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*.
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 | .003 | .003 | .003 | |
0.30 | 0.30 | 0.70 | .072 | .280 | .438 | .609 | .233 | .240 | .250 | .273 |
0.50 | 0.50 | .045 | .189 | .318 | .483 | .178 | .184 | .192 | .211 | |
0.70 | 0.30 | .032 | .143 | .250 | .400 | .115 | .119 | .125 | .138 | |
0.80 | 0.20 | .028 | .127 | .226 | .368 | .080 | .083 | .087 | .097 | |
0.90 | 0.10 | .025 | .115 | .206 | .341 | .041 | .043 | .045 | .051 | |
0.95 | 0.05 | .024 | .109 | .197 | .329 | .021 | .022 | .023 | .026 | |
0.50 | 0.30 | 0.70 | .032 | .143 | .250 | .400 | .414 | .424 | .438 | .467 |
0.50 | 0.50 | .020 | .091 | .167 | .286 | .336 | .345 | .357 | .385 | |
0.70 | 0.30 | .014 | .067 | .125 | .222 | .233 | .240 | .250 | .273 | |
0.80 | 0.20 | .012 | .059 | .111 | .200 | .168 | .174 | .182 | .200 | |
0.90 | 0.10 | .011 | .053 | .100 | .182 | .092 | .095 | .100 | .111 | |
0.95 | 0.05 | .010 | .050 | .095 | .174 | .048 | .050 | .053 | .059 | |
0.70 | 0.30 | 0.70 | .014 | .067 | .125 | .222 | .623 | .632 | .645 | .671 |
0.50 | 0.50 | .008 | .041 | .079 | .146 | .541 | .551 | .565 | .593 | |
0.70 | 0.30 | .006 | .030 | .058 | .109 | .414 | .424 | .438 | .467 | |
0.80 | 0.20 | .005 | .026 | .051 | .097 | .320 | .329 | .341 | .368 | |
0.90 | 0.10 | .005 | .023 | .045 | .087 | .191 | .197 | .206 | .226 | |
0.95 | 0.05 | .004 | .022 | .043 | .083 | .105 | .109 | .115 | .127 |