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Academy · Research Writing · P-value and confidence interval
P-Value and Confidence Interval: Definitions, Interpretation and Reporting
A p-value addresses a narrower question than many readers assume, and the confidence interval reported alongside it is usually the more informative of the two statistics.
A p-value is the probability of observing data at least as extreme as what was found, assuming the null hypothesis is true. A confidence interval is a range of values, calculated from the data, that would contain the true population parameter a specified proportion of the time under repeated sampling. They answer related but distinct questions, and neither is a probability that the hypothesis itself is true.
Learning objectives
- What a p-value is a probability of, and what it is not.
- What a 95% confidence interval means, and the common misreading to avoid.
- Why reporting both together, rather than either alone, gives a more complete picture.
Common misconceptions
- “A p-value is the probability that the null hypothesis is true.” A p-value is calculated on the assumption that the null hypothesis is true; it is the probability of the observed data (or more extreme data) under that assumption, not the probability that the assumption itself is correct. This is a common and consequential misinterpretation.
- “A 95% confidence interval means there is a 95% chance the true value lies within this specific calculated range.” Strictly, a 95% confidence interval means that if the study were repeated many times, 95% of the intervals so calculated would contain the true population value; the specific interval from one study either does or does not contain it, with no probability attached to that single instance under the classical (frequentist) interpretation.
Definition of the p-value as a probability
du Prel and colleagues define the p-value as the probability, calculated on the assumption that the null hypothesis is true, of observing a result as extreme as or more extreme than the one actually obtained1. It conveys no direct information about the size of an effect, its clinical importance, or the probability that the null hypothesis itself is true or false; a small p-value from a very large sample may be associated with a trivially small, clinically unimportant effect.
Interpretation of the confidence interval
A confidence interval is derived from the same data but addresses a different question: the range of plausible values for the true population parameter, given the observed data, at a stated confidence level (conventionally 95%)1. Unlike a p-value, a confidence interval directly conveys both the estimated effect size and its precision: a narrow interval indicates a precisely estimated effect and a wide interval indicates substantial uncertainty, information that a p-value alone does not provide.
Complementary information provided by p-values and confidence intervals
du Prel and colleagues argue, in agreement with most current reporting guidance, that confidence intervals should generally be reported alongside the p-value and are often more informative than the p-value alone, because the interval shows the plausible range of effect sizes consistent with the data and allows readers to judge clinical relevance directly rather than inferring it from statistical significance1. A result can be statistically significant (p < 0.05) with a confidence interval that includes both trivially small and substantial effect sizes, which the p-value alone would not reveal.
Key points
Key points
A p-value is the probability of the observed data under the null hypothesis, not the probability the null is true; a confidence interval conveys effect size and precision together, and current reporting practice favours showing both rather than relying on a p-value in isolation.
Practical application
Practical application
- A confidence interval should be reported alongside every p-value, not in place of it. The point estimate, its confidence interval and the p-value should be presented together in results tables, in line with current reporting-guideline expectations.
- A wide confidence interval should be interpreted as an indication of imprecision, even when the result is statistically significant. A significant p-value with a wide confidence interval spanning trivial-to-large effects should be discussed as imprecisely estimated, not simply as a positive finding.
- A p-value should not be described as the probability that the hypothesis is true or false. It should instead be described as what it formally is: the probability of data as extreme as, or more extreme than, those observed, under the null hypothesis.
Frequently asked questions
Not necessarily. It may reflect a true absence of effect or a study too small or too imprecise to detect a real effect; the width of the confidence interval helps to distinguish between these possibilities.
Because treating p < 0.05 as a strict threshold separating “real” from “not real” effects encourages neglect of effect size and precision, which confidence intervals convey directly and a bare threshold does not.
Yes, particularly in very large samples, in which even a trivial difference can reach statistical significance; a reported confidence interval enables readers to identify this situation.
References
- du Prel J-B, Hommel G, Röhrig B, Blettner M. Confidence interval or p-value? Part 4 of a series on evaluation of scientific publications. Deutsches Ärzteblatt International. 2009;106(19):335-339. read 10 October 2026. View on PubMed Central
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Pubrica Academy. (2026, October 10). P-Value and Confidence Interval: Definitions, Interpretation and Reporting. Pubrica. https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/
Pubrica Academy. “P-Value and Confidence Interval: Definitions, Interpretation and Reporting.” Pubrica, 10 Oct. 2026, pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/.
Pubrica Academy (2026) P-Value and Confidence Interval: Definitions, Interpretation and Reporting. Pubrica. Available at: https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/ (Accessed: 15 October 2026).
Pubrica Academy. “P-Value and Confidence Interval: Definitions, Interpretation and Reporting.” Pubrica. October 10, 2026. https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/
Pubrica Academy, ‘P-Value and Confidence Interval: Definitions, Interpretation and Reporting’ (Pubrica, 10 October 2026) <https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/> accessed 15 October 2026.
Pubrica Academy. P-Value and Confidence Interval: Definitions, Interpretation and Reporting. [Internet]. Pubrica; 2026 Oct 10 [cited 2026 Oct 15]. Available from: https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/
Pubrica Academy, “P-Value and Confidence Interval: Definitions, Interpretation and Reporting,” Pubrica, Oct. 10, 2026. [Online]. Available: https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/
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title = {P-Value and Confidence Interval: Definitions, Interpretation and Reporting},
howpublished = {Pubrica},
year = {2026},
month = {oct},
url = {https://pubrica.com/academy/concepts-definitions/p-value-and-confidence-interval/},
note = {Accessed: <span data-cite-acc="iso">2026-10-15</span>}
}This article is written to be learned from. Cite it if you are referring to what it says; if you are using the evidence behind it, cite the sources listed above instead.
P-value/CI reporting check
For use when drafting the results section.
[ ] Confidence interval reported alongside every p-value [ ] P-value described correctly (probability of data under null), not as probability the hypothesis is true [ ] Confidence interval width discussed where wide, as a precision caveat [ ] Clinical relevance of the effect size assessed, not inferred from significance alone
Pubrica AcademyWritten and maintained by Pubrica’s subject matter experts. Articles are revised when the underlying standards change, and each article states the date on which it was last reviewed.
How Pubrica can help
Pubrica verifies that every effect estimate in a results section is accompanied by its confidence interval and that the surrounding text describes both correctly.