What Is a p-Value? Meaning, Interpretation and Examples
Reviewed by Prof. Dr. Alexander Holtermann · Updated 16 October 2026 · 6 min read
The p-value is the probability of a result at least as extreme as yours if the null hypothesis were true. p < .05 is usually called significant.
Key takeaways
- The p-value answers: if there were really no effect (null hypothesis), how likely is a result at least as extreme as the one observed?
- If p is smaller than the significance level α (usually .05), you reject the null hypothesis and call the result statistically significant.
- The p-value is not the probability that the null hypothesis is true, and 1 − p is not the probability that your hypothesis is true.
- Statistical significance is not practical importance: always report an effect size and, ideally, a confidence interval alongside p.
- APA style: report exact p-values with two or three decimals and no leading zero (p = .005); below .001 write p < .001.
Definition of the p-value
Every significance test starts with a null hypothesis (H₀), usually “there is no difference” or “there is no relationship”. The test then computes a test statistic from your data, such as t, F or χ², and asks how surprising this value would be if H₀ were true.
The p-value is the probability of obtaining a test statistic at least as extreme as the observed one, assuming that the null hypothesis is true. Formally: p = P(data at least this extreme | H₀).
A small p-value means your data would be unusual in a world without an effect. That is taken as evidence against H₀. A large p-value means your data are compatible with H₀, which does not show that H₀ is true.
Worked example: do students study more than planned?
The course handbook plans 20 hours of study per week before an exam. Ten students report: 21, 25, 19, 23, 26, 22, 24, 20, 27, 23 hours. M = 23.00, SD = 2.58.
H₀: the population mean is 20 hours (μ = 20). H₁: it differs from 20 hours (μ ≠ 20). One-sample t-test:
t = (M − μ₀) / (SD / √n) = (23.00 − 20) / (2.58 / √10) = 3.00 / 0.82 = 3.67, df = 9.
| Quantity | Value |
|---|---|
| Test statistic | t(9) = 3.67 |
| Critical value (two-sided, α = .05) | 2.26 |
| p-value, two-sided | .005 |
| p-value, one-sided (μ > 20) | .003 |
| Effect size | d = 3.00 / 2.58 = 1.16 |
| 95% confidence interval for μ | [21.15, 24.85] |
Significance level, critical values and decisions
Before collecting data, you fix the significance level α, the risk you accept of rejecting a true null hypothesis (Type I error). Common choices are .05 and, more strictly, .01 or .001. The decision rule is simple: if p ≤ α, reject H₀; otherwise, do not reject it.
Equivalent: compare the test statistic with the critical value. With df = 9 the two-sided critical t-value is 2.26; your t = 3.67 is larger, so the result is significant.
| p-value | Common wording | Better practice |
|---|---|---|
| p < .001 | highly significant | Report p < .001 plus effect size |
| p = .004 | significant at .01 | Report p = .004 plus effect size |
| p = .032 | significant at .05 | Report p = .032 plus effect size |
| p = .053 | not significant (sometimes “marginally”) | Report p = .053, avoid “trend” language, look at the CI |
| p = .41 | not significant | Report p = .41; absence of evidence is not evidence of absence |
One-sided vs. two-sided p-values
A two-sided (two-tailed) test asks whether there is a difference in either direction. A one-sided test only looks in the direction you predicted. For symmetric test statistics like t, the one-sided p-value is half the two-sided one if the effect goes in the predicted direction (here .003 instead of .005).
Use a one-sided test only if you specified the direction before seeing the data and a result in the opposite direction would be of no interest. Switching to one-sided after seeing p = .07 is a questionable research practice. Two-sided tests are the standard in most fields.
What the p-value does not tell you
In 2016, the American Statistical Association published a statement because misinterpretations were so widespread (Wasserstein & Lazar, 2016). Its key principles, in short:
- A p-value indicates how incompatible the data are with a specified statistical model, nothing more.
- It does not measure the probability that the hypothesis is true or that the data were produced by chance alone.
- Scientific conclusions should not rest only on whether p passes a threshold such as .05.
- Proper inference requires full reporting and transparency: report all analyses you ran, not only the significant ones.
- A p-value does not measure the size of an effect or the importance of a result.
- By itself, a p-value is not a good measure of evidence for a model or hypothesis.
Why sample size changes p but not the effect
The p-value depends on two things: how large the effect is and how many observations you have. With a huge sample, a trivial difference becomes significant; with a tiny sample, even a large difference can miss significance. This is why a p-value alone can never tell you whether a result matters.
Think of the study-hours example: with the same mean (23.00) and SD (2.58) but only n = 4, the t-value would be 3.00 / (2.58 / 2) = 2.32 with df = 3, which is below the critical value of 3.18, so not significant, even though the effect is exactly the same size. Report the effect size (here d = 1.16) and a confidence interval so that readers see both magnitude and precision.
How to report p-values in APA style
APA 7 recommends exact p-values to two or three decimals. Use no leading zero, because p cannot exceed 1. Values below .001 are reported as p < .001. Never write p = .000. Put the p-value after the test statistic and its degrees of freedom, and follow it with an effect size.
Frequently asked questions
What does p < .05 mean?
If the null hypothesis were true, a result at least as extreme as yours would occur in fewer than 5% of studies. You therefore reject the null hypothesis at the 5% significance level.
Is a p-value of .06 significant?
Not at α = .05. Report it exactly (p = .06), avoid calling it a “trend”, and look at the effect size and the confidence interval. It may indicate that the study was underpowered.
Is the p-value the probability that the null hypothesis is true?
No. The p-value is computed assuming the null hypothesis is true. It tells you how surprising the data are under H₀, not how likely H₀ is given the data.
Why do I need an effect size if I have a p-value?
Because p depends on sample size. A tiny effect can be significant in a large sample. The effect size, for example Cohen’s d or r, shows how large the difference or relationship is.
How do I report p = 0.000 from my software?
Write p < .001. The software only rounds; a p-value is never exactly zero.
Sources and further reading
- Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133.
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.).
- Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
Your university’s examination regulations and style guide always take precedence.
Related articles
- Hypothesis testing in 7 stepsHypothesis testing in 7 steps: state H₀ and H₁, set α, choose the test, check assumptions, compute the statistic, decide with p, report the effect size.
- Effect sizeAn effect size tells you how large a difference or relationship is, independent of sample size. Cohen’s d of 0.2, 0.5 and 0.8 is small, medium, large.
- Confidence intervalA 95% confidence interval gives a range of plausible values for a population parameter. It shows both the size of an estimate and its precision.
- Type I and Type II errorsA Type I error is a false positive (rejecting a true null hypothesis, risk α); a Type II error is a false negative (missing a real effect, risk β).
- Reporting statistics in APAAPA style reports test statistic, degrees of freedom, exact p-value and effect size, e.g. t(13.46) = 3.42, p = .004, d = 1.71. Examples for every test.
