Table 1.
Empirical type I error rates at 0.05 and 0.01 nominal significance levels of the proposed tests
|
Nominal |
Sample size |
p |
Model |
||||||
|---|---|---|---|---|---|---|---|---|---|
| Level α | s | n | m | Unr | Dom | Rec | Mult | Add | |
| |
|
|
|
0.5 |
0.04989 |
0.04985 |
0.04867 |
0.05028 |
0.05138 |
| |
|
|
25 |
0.2 |
0.04152 |
0.05057 |
0.04240 |
0.05214 |
0.05364 |
| 0.05 |
50 |
100 |
|
0.1 |
0.03517 |
0.05006 |
0.02672 |
0.04979 |
0.05230 |
| 0.05 |
0.05327 |
0.05093 |
0.05038 |
0.05138 |
0.05685 |
||||
| |
|
|
|
0.5 |
0.04921 |
0.05055 |
0.05135 |
0.05149 |
0.05330 |
| |
|
|
0 |
0.2 |
0.03999 |
0.05073 |
0.03637 |
0.05156 |
0.05222 |
| |
|
|
|
0.1 |
0.03534 |
0.05088 |
0.02611 |
0.05249 |
0.05199 |
| |
|
|
|
0.05 |
0.05944 |
0.04916 |
0.06505 |
0.05230 |
0.05609 |
| |
|
|
|
0.5 |
0.00907 |
0.01039 |
0.00973 |
0.00972 |
0.01031 |
| |
|
|
25 |
0.2 |
0.00759 |
0.01031 |
0.00568 |
0.01043 |
0.01117 |
| 0.01 |
50 |
100 |
|
0.1 |
0.00699 |
0.01011 |
0.00504 |
0.01054 |
0.00936 |
| |
0.05 |
0.01010 |
0.01072 |
0.00966 |
0.01021 |
0.01200 |
|||
| |
|
|
|
0.5 |
0.00831 |
0.0098 |
0.01008 |
0.00998 |
0.01043 |
| |
|
|
0 |
0.2 |
0.00723 |
0.01075 |
0.00489 |
0.01054 |
0.01097 |
| |
|
|
|
0.1 |
0.00676 |
0.01065 |
0.00477 |
0.01040 |
0.01014 |
| |
|
|
|
0.05 |
0.01054 |
0.01054 |
0.01204 |
0.01104 |
0.01163 |
| |
|
|
|
0.5 |
0.04974 |
0.05003 |
0.05093 |
0.04951 |
0.05178 |
| |
|
|
50 |
0.2 |
0.04641 |
0.04976 |
0.05019 |
0.05005 |
0.05201 |
| 0.05 |
50 |
200 |
|
0.1 |
0.03539 |
0.04977 |
0.02236 |
0.04996 |
0.05236 |
| |
0.05 |
0.04095 |
0.05142 |
0.03730 |
0.04990 |
0.05288 |
|||
| |
|
|
|
0.5 |
0.05121 |
0.05027 |
0.05121 |
0.05039 |
0.05098 |
| |
|
|
0 |
0.2 |
0.04360 |
0.05128 |
0.04991 |
0.05210 |
0.05249 |
| |
|
|
|
0.1 |
0.03503 |
0.05018 |
0.02303 |
0.05146 |
0.05108 |
| |
|
|
|
0.05 |
0.04521 |
0.05156 |
0.04011 |
0.05423 |
0.04997 |
| |
|
|
|
0.5 |
0.01042 |
0.00967 |
0.01010 |
0.00961 |
0.01050 |
| |
|
|
50 |
0.2 |
0.00872 |
0.00962 |
0.00914 |
0.01020 |
0.01101 |
| 0.01 |
50 |
200 |
|
0.1 |
0.00642 |
0.00986 |
0.00430 |
0.01056 |
0.01043 |
| |
0.05 |
0.00769 |
0.01125 |
0.00705 |
0.01091 |
0.01133 |
|||
| |
|
|
|
0.5 |
0.00987 |
0.00976 |
0.00987 |
0.00991 |
0.01002 |
| |
|
|
0 |
0.2 |
0.00799 |
0.01030 |
0.00828 |
0.01059 |
0.01062 |
| |
|
|
|
0.1 |
0.00629 |
0.01012 |
0.00443 |
0.00994 |
0.01089 |
| |
|
|
|
0.05 |
0.00900 |
0.01027 |
0.00769 |
0.01076 |
0.00924 |
| |
|
|
|
0.5 |
0.05032 |
0.05009 |
0.05048 |
0.04870 |
0.04895 |
| |
|
|
125 |
0.2 |
0.05091 |
0.05029 |
0.05025 |
0.04965 |
0.05111 |
| 0.05 |
50 |
500 |
|
0.1 |
0.04178 |
0.04998 |
0.04298 |
0.05023 |
0.05021 |
| |
0.05 |
0.03380 |
0.05043 |
0.02511 |
0.05020 |
0.05081 |
|||
| |
|
|
|
0.5 |
0.04957 |
0.05049 |
0.05056 |
0.05150 |
0.05048 |
| |
|
|
0 |
0.2 |
0.05071 |
0.04963 |
0.0522 |
0.04954 |
0.05084 |
| |
|
|
|
0.1 |
0.03980 |
0.05037 |
0.03109 |
0.04936 |
0.05067 |
| |
|
|
|
0.05 |
0.03491 |
0.05012 |
0.02749 |
0.05031 |
0.05107 |
| |
|
|
|
0.5 |
0.01032 |
0.00957 |
0.01016 |
0.00963 |
0.00928 |
| |
|
|
125 |
0.2 |
0.01006 |
0.01045 |
0.01031 |
0.01040 |
0.01062 |
| 0.01 |
50 |
500 |
|
0.1 |
0.00707 |
0.0098 |
0.00502 |
0.01051 |
0.01008 |
| |
0.05 |
0.00640 |
0.00996 |
0.00473 |
0.00979 |
0.01077 |
|||
| |
|
|
|
0.5 |
0.00971 |
0.01057 |
0.00974 |
0.01024 |
0.00998 |
| |
|
|
0 |
0.2 |
0.00978 |
0.00999 |
0.01081 |
0.00955 |
0.01010 |
| |
|
|
|
0.1 |
0.00725 |
0.01007 |
0.00484 |
0.00974 |
0.01078 |
| 0.05 | 0.00677 | 0.00990 | 0.00525 | 0.01010 | 0.01044 | ||||