How the p-Value Calculator works
A p-value is the probability of seeing a test statistic at least as extreme as yours if the null hypothesis were true. For z-scores the calculator integrates the standard normal distribution, and for t-statistics it uses the t-distribution with your degrees of freedom, which has heavier tails in small samples.
Two-tailed p = 2 × P(Z > |z|), or for t: p = Idf/(df+t²)(df/2, 1/2)
Example: z = 1.96 gives a two-tailed p of 0.05 exactly at the classic threshold, while the same 1.96 as a t-statistic with 10 degrees of freedom gives p = 0.078, not significant, showing why small samples demand bigger effects.
Frequently asked questions
What does p < 0.05 actually mean?
If there were truly no effect, results this extreme would occur less than 5% of the time by chance. It does not measure the size or importance of the effect, only its surprisingness under the null.
One-tailed or two-tailed?
Two-tailed unless you pre-specified a direction before collecting data. Switching to one-tailed after seeing results is a classic way to manufacture significance.
When do t and z give different answers?
With small samples. Below about 30 degrees of freedom the t-distribution's heavier tails raise the p-value noticeably; by df of 100 the two are nearly identical.