide RR interval says exactly that.

Notice how close the primary result is to the threshold: the upper CI limit is barely below zero, and with Yates' continuity correction or Fisher's exact test the same table gives P = .047 instead of .03. That is why the prespecified test matters, and why the interval is more informative than the verdict.

Common mistakes reviewers flag

• P-hacking and selective reporting: trying several tests, covariate sets, cut-offs or subgroups and reporting the one that crossed 0.05. The ASA statement calls for reporting every analysis performed. Prespecify the analysis plan and label exploratory analyses as such (the ICMJE asks authors to distinguish prespecified from exploratory analyses).
• Multiple comparisons without adjustment or acknowledgement: with many outcomes or subgroups, some will be "significant" by chance. The Bonferroni method divides alpha by the number of tests (0.05 / 5 = 0.01 for five tests); Bland and Altman note it is conservative. Whatever you choose, say so.
• "Trend toward significance" or "marginally significant": JAMA's instructions explicitly ask authors not to use these hedges for non-significant results.
• Missing confidence intervals: P values with no estimate or CI, especially for secondary outcomes and adjusted models.
• "No difference" from a non-significant P value, with no look at the CI width or the minimal clinically important difference.
• P values that do not match the CI: a 95% CI excluding the null with P > .05 (or the reverse) usually means a transcription error or two different methods; reviewers catch this. CliniPaper recomputes P values and intervals from your tables and flags inconsistencies between the abstract, text and tables.
• Software output pasted as is: P = 0.000, eight decimals, or "NS".

For the effect measures themselves, see our guide on odds ratio vs relative risk vs hazard ratio. When a reviewer raises any of the points above, our guide on how to respond to reviewer comments shows how to answer point by point. If you used generative AI anywhere in preparing the analysis or text, you remain responsible for every number, and your AI disclosure statement should say so.