| Selected p-value | 0.031555 |
| Two-tailed p-value | 0.031555 |
| Left-tail probability | 0.984222 |
| Right-tail probability | 0.015778 |
p = 0.031555 is below α = 0.05, so the result is statistically significant at that level.
A p-value is the probability of a result at least as extreme as yours, assuming the null hypothesis is true. It is not the probability that the null hypothesis is true. Pick the tail that matches your alternative hypothesis: two-tailed when a difference in either direction counts, right-tailed when you only care about an increase. Use a z test when the population standard deviation is known or the sample is large, and a t test with n − 1 degrees of freedom otherwise.
Get the p-value for a z or t test statistic, one-tailed or two-tailed. A p-value is the probability of a test statistic at least as extreme as the one you observed, if the null hypothesis were true. This calculator turns a z statistic, or a t statistic with its degrees of freedom, into one-tailed and two-tailed p-values, and compares the result with your significance level. It works from the statistic you already have; it does not compute a t statistic from raw data. The normal case uses the standard normal distribution, and the t case uses the Student t distribution.
A p-value converts any test statistic onto one scale: the probability of a result this extreme under the null. With the statistic in hand, the p-value and your significance level decide the conclusion. 100% free, no registration, and complete privacy — everything runs locally in your browser, so your data never touches a server.
Pick the normal or the Student t distribution to match the test you ran.
Left, right and two-tailed p-values in one table, with the tail you chose highlighted.
Compares the p-value with α and states whether the result is significant at that level.
Tail areas come from the normal CDF and the regularized incomplete beta function, checked against published t values.
Standard normal probabilities and critical z values.
Z score, percentile and tail probabilities for a value.
Confidence intervals for a mean and a proportion.
Sample standard deviation for the data behind a t statistic.
One-sample, Welch and paired t tests with the p-value.
If the null hypothesis were true, a result at least this extreme would occur about 3% of the time. It is evidence against the null. It is not the probability that the null is true, and it is not a measure of effect size.
Choose two-tailed when a difference in either direction matters, which is the usual default. Choose one-tailed only when you decided before seeing the data that only one direction is of interest.
For a one-sample t test, df = n − 1. For a two-sample Welch test the formula is more involved, so use the value your software reports. Using the smaller of n1 − 1 and n2 − 1 is a conservative shortcut.
Use z when the population standard deviation is known, or as an approximation for large samples. Use t when you estimate the standard deviation from the sample, especially for small samples.
No. It shows the data are unusual under the null at the chosen level. Study design, effect size and replication matter as well, as the ASA statement on p-values explains.
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