Pick the test your statistic came from, enter the score (and degrees of freedom for t or χ²), and get the exact p-value for a left-tailed, right-tailed and two-tailed test, plus a plain-English verdict at your significance level.
Use two-tailed when your alternative hypothesis is "different from"; one-tailed when it is specifically "greater than" or "less than".
A p-value is the probability of getting a test statistic at least as extreme as yours if the null hypothesis were true. The calculator finds the area in the tail (or tails) of the matching distribution: the standard normal curve for a z-score, Student's t distribution for a t-statistic, and the chi-square distribution for χ².
For a z or t score, the left-tailed p-value is the area to the left of your score, the right-tailed p-value is the area to the right, and the two-tailed p-value doubles the smaller of the two. For example, z = 1.96 gives a two-tailed p of 0.0500, the familiar 95% cut-off. The same score as a t-statistic with 10 degrees of freedom gives p ≈ 0.0784, because the t distribution has heavier tails when samples are small.
Chi-square tests (goodness of fit, independence) are almost always right-tailed, so the headline result for χ² is the right-tail area. χ² = 3.84 with 1 degree of freedom gives p ≈ 0.0500.
It is the probability of seeing a result at least as extreme as yours, assuming the null hypothesis is true. A small p-value (below your chosen α, often 0.05) means the data would be unusual under the null hypothesis, so you reject it.
Use two-tailed when your alternative hypothesis is that the value is simply different (higher or lower). Use one-tailed only when you decided in advance that only one direction matters, for example "the new drug lowers blood pressure".
The t distribution has heavier tails than the normal distribution to account for the extra uncertainty of estimating the standard deviation from a small sample. As degrees of freedom grow, t approaches z and the p-values converge.
For a one-sample or paired t-test, use n − 1. For a two-sample t-test with equal variances, use n₁ + n₂ − 2. For a chi-square test of independence, use (rows − 1) × (columns − 1); for goodness of fit, use categories − 1.
Not necessarily. Statistical significance says the effect is unlikely to be zero, not that it is large or meaningful. With a big enough sample, tiny effects become significant, so report the effect size and confidence interval too.
