Skip to content
Statistics InferenceStatistics Inference

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

A p-value is NOT the probability that the null hypothesis is true, and it is not the probability that your result happened “by chance”. It is the probability of the data given the null hypothesis — not the probability of the hypothesis given the data.

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.