P-Value, Honestly Explained
A p-value answers one narrow question: if the null hypothesis were true, how likely is a result at least this extreme? Small p means your data would be surprising under the null — nothing more, nothing less.
From z-score to p-value
For a z-test, the p-value is read straight off the z table: left-tailed p = P(Z < z); right-tailed p = 1 − P(Z < z); two-tailed p = 2 × the tail. For z = −2.5, the table’s 0.00621 becomes a two-tailed p of 0.0124.
The thresholds
| p-value | Convention |
|---|---|
| < 0.05 | "Statistically significant" — the common default |
| < 0.01 | Stronger evidence standard |
| ≥ 0.05 | "Not significant" — insufficient evidence, not proof of no effect |
What a p-value is NOT
It is not the probability the null hypothesis is true, not the probability your result is due to chance, and not a measure of how large or important an effect is. A tiny effect in a huge sample can have a microscopic p-value; a big effect in a small sample can miss 0.05. Report effect sizes and confidence intervals alongside p — the interval says what the p-value can’t: how big, and how uncertain.