What Is a P-Value? A Plain-English Guide
What a p-value actually means, the 0.05 threshold, one- vs two-tailed tests, and the misconception to avoid — explained simply.
6 min read · Reviewed August 2026
What a p-value actually means
A p-value is the probability of seeing results at least as extreme as the ones you got, assuming the null hypothesis (the “nothing is going on” assumption) is true. A small p-value means your data would be surprising if there were really no effect — so it counts as evidence against the null hypothesis.
The smaller the p-value, the stronger the evidence against the null. A p-value of 0.01 means that if the null were true, you would see data this extreme only about 1% of the time.
The one thing a p-value is NOT
This is the single most common misinterpretation. A p-value of 0.03 does not mean “there is a 3% chance there is no effect”. It means “if there were no effect, data this extreme would occur 3% of the time”.
The 0.05 threshold (significance level)
Before running a test you choose a significance level, alpha (α) — most commonly 0.05. You then compare your p-value to it:
- p ≤ α → reject the null hypothesis; the result is “statistically significant”.
- p > α → fail to reject the null hypothesis; there is not enough evidence.
The 0.05 line is a convention, not a law of nature. Fields that need more certainty use stricter levels like 0.01, and a p-value of 0.049 is not meaningfully different from 0.051 — treat the threshold as a guide, not a cliff edge.
One-tailed vs. two-tailed
A two-tailed test asks “is there any difference?” and splits the significance across both tails. A one-tailed test asks a directional question (“is it greater?” or “is it less?”) and puts all of it in one tail. Two-tailed is the safer default unless you have a strong prior reason to test a single direction.
Significant ≠ important
A tiny, meaningless effect can be statistically significant if the sample is large enough, and a big, important effect can be non-significant if the sample is small. Always read the p-value alongside the effect size and a confidence interval, which tell you how large the effect is, not just whether it is detectable.
Frequently asked questions
What does a p-value of 0.05 mean?
It means that if the null hypothesis were true, you would see data at least as extreme as yours about 5% of the time. At the common α = 0.05 threshold, a p-value of exactly 0.05 sits right on the line for statistical significance.
Is a lower p-value better?
A lower p-value is stronger evidence against the null hypothesis, but “better” depends on your question. A very low p-value on a trivial effect is not necessarily meaningful — pair it with the effect size and a confidence interval.
What does it mean if the p-value is greater than 0.05?
You fail to reject the null hypothesis: there is not enough evidence to conclude an effect exists. This is not proof that there is no effect — only that your data did not provide strong enough evidence.