Type I / Type II Error and Power

Two sampling distributions: H0 (solid) and Ha (dashed), split by the critical value x*. Gold = α (Type I), coral = β (Type II), teal = Power = 1−β. Larger effect size or larger n separates the curves and raises power.

Significance level (α)

Tail mode

α (Type I)
0.05
P(reject | H0 true)
β (Type II)
0
P(fail | Ha true)
Power
0
1 − β

Try: α = 0.01 shrinks gold but grows coral — power drops. Raise n to 150 and the curves narrow apart, power recovers. Push effect size to 3.0 and power jumps toward 1. Two-tail always has slightly lower power than right-tail at the same settings.