P Value Calculator
P value calculator. Pick the test (z, Student's t, chi-square, or F), enter the test statistic and degrees of freedom where needed, and choose left-, right-, or two-tailed. The calculator returns the exact p-value using the proper distribution, compares it to your significance level (default 0.05), and explains the result in plain words. Runs fully in the browser.
How to use
- Choose z, Student's t, chi-square, or F.
- Enter the test statistic. Add degrees of freedom for t or chi-square, or df1 and df2 for F.
- Choose a left-tailed, right-tailed, or two-tailed test. Chi-square and F start on the right tail.
- Enter alpha, or leave 0.05, and read the p-value, the distribution, and whether the result is significant.
Formula
A z statistic uses the standard normal distribution. A t statistic uses Student's t with the degrees of freedom you enter. Chi-square and F use those distributions. A one-tailed p-value is the probability in the tail you chose. A two-tailed p-value is twice the smaller tail, which for z and t is the chance of a statistic at least this far from zero in either direction. The result is significant when the p-value is less than or equal to alpha.
Example. A two-tailed z of 1.96 has a p-value of 0.0500 and is significant at alpha 0.05. A two-tailed t of 2.0 with 10 degrees of freedom has a p-value of 0.0734, which is not significant at 0.05.
Example. A right-tailed chi-square of 3.84 with 1 degree of freedom has a p-value of 0.0500. A right-tailed F of 4.0 with df1 = 2 and df2 = 20 has a p-value of 0.0346.
What significant means here
Significant means the p-value is less than or equal to the alpha you entered. It is not a measure of how large the effect is, and it does not by itself prove or disprove a hypothesis.
Frequently asked questions
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. Smaller values mean stronger evidence against the null.
How do I know if my result is significant?
Compare the p-value to your significance level, usually 0.05. If the p-value is less than or equal to alpha, the result is statistically significant.
Should I use a one-tailed or two-tailed test?
Use two-tailed when you care about a difference in either direction. Use one-tailed only when your hypothesis predicted the direction before you saw the data.
Which test statistic should I enter?
Use z for large samples with a known standard deviation, t for means with an estimated standard deviation, chi-square for counts and goodness of fit, and F for ANOVA or comparing variances.
Why do I need degrees of freedom?
The t, chi-square and F distributions change shape with degrees of freedom, so the same statistic gives a different p-value for different sample sizes.
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