P-Value Calculator
P-value from a z, t, chi-square, F or r statistic. Runs in your browser.
About this p-value calculator
This p-value calculator turns a test statistic into a p-value. Enter a z score, t statistic, chi-square value, F ratio or Pearson correlation r with its degrees of freedom, pick the tail, and you get the p-value, a significant or not significant verdict at your α, and the critical values.
It is for students working through hypothesis tests by hand, and for anyone reading a paper or software output that gives the statistic but not the p-value. The shaded curve shows exactly which area the p-value is, which is the part most textbooks rush past.
The distribution functions are computed in your browser with the incomplete beta and gamma functions, and they were checked against standard statistical table values.
Features
Five statistics
z (standard normal), Student's t, chi-square, F and Pearson r. For r, the calculator converts to t with n − 2 degrees of freedom and shows the conversion.
Left, right or two-tailed
All three tail probabilities are shown at once, and the one you choose is the headline result. Switching tails never needs a new calculation.
Critical values
For your α and tail, you get the cut-off values of the rejection region, so you can check the decision the old way with a table.
Shaded distribution curve
The curve for your exact degrees of freedom is drawn with the p-value area shaded and the critical values marked with dashed lines.
Ready-to-paste result
A line like t(14) = 2.31, p = .037 is built in the APA style used in psychology and the social sciences, and can be copied with one click.
Accurate in the far tails
Very small p-values such as 6.2e−16 for z = 8 keep their precision instead of collapsing to 0.
How to use the p-value calculator
- 1Pick the test statistic: z, t, chi-square, F or Pearson r.
- 2Enter the statistic, its degrees of freedom and the tail of your test.
- 3Read the p-value, the significance verdict and the critical values.
When to use it
Hand-worked t-tests
You have computed t = 2.31 with 14 degrees of freedom on a homework problem. The calculator gives p = 0.0366 two-tailed, below 0.05. The scientific calculator is handy for the t statistic itself.
Chi-square tests of independence
A 3 × 4 contingency table has (3 − 1) × (4 − 1) = 6 degrees of freedom. Enter χ² and 6 to get the right-tailed p-value.
ANOVA tables
An F of 4.2 with 2 and 27 degrees of freedom, from three groups of ten, gives p = 0.0258.
Reading research
A paper reports r = 0.45 from 20 people but no p-value. Enter both to find p = 0.0465 two-tailed.
What is a p-value?
A p-value is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. A small p-value means your data would be surprising under the null hypothesis.
It is not the probability that the null hypothesis is true, and it says nothing about how large or important an effect is. The American Statistical Association's 2016 statement on p-values makes both points, and adds that a decision should not rest on whether p crosses 0.05 alone.
How do you get a p-value from a t statistic?
Find the area under the t distribution with your degrees of freedom beyond your t value. For a two-tailed test, double the smaller tail. With t = 2.31 and 14 degrees of freedom, the right tail is 0.0183, so the two-tailed p-value is 0.0366.
The degrees of freedom depend on the test. A one-sample t-test uses n − 1. A two-sample test with equal variances uses n₁ + n₂ − 2. Welch's test uses a fractional value that your software reports, and you can type decimals here.
One-tailed or two-tailed test?
Use a two-tailed test when any difference matters, in either direction. Use a one-tailed test only when you stated the direction before seeing the data and a result in the other direction would mean the same as no result.
A one-tailed p-value is half the two-tailed one for z and t, so switching after the fact to get under 0.05 is a well-known way to fool yourself. Chi-square and F tests are different. They are almost always right-tailed, because large values are the extreme ones.
Common critical values
These are the values the calculator reproduces at α = 0.05, useful as a quick check:
- z, two-tailed: ±1.960. One-tailed: 1.645
- t with 10 df, two-tailed: ±2.228. With 30 df: ±2.042
- χ² with 1 df: 3.841. With 5 df: 11.070. With 10 df: 18.307
- F with (5, 10) df: 3.326. With (1, 10) df: 4.965
Why use Mavros
| Mavros | Typical upload sites | |
|---|---|---|
| Distributions | z, t, chi-square, F and Pearson r | One calculator per distribution |
| Tails | Left, right and two-tailed shown together | Pick one and recalculate |
| Critical values | Included for any α | A separate table or tool |
| Visual | Curve with the p-value area shaded | Number only |
| Reporting | APA-style line to copy | Not offered |
| Privacy | Runs in your browser | Server request per calculation |
Tips
- Need the statistic first? Work out the mean and standard deviation of each group with the statistics calculator.
- Report the exact p-value, like p = 0.037, rather than just p < 0.05. Below 0.001, writing p < .001 is the usual convention. For rounding the other numbers in a lab report, the significant figures calculator shows the rules.
- A non-significant result is not proof of no effect. It may mean the sample was too small to detect one.
- For chi-square and F, a negative statistic is impossible. If you have one, recheck the calculation.
- Running many tests? Each one has a 5% false positive chance at α = 0.05, so twenty tests will often turn up one by luck. Roll a d20 twenty times in the dice roller to see how often a 1 in 20 shows up. A Bonferroni correction divides α by the number of tests.
Questions
What does p < 0.05 mean?
It means data this extreme would occur less than 5% of the time if the null hypothesis were true. By the usual convention you reject the null at the 0.05 level, but the effect could still be tiny.
How do I calculate a p-value from a z score?
Choose z, enter the score and pick the tail. For z = 1.96, the two-tailed p-value is 0.05 and the one-tailed value is 0.025, because each tail of the normal curve holds 2.5%.
What degrees of freedom should I use for a chi-square test?
For a test of independence, use (rows − 1) × (columns − 1). For a goodness-of-fit test, use the number of categories minus 1, minus any parameters you estimated from the data.
Is a p-value of 0.06 significant?
Not at α = 0.05. It is significant at α = 0.10. Choose α before you run the test, and report 0.06 as it is rather than calling it nearly significant.
Why is the two-tailed p-value double the one-tailed value?
For symmetric distributions like z and t, a two-tailed test counts extreme results on both sides. The area beyond −t equals the area beyond +t, so the total is twice one tail.
Can a p-value be 0?
No, but it can be extremely small. The calculator shows values like 6.2e−16 in scientific notation. Report them as p < .001 in most writing.
How is the p-value for a correlation calculated?
The correlation r is turned into t = r × √(n − 2) ÷ √(1 − r²), then compared with a t distribution with n − 2 degrees of freedom. For r = 0.45 and n = 20, t = 2.14 and p = 0.0465.
What is the difference between the p-value and α?
α is the cut-off you choose in advance, often 0.05. The p-value comes from your data. If p is less than or equal to α, the result is called statistically significant.