Null distribution

The null distribution is the sampling distribution of a statistic when the null hypothesis is true; a p-value is an area in its tail.

Every p-value is measured against the null distribution, which answers what your statistic would look like if the null hypothesis were correct. You get that distribution either from theory (a normal, t, or chi-square model) or from simulation, as in a randomization test. For example, under H0:p=0.50H_0: p = 0.50 with n = 100, the null distribution of p-hat (the sample proportion) is approximately normal, centered at 0.50 with standard deviation 0.50(0.50)/100=0.05\sqrt{0.50(0.50)/100} = 0.05. An observed p-hat of 0.60 then sits two standard deviations out, giving a two-sided p-value of about 0.0455.

Where this comes up

More hypothesis testing terms, or browse the full statistics glossary.