P-value vs confidence interval: what each one tells you

A p-value asks whether the data look surprising under a null model. A confidence interval asks which effect sizes remain plausible.

P-values and confidence intervals answer different questions. Use the p-value for evidence against a null model, and the interval for the size and uncertainty of the effect.

By the Math Says Yes editorial team

Human-reviewed under our source and correction standards.

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THE TRAP

Thinking the p-value and the confidence interval are interchangeable because both often appear in the same study table.

A horizontal range bar with a center dot on the left, and a dashed threshold line with a marker crossing it on the right.

The short difference

A starts with a null model, such as no difference between two groups, and asks how unusual the observed data would be if that model were true. A starts with an estimate, such as a difference, and shows a range of effect sizes that remain plausible under the method used. The first is mainly about surprise under a model. The second is mainly about magnitude and precision.

Quick Comparison

P-value

Confidence interval

What it answers

If there were no real improvement, how unusual would this result be?

Which improvement sizes still fit the data?

Common mistake

Treating p as the probability that the claim is false.

Treating 95% as a personal probability for one finished interval.

Use when

You need evidence against a specific null model.

You need size, direction, and precision of the effect.

Worked example

Suppose a study estimates that a treatment improves a score by 4 points, with a 95% from 1 to 7 points and p = 0.02 for the of zero improvement. The says that data at least this favorable would be unusual if the true improvement were exactly zero under the tested model. The interval says the effect is estimated around 4 points, but values from 1 to 7 remain compatible with the procedure.

What people get wrong

The common mistake is reading p = 0.02 as a 98% that the claim is true, or reading a 95% as a personal 95% probability that the finished interval contains the true value. Neither wording is the frequentist definition. Another mistake is ignoring : a tiny can come from a huge and a trivial effect, while a wide interval can show that a study has not pinned down the practical size of the effect.

When it applies

Use a when the question is whether the observed data are hard to reconcile with a specific null model. Use a when the question is how big the effect could reasonably be. In most applied reading, you want both: the p-value can flag a surprising pattern, while the interval helps you judge whether the pattern is large enough, precise enough, and useful enough to matter.

Source note

The ASA statement sets out the limits of interpretation, especially the warning that p-values do not measure the that a hypothesis is true or the size of an effect. Morey and colleagues directly discuss common confidence-interval fallacies. Together, those sources support the page’s practical rule: use p-values and intervals as complementary summaries, not interchangeable proof machines.

Try It

P-value vs. confidence interval

Move the estimate and watch both summaries change.

estimate: +1.5

null value

estimate

-0.5 to +3.5

95% interval

.134

p-value

At an estimate of +1.5, the 95% interval still spans the null value and p = .134. The two agree: an interval that includes 0 is exactly the case where p stays above 0.05.

FAQ

Is a confidence interval better than a p-value?

It is not simply better; it answers a different question. A confidence interval gives effect size and uncertainty, while a p-value summarizes surprise under a null model.

Can a result be statistically significant but still unimportant?

Yes. With a large enough sample, even a tiny effect can produce a small p-value. The confidence interval and the practical context tell you whether the effect matters.