What a p-value is
A p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. From a z-score, it's the area in the tail(s) of the standard normal distribution beyond that z. For z = 1.96, the two-tailed p-value is about 0.05 — the conventional cutoff for statistical significance.
Note what it does not say: the p-value is not the probability that the null hypothesis is true, nor the chance your result was a fluke. A p-value is a tail probability, and the probability calculator covers the simpler cases behind it.
How to use this calculator
Enter the z-score and choose 1 or 2 tails. Use two-tailed when you're testing for a difference in either direction, one-tailed when you have a directional hypothesis. Get the z-score first from the z-score calculator.
The sign of the z-score does not change a two-tailed p-value, since both tails are counted — a z of −1.96 gives the same 0.05. Decide on one or two tails before you look at the data.
Reading the result
Larger z-scores sit further out in the tail, so they produce smaller p-values. Useful landmarks for a two-tailed test:
- z = 1.645 gives p ≈ 0.10
- z = 1.96 gives p ≈ 0.05
- z = 2.576 gives p ≈ 0.01
Compare the p-value with the threshold you fixed in advance. Falling below it means the result is statistically significant; failing to is not proof of no effect, since the sample may simply be too small. Significance and precision are two sides of one coin, so read the result alongside a confidence interval.
Frequently asked questions
- How do I find a p-value from a z-score?
- Take the tail area of the normal distribution beyond the z-score: one tail for a directional test, doubled for a two-tailed test. z = 1.96 gives a two-tailed p of about 0.05.
- What p-value is significant?
- By common convention, p < 0.05 is considered statistically significant, though the threshold depends on the field and study.
- What is the difference between one- and two-tailed?
- One-tailed tests a difference in a specific direction; two-tailed tests for any difference and so doubles the tail probability.
- Is this exact?
- It uses a very accurate normal approximation, suitable for large-sample z-tests. Small samples may need a t-distribution instead.
- Does a small p-value mean the effect is large or important?
- No. A p-value only measures how surprising the data would be if the null hypothesis were true, and it shrinks as the sample grows. A trivial effect can reach p < 0.001 in a big study, so always report the effect size too.