Variance
Calculator
Sample and population variance from any data set.
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Statistics — Significance
P-Value Calculator
Enter a z-score or t-score and choose one- or two-tailed to get the exact p-value from the normal or Student t distribution.
P-value
—
Probability under the null hypothesis.
| Test statistic | — |
|---|---|
| Distribution | — |
| At α = 0.05 | — |
| At α = 0.01 | — |
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Enter your figures above to see the step-by-step working.
For a one-sample t test, degrees of freedom are usually n − 1Everything computed client-side — nothing leaves this page
How the P-Value Calculator Works
A p-value is the probability of getting a test statistic at least as extreme as the one you observed, assuming the null hypothesis is true. Enter your test statistic, choose the standard normal (z) or Student’s t distribution — giving the degrees of freedom for t — and pick a one- or two-tailed test. The desk returns the p-value from the exact distribution.
For a two-tailed test the calculator doubles the tail area beyond the absolute value of your statistic. A common threshold is 0.05: a p-value below it is usually called statistically significant, meaning the result would be unlikely by chance alone. The t distribution requires degrees of freedom, which for a simple sample is usually the sample size minus one.
two-tailed p = 2 × (1 − CDF(|statistic|))
Frequently Asked Questions
What does the p-value mean?
It is the probability, if the null hypothesis were true, of observing a result at least as extreme as yours. A small p-value means your data would be unlikely under the null hypothesis, which is treated as evidence against it.
Should I use the z or t distribution?
Use z (standard normal) when the population standard deviation is known or the sample is large. Use t, with the appropriate degrees of freedom, for a small sample where you estimated the standard deviation from the data. For a one-sample test, df is usually n minus 1.
Is a p-value below 0.05 always significant?
0.05 is a common convention, not a law. A p-value just below 0.05 is weak evidence, and significance does not measure effect size or importance. Always report the p-value itself and interpret it in context.
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