P-Value Calculator

In short A p-value is the probability of getting a result at least as extreme as the one you observed, IF the null hypothesis is true. It is a statement about data given a hypothesis, and reversing those two is the most common mistake in statistics. A two-tailed z of 2 gives p = 0.0455, z = 3 gives 0.0027 — about 1 in 370 — and z = 5 gives 5.7 × 10⁻⁷, which is roughly 1 in 1.7 million. This page converts z, t and chi-square statistics, one or two-tailed, and prints the critical value at each usual threshold so you can see the same decision from both ends. Use two tails unless the direction was predicted before the data was seen; halving a p-value after looking is not a one-tailed test, it is a way of getting a smaller number. Chi-square tests are naturally upper-tailed, because departures in either direction make the statistic larger, never smaller. What a p-value is not: it is not the probability that the null hypothesis is true, not the probability the result was a fluke, and not a measure of how big or important the effect is. With a large enough sample a trivial difference produces a tiny p, which is why a p-value should always be read next to an effect size and a confidence interval. And the 0.05 line is a convention proposed as a rough working threshold, not a law — p = 0.049 and p = 0.051 are the same evidence.