How to Interpret P-Values and Confidence Intervals

What a p-value does and does not mean

A p-value is the probability, assuming the specified statistical model and null hypothesis, of observing results at least as incompatible with that null as those actually observed. It is not the probability that the null hypothesis is true, nor the probability that a finding occurred “by chance.”

Thresholds such as 0.05 are conventions. A result can be statistically significant while the effect is too small to be clinically useful; conversely, an important potential effect may be estimated imprecisely in a small study.

Interpret the confidence interval alongside the effect

Suppose an illustrative two-group study estimates a mean difference of −4.0 points with a 95% confidence interval from −6.5 to −1.5. The interval communicates a range of values compatible with the estimate under the model and sampling assumptions. Whether a 4-point difference matters clinically depends on the measurement scale and prespecified minimal important difference.

Contrast that with an estimate of −4.0 (95% CI −10.0 to 2.0). The point estimate is unchanged, but uncertainty is much greater and the interval includes both important benefit and potential harm, depending on scale direction.

A good results sentence

“Mean symptom score was 4.0 points lower in Group A than Group B (mean difference −4.0, 95% CI −6.5 to −1.5; p = [verified value]).” Only enter a p-value computed from the data; never fabricate it to match an interpretation.

Checklist

• Identify the contrast and its reference group.
• Report the estimated magnitude, units, precision and p-value where relevant.
• Distinguish statistical association from causal inference.
• Discuss study design, bias, missing data and multiplicity.
• Avoid claims of “no effect” based only on p > 0.05.

ResearchTry Statistical Analysis helps organize summaries and outputs, but scientific interpretation remains the investigator's responsibility.

Frequently asked questions

Does p < 0.05 prove a clinically important effect?

No. Consider the point estimate, compatible effect range, research design, multiplicity and clinical context.

What should I report alongside a p-value?

An appropriate effect estimate, confidence interval, group sample sizes, test/model and relevant assumptions.

Further reading and primary guidance

• ICMJE manuscript preparation: statistics, tables and references