P-Value Calculator
Convert a z-score or t-statistic into a p-value, for one or two tails.
What a p-value tells you
The p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. A small p-value, usually below 0.05, is taken as evidence against the null hypothesis.
Choosing the test type
- Two-tailed: you care about a difference in either direction.
- Left-tailed or right-tailed: you care about a decrease or an increase only.
Example
On the first tab (from a z-score) with the starting values shown (Z-score 1.96; Test type Two-tailed), P-value comes out as 0.049996. Other results include significant at 0.05?: Yes (p < 0.05); significant at 0.01?: No (p ≥ 0.01); left-tail probability: 0.975002.
The p-value does not give the probability that the null hypothesis is true, and a significant result is not the same as an important one. Use the t-distribution when the population standard deviation is unknown, especially for small samples.
What a p-value is
The p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. A small p-value, usually below 0.05, is taken as evidence against the null hypothesis. It does not measure the probability that the null hypothesis is true, and it does not measure the size of an effect.
| Significance level | Critical z |
|---|---|
| 0.10 | 1.645 |
| 0.05 | 1.960 |
| 0.01 | 2.576 |
Examples
- A z-score of 1.96 gives a two-tailed p-value of about 0.05.
- A t-statistic of 2.228 with 10 degrees of freedom also gives a two-tailed p-value of about 0.05.
Choosing one or two tails
Use a two-tailed test when you care about a difference in either direction. Use a one-tailed test only when you decided, before collecting data, to look at one direction. For t-tests, use the degrees of freedom of your test, usually the sample size minus 1 for a single sample.
Next steps: Z-Score Calculator, Confidence Interval Calculator, Sample Size Calculator.
Frequently asked questions
How do I calculate a p-value from a z-score?
Find the area in the tail of the normal distribution beyond your z-score, and double it for a two-tailed test.
What does p < 0.05 mean?
The result would be unlikely (under 5% chance) if the null hypothesis were true, so it is called statistically significant at the 5% level.
Is a smaller p-value always better?
A smaller value is stronger evidence against the null, but it does not show the effect is large or important.
What are degrees of freedom?
A number that sets the shape of the t-distribution, often the sample size minus 1.
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