Definition

Type I and Type II errors

A Type I error is a false positive (rejecting a true null); a Type II error is a false negative (missing a real effect).

The two error rates trade off. Alpha (usually 5%) caps the false-positive rate; beta is the false-negative rate, and power = 1 − beta. Tightening alpha without increasing the sample makes misses more likely, and vice versa.

Which error matters more depends on the stakes: screening tests tolerate false positives to avoid misses; expensive interventions demand low false-positive rates. Good design states the trade-off; multiple-comparison corrections exist because running many tests inflates the effective Type I rate.