Enter your test statistic (z or t value) from your statistical test. If you're performing a t-test, supply the degrees of freedom; leave it blank for a z-test. Select one-tailed (testing direction in one direction) or two-tailed (testing if a difference exists in either direction). The calculator uses the standard normal cumulative distribution function (CDF) to compute the p-value. For t-tests, it applies a normal approximation, which is accurate for large degrees of freedom but may drift slightly for small samples.
A p-value is the probability of your observed data (or more extreme data) occurring if the null hypothesis is true. It does not tell you the probability that the null hypothesis is true, nor does it measure the size or importance of an effect.
Use one-tailed if you predicted the direction of the effect in advance (e.g., "mean A is greater than mean B"). Use two-tailed if you only care whether a difference exists, without predicting direction. Two-tailed tests are more conservative and are standard when direction is unknown.
Use z-tests when the population standard deviation is known or the sample size is very large (>30). Use t-tests for small samples where you estimate the standard deviation from the sample. t-tests account for additional uncertainty in small samples.
No. A small p-value indicates strong evidence against the null hypothesis, but it does not prove your alternative hypothesis is true. It also does not account for prior probability, effect size, or the number of tests you've run. Always consider context and avoid p-hacking.
The normal approximation simplifies calculation and is accurate for many practical cases, especially with larger degrees of freedom. For very small samples or critical decisions, use a dedicated statistics package (R, Python, SAS) that computes exact t distribution values.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.