P-Value Calculator

What Is a P-Value?

A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value indicates that the observed data would be unlikely under the null hypothesis, providing evidence against it. This calculator converts a z, t, or chi-square test statistic into its corresponding p-value using exact numerical approximations of each distribution.

One-Tailed vs Two-Tailed Tests

A one-tailed (left- or right-tailed) test looks for an effect in a single direction, placing the entire rejection region in one tail. A two-tailed test looks for any difference regardless of direction and splits the rejection region between both tails. Chi-square goodness-of-fit tests are right-tailed by convention, so two-tailed is not applicable for that distribution.

Significance Level α

The significance level α (commonly 0.05) is the threshold below which a result is declared statistically significant. If the p-value is less than α, the result is considered significant. Remember that a p-value is not the probability that the null hypothesis is true, nor the probability that your result occurred by chance alone. A non-significant result does not prove the null hypothesis, and statistical significance does not imply practical importance.

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