How to Read a P-Value
A Plain-English Guide

What Is a P-Value?

A p-value is the probability of observing a test result at least as extreme as the one you calculated, assuming the null hypothesis is true. It does not tell you the probability that the null hypothesis is true. It does not tell you how big or important an effect is. It tells you only how surprising the data would be if the null hypothesis were correct.

If a hypothesis test produces p = 0.03, it means: if the null hypothesis were true, there is a 3% chance of seeing a result this extreme just by random chance. Since 3% is below the typical threshold of 5% (α = 0.05), you would reject the null hypothesis.

What the P-Value Does NOT Mean

It is not the probability the null hypothesis is true

This is the most common misconception. A p-value of 0.03 does not mean there is a 3% chance H₀ is true, or a 97% chance the effect is real. It only describes the behavior of the data under a hypothetical world where H₀ is true.

It is not a measure of effect size

A very small p-value can come from a large sample detecting a tiny, practically meaningless effect. A p-value of 0.0001 doesn’t mean the effect is large — it may just mean you had a lot of data. Always report effect size (Cohen’s d, R², etc.) alongside the p-value.

p > 0.05 does not mean “no effect”

Failing to reject H₀ means the data didn’t provide enough evidence against it — not that H₀ is true. “Absence of evidence is not evidence of absence.”

How to Report a P-Value in a Paper or Assignment

Standard reporting format: state the test used, the test statistic, degrees of freedom, and the p-value. Example:

Report the exact p-value rather than writing “p < 0.05” unless the exact value is very small (p < .001 is acceptable). Never write “p = 0.000” — always write “p < .001”.

One-Tailed vs Two-Tailed P-Values

A two-tailed test checks for a difference in either direction (greater or less than). A one-tailed test checks only one direction. The p-value for a one-tailed test is half the p-value for the equivalent two-tailed test. Use one-tailed tests only when you have a strong theoretical reason to expect an effect in one specific direction, stated before seeing the data.

Common P-Value Thresholds

• p < 0.05 — statistically significant at the 5% level (most common threshold)
• p < 0.01 — significant at the 1% level (stricter, used in medical research)
• p < 0.001 — highly significant (often reported as p < .001)
• p ≥ 0.05 — not statistically significant at the 5% level

P-Value vs Statistical Significance

Statistical significance is a binary decision — either you reject H₀ or you don’t — based on comparing p to α. But the p-value itself is continuous. p = 0.049 and p = 0.051 represent nearly identical evidence; the threshold at 0.05 is a convention, not a natural law. Many researchers now recommend reporting exact p-values and letting readers interpret them rather than just saying “significant” or “not significant”.

Run a Hypothesis Test with Full P-Value Explanation →