Enter a z or t test statistic, choose one-tailed or two-tailed, and read the exact p-value, a significance verdict at the .05 and .01 levels, and a plain statement of what it means. For a full test run and written up, hand it to a statistician.
Needed only when the distribution is t. For a z statistic you can leave this blank.
A p-value is the probability of seeing a test statistic at least as extreme as yours if the null hypothesis were true. It answers one narrow question: how surprising is this data in a world where there is no real effect. A small p-value says your result would rarely happen by chance alone, so it counts as evidence against the null. A large p-value says the data fit comfortably with the null, so you do not have enough evidence to reject it.
The p-value on its own does not decide anything until you compare it with a threshold, called alpha, that you set before running the test. The two common thresholds are .05 and .01. If the p-value is below .05 the result is called statistically significant, and if it is below .01 the evidence is stronger still. This calculator checks both levels for you, but the choice of alpha is yours, and you should fix it in advance rather than pick it to fit the result.
SPSS, Jamovi, and similar programs round the p-value to three decimal places. A reading of .000 does not mean the p-value is zero, because a p-value is never exactly zero. It means the value is smaller than .0005, so the correct way to write it is p < .001. Never report p = .000 in a results section. This calculator applies the same rule and shows "< .001" whenever the p-value falls below that point.
A two-tailed test looks for a difference in either direction and splits the probability across both ends of the distribution. A one-tailed test looks in a single direction that you predicted in advance, and puts the whole probability in one tail, which makes it easier to reach significance. Because of that, a one-tailed test is only honest when you committed to the direction before seeing the data. Most course assignments and journals expect two-tailed unless you state a directional hypothesis first, so two-tailed is the default here.
A p-value is not the probability that the null hypothesis is true. It is worked out by assuming the null is true, so it cannot turn around and tell you the chance that the null holds. It also does not measure the size of an effect: a tiny, unimportant difference can still produce a small p-value in a large sample. Report an effect size and a confidence interval alongside the p-value so readers see both whether an effect exists and how big it is.
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