Pharmaceutical Statistics Using SAS

10.9. Table of Crucial Error Rates

Table 10.6 shows how α^* and β^* depend on γ, α and β. Type I errors are more frequent early in the March of Science (low γ), whereas Type II errors are more frequent later in the March. Reducing either α or β reduces both α^* and β^*. Note also that when γ = 0.50 and α = β, then α =α^* = β = β^*.

Table 10-6. Crucial Type I and Type II Error Rates as a Function of γ, α and Power

γ : Pr[H0 false]	Power	β	α*: Pr[H0 true | p ≤ α]				β*: Pr[H0 false | p > α]
			α: 0.01	0.05	0.10	0.20	α: 0.01	0.05	0.10	0.20
0.05	0.30	0.70	.388	.760	.864	.927	.036	.037	.039	.044
	0.50	0.50	.275	.655	.792	.884	.026	.027	.028	.032
	0.70	0.30	.213	.576	.731	.844	.016	.016	.017	.019
	0.80	0.20	.192	.543	.704	.826	.011	.011	.012	.013
	0.90	0.10	.174	.514	.679	.809	.005	.006	.006	.007
	0.95	0.05	.167	.500	.667	.800	.003