Statistical significance

A result is statistically significant when its p-value is at or below alpha: a result at least this extreme would be unlikely if the null hypothesis were true.

Statistical significance is a statement about surprise under the null hypothesis, not about size or importance. Its biggest trap is sample size: with enough data, a difference far too small to care about still comes out significant. For example, testing H0:p=0.50H_0: p = 0.50 with p-hat (the sample proportion) equal to 0.51 gives z=0.63z = 0.63 and no significance when n = 1000, but the identical 1 percentage point gap gives z=6.32z = 6.32 when n = 100,000. Read significance next to practical significance and a confidence interval, which shows how big the effect might actually be.

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