Table 2: Comparisons of type I error and power between the one-sample t-test, where Type I error* and Power* represent type I error and power for reduced data, respectively.

Standard deviation Mean Size Type I error Type I error* Power Power*
1 0.5 20 0.047 0.047 0.564 0.643
40 0.050 0.000 0.881 1.000
60 0.051 0.000 0.974 1.000
1 20 0.047 0.000 0.995 1.000
40 0.050 0.000 1.000 1.000
60 0.051 0.000 1.000 1.000
0.7 0.5 20 0.047 0.000 0.863 1.000
40 0.050 0.000 0.997 1.000
60 0.051 0.000 1.000 1.000
1 20 0.047 0.000 1.000 1.000
40 0.050 0.000 1.000 1.000
60 0.051 0.000 1.000 1.000

*: Type I error==Prob [ | Y ¯ | μ 0  when data generated under  H 0  ]  and Power=1β=Prob| Y ¯ | μ 0  when data generated under  H 1  ] .