Statistical Significance vs Practical Significance

Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.

Statistical significance

Hypothesis testing

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.

Full entry for statistical significance

Practical significance

Hypothesis testing

Practical significance asks whether an effect is large enough to matter in context, a judgment no p-value can make for you.

A hypothesis test tells you whether there is convincing evidence of an effect; practical significance tells you whether anyone should change what they do about it. The size of the effect and the setting decide that, so the same difference can matter enormously in one context and not at all in another. For example, a supplement that lowers average blood pressure by 0.4 mmHg could be statistically significant with 100,000 subjects and still be clinically pointless. A confidence interval helps you judge it, since a narrow interval that excludes zero but sits close to it says the effect is real and small.

Full entry for practical significance

Where each one fits in the course