Estimate p-values from a test statistic for Normal, T, or Chi-Square distributions
This p-value calculator estimates the probability of observing a test statistic as extreme as the one provided, assuming the null hypothesis is true. It supports the standard normal (Z) distribution, Student's T distribution, and the Chi-Square distribution. The calculator shows both one-tailed and two-tailed p-values and indicates statistical significance at the \u03b1 = 0.05 level.
For the normal distribution, this calculator uses the Abramowitz and Stegun approximation for the cumulative distribution function (CDF). For the T distribution, it uses an approximation based on the regularized incomplete beta function. These provide accurate estimates suitable for most practical purposes.
A p-value less than 0.05 means there is less than a 5% probability that the observed result occurred by random chance alone under the null hypothesis. This is conventionally considered statistically significant, providing evidence to reject the null hypothesis in favor of the alternative.
A one-tailed p-value tests for an effect in a specific direction (e.g., greater than or less than). A two-tailed p-value tests for an effect in either direction (both greater than and less than). Two-tailed tests are more conservative and are generally recommended unless there is a strong prior justification for a directional hypothesis.