How this calculator works
The reference distribution describes the statistic under the null hypothesis. A right-tailed test uses the survival probability, a left-tailed test uses the cumulative probability, and the two-sided option doubles the smaller tail. For asymmetric F and chi-square distributions this is an equal-tail convention; use the tail appropriate to the original test. The decision compares p with the chosen alpha. It does not state the probability that the null hypothesis is true.
Formula
pright = P(T ≥ t); pleft = P(T ≤ t); ptwo = min(1, 2 × min(pleft, pright)).
Worked example
A standard normal statistic of 1.96 gives a right-tailed p-value about 0.024998 and a two-sided p-value about 0.049996. A t statistic of 1 with one degree of freedom gives right-tail probability 0.25.
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Frequently asked questions
Is p the probability that the null is true?
No. It is calculated assuming the null model and describes how extreme the observed statistic is under that model.
Why choose a tail in advance?
Changing direction after seeing the data changes the false-positive rate and invalidates the stated test.
Which tail applies to an ANOVA F statistic?
The usual ANOVA test rejects for a large F, so use the right tail rather than the equal-tail two-sided option.