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.
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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?
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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?
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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?
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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?
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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?
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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.
