Direct comparison
P-Value vs Confidence Interval
A p-value tests surprise under the null hypothesis. A confidence interval estimates a range of plausible effect sizes. Report both, per ASA guidance.
Written and maintained by CASRAI Editorial Board
Last updated
Ask CASRAI · free to try
Ask about P-Value vs Confidence Interval
Ask your first 2 questions free below. Subscribers get 150 a day for $29 a month.
An AI assistant specialized in research administration. It cites the sources behind every answer, labels web answers and says when it can't answer.
Answers draw on CASRAI's guides and dictionary plus the federal and funder documents we index: Federal Register, Grants.gov, Regulations.gov and UKRI.
Works on this site and inside Claude, Cursor and the AI tools you already use.
Everything CASRAI publishes — this page, the dictionary, the guides and the news — stays free to read, with no account and no card.
How do P-Value, Confidence Interval compare side by side?
The table below compares P-Value, Confidence Interval across 9 procurement-relevant dimensions, from what it is through governing methodological statement.
Side-by-side comparison
| Dimension | P-Value | Confidence Interval |
|---|---|---|
| What it is | A conditional probability: P(data this extreme or more | the null hypothesis is true) | A range of plausible values for the population parameter, at a stated confidence level (commonly 95%) |
| Question it answers | How surprising would this data be if there were truly no effect? | What range of effect sizes is this data consistent with? |
| Tells you about effect size? | No — a tiny p-value can come from a trivially small effect given a large enough sample | Yes — directly, as the width and location of the interval |
| Tells you about precision? | No | Yes — a narrow interval means a precise estimate; a wide one means the study may be underpowered |
| Common misinterpretation | Read backward as P(null hypothesis is true | the data) — explicitly flagged as an error by the ASA | Read as "95% probability the true value is in this range" — the correct frequentist reading is about the long-run reliability of the procedure, not this one interval |
| Conventional threshold | α = 0.05, an arbitrary Fisher-era convention, not a mathematical law | 95% confidence level, equally a convention (90% and 99% are also used) |
| Relationship to significance | p < α is conventionally called "statistically significant" | An interval excluding the null value (0 for a difference, 1 for a ratio) agrees with a significant p-value at the same threshold — they're mathematically linked |
| What large sample size does to it | Can drive it arbitrarily small even for a trivial effect | Narrows the interval — precision improves, but the point estimate doesn't automatically get "more significant" |
| Governing methodological statement | ASA's 2016 "Statement on p-Values: Context, Process, and Purpose" (Wasserstein & Lazar) | Same ASA statement recommends reporting CIs alongside p-values for exactly this reason |
Common questions
Common questions about P-Value vs Confidence Interval
If I already have a p-value, why do I also need a confidence interval?
+
Because a p-value alone can't tell you whether a significant result is practically meaningful or precisely estimated. With a large enough sample, even a trivially small effect produces a tiny p-value. A confidence interval shows the actual range of plausible effect sizes — a narrow interval close to a meaningful value tells a very different story than a wide interval that barely excludes zero, even if both produced the same p-value.
Does a 95% confidence interval mean there's a 95% chance the true value is in that range?
+
No, and this is one of the most common statistical misstatements in published research. In the standard frequentist framework, the population parameter is a fixed constant, not a random variable — it either is or isn't in any specific calculated interval, with no probability left to assign once the interval is calculated. The 95% describes the long-run reliability of the estimation procedure: if repeated on many samples, about 95% of the resulting intervals would contain the true value. A true probability statement about the parameter itself is what a Bayesian credible interval provides instead.
Can a result be statistically significant by p-value but the confidence interval still look unimpressive?
+
Yes, and this is exactly why the ASA recommends reporting both. A p just under 0.05 with a confidence interval that barely excludes the null value shows a real but marginal, imprecisely estimated effect — very different from a p = 0.0001 with a narrow interval far from the null, even though both would be labeled "significant" on the p-value alone.
Are a significant p-value and a confidence interval excluding the null always in agreement?
+
Yes, for the same test at the same confidence/significance level — they're mathematically linked, so a p-value below α and a confidence interval that excludes the corresponding null value (0 for a difference, 1 for a ratio) will always agree on the significant/non-significant call. What they don't agree on is how much additional information they carry about effect size and precision.
Why did the American Statistical Association issue a formal statement about p-values?
+
Because of well-documented, persistent misuse and misinterpretation across the scientific literature — treating p-values as the probability a hypothesis is true, as a measure of effect size, or as a hard significant/non-significant line rather than one piece of evidence. The ASA's 2016 statement (Wasserstein & Lazar, The American Statistician) set out six principles correcting these errors and recommending p-values be reported alongside effect sizes and confidence intervals rather than as a standalone verdict.
