P-Value Calculator
The p-value for a z, t, chi-square or F test statistic, one-tailed or two-tailed, with the areas on each side and a comparison with your significance level.
Result
P-value: 0.108433
Exact tail areas of the named distribution. Whether that distribution fits your test is a question the page cannot check.
- Compared with α
- p = 0.1084 is above α = 5%, so the result is not statistically significant at that level.
- Area to the left, P(X ≤ x)
- 0.945783
- Area to the right, P(X ≥ x)
- 0.054217
https://calcgallery.com/statistics/p-value-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the P-Value Calculator
- Choose the distribution your test statistic follows. A t-test gives t, a large-sample test of a mean or proportion gives z, a goodness-of-fit or independence test gives chi-square, and an ANOVA or variance-ratio test gives F.
- Enter the statistic and its degrees of freedom, two of them for F.
- Pick the tail that matches your alternative hypothesis, then read the p-value and how it compares with your significance level.
How the p-value is found
left area P(X ≤ x)right area P(X ≥ x)p (right) right areap (left) left areap (two) 2 × the smaller area, at most 1For z the areas come from the standard normal distribution; for t, chi-square and F they come from the regularised incomplete beta and gamma functions, the same functions statistical software uses. Each area is computed from its own end of the curve, so a tiny tail is accurate.
Degrees of freedom
A one-sample t-test has n − 1. A two-sample Welch test has a fractional value from the Welch–Satterthwaite formula, which you can enter as it is. A chi-square goodness-of-fit test has categories − 1, less one for each parameter estimated from the data. A one-way ANOVA has groups − 1 for the numerator and total observations − groups for the denominator.
What the diagram shows
The density curve of the chosen distribution with your statistic marked. The shaded area is the p-value: one tail, or both tails for a two-tailed z or t test.
With your numbers
- Area to the left = 0.945783; area to the right = 0.054217
- p = 2 × min(0.945783, 0.054217) = 0.108433
Quick reference
Exact tail areas of the named distribution. Whether that distribution fits your test is a question the page cannot check.
| Example | P-value |
|---|---|
| t = 1.782, 9 df, two-tailed | 0.108433 |
| t = 2.262, 9 df, two-tailed | 0.050013 |
| z = 1.96, two-tailed | 0.049996 |
| z = 2.33, right-tailed | 0.009903 |
| χ² = 3.841, 1 df | 0.050014 |
| χ² = 3, 4 df | 0.557825 |
| F = 9.59 with 2 and 12 df | 0.00325 |
| F = 3.89 with 2 and 12 df | 0.049857 |
Common questions about the P-Value Calculator
- What does a p-value mean?
- It is the probability of getting a statistic at least as extreme as yours if the null hypothesis were true. A p-value of 0.03 says data this far from the null would turn up about 3 times in 100 by chance alone. It is not the probability that the null hypothesis is true, and it says nothing about how large or important the effect is.
- One-tailed or two-tailed?
- Two-tailed when your alternative is "different from", in either direction; one-tailed when it is "greater than" (right) or "less than" (left) and was decided before you saw the data. For a symmetric distribution the two-tailed p-value is exactly twice the one-tailed one, which is why switching after the fact halves the p-value and is not allowed.
- Why is a chi-square or F test right-tailed?
- Both statistics grow as the data move away from the null hypothesis, whichever way they move, so only large values count against it. A left tail is used only for special questions, such as whether data fit a model suspiciously well. The two-tailed option doubles the smaller area, the convention for comparing two variances.
- Why does my p-value show as 0?
- The p-value is shown to six decimal places, so anything below 0.0000005 rounds to 0. Below 0.0001 the page also prints it in scientific notation, so a z of 8 gives 1.244 × 10^-15 rather than nothing. The tail is calculated directly, not as 1 minus a number close to 1, so those digits are real.
- Is 0.05 the right significance level?
- It is a convention, not a law of statistics. Some fields use 0.01 or 0.001, and a result at 0.049 is not meaningfully different from one at 0.051. Set α to whatever your course, journal or protocol specifies before you look at the result.