Table of Contents
- 1. D'Agostino (1971, p. 343)
- 2. Cabana-Cabana (1994, p. 1454)
- 3. Chen-Shapiro (1995, p. 283)
- 4. Coin (2008, p. 2188)
- 5. Epps-Pulley (1983, p. 725)
- 6. Filliben (1973, p. 113)
- 7. Glen-Leemis-Barr (2001, p. 212)
- 8. Martinez-Iglewicz (1981, p. 332)
- 9. Rahman-Govindarajulu (1997, p. 226)
- 10. Spiegelhalter (1977, p. 417)
- 11. Zhang (1999, p. 523)
- 12. Zhang-Wu (2005, p. 712)
1 D'Agostino (1971, p. 343)
N |
0.5 |
1 |
2.5 |
5 |
10 |
90 |
95 |
97.5 |
99 |
99.5 |
50 |
-3.949 |
-3.442 |
-2.757 |
-2.220 |
-1.661 |
0.759 |
0923 |
1.038 |
1.140 |
1.192 |
60 |
-3.846 |
-3.360 |
-2.699 |
-2.179 |
-1.634 |
0.807 |
0.986 |
1.115 |
1.236 |
1.301 |
70 |
-3.762 |
-3.293 |
-2.652 |
-2.146 |
-1.612 |
0.844 |
1.036 |
1.176 |
1.312 |
1.388 |
80 |
-3.693 |
-3.237 |
-2.613 |
-2.118 |
-1.594 |
0.874 |
1.076 |
1.226 |
1.374 |
1.459 |
90 |
-3.635 |
-3.100 |
-2.580 |
-2.095 |
-1.579 |
0.899 |
1.109 |
1.268 |
1.426 |
1.518 |
100 |
-3.584 |
-3.150 |
-2.552 |
-2.075 |
-1.566 |
0.920 |
1.137 |
1.303 |
1.470 |
1.569 |
150 |
-3.409 |
-3.009 |
-2.452 |
-2.004 |
-1.520 |
0.990 |
1.233 |
1.423 |
1.623 |
1.746 |
200 |
-3.302 |
-2.922 |
-2.391 |
-1.960 |
-1.491 |
1.032 |
1.290 |
1.496 |
1.715 |
1.853 |
250 |
-3.227 |
-2.861 |
-2.348 |
-1.926 |
-1.471 |
1.060 |
1.328 |
1.545 |
1.779 |
1.927 |
300 |
-3.172 |
-2.816 |
-2.316 |
-1.906 |
-1.456 |
1.080 |
1.357 |
1.528 |
1.826 |
1.983 |
350 |
-3.129 |
-2.781 |
-2.291 |
-1.888 |
-1.444 |
1.096 |
1.379 |
1.610 |
1.863 |
2.026 |
400 |
-3.094 |
-2.753 |
-2.270 |
-1.873 |
-1.434 |
1.108 |
1.396 |
1.633 |
1.893 |
2.061 |
450 |
-3.064 |
-2.729 |
-2.253 |
-1.861 |
-1.426 |
1.119 |
1.411 |
1.652 |
1.918 |
2.090 |
500 |
-3.040 |
-2.709 |
-2.239 |
-1.850 |
-1.419 |
1.127 |
1.423 |
1.668 |
1.938 |
2.114 |
550 |
-3.019 |
-2.691 |
-2.226 |
-1.841 |
-1.413 |
1.135 |
1.434 |
1.682 |
1.957 |
2.136 |
600 |
-3.000 |
-2.676 |
-2.215 |
-1.833 |
-1.408 |
1.141 |
1.443 |
1.694 |
1.972 |
2.154 |
650 |
-2.984 |
-2.663 |
-2.206 |
-1.826 |
-1.403 |
1.147 |
1.451 |
1.704 |
1.986 |
2.171 |
700 |
-2.969 |
-2.651 |
-2.197 |
-1.820 |
-1.399 |
1.152 |
1.458 |
1.714 |
1.999 |
2.185 |
750 |
-2.956 |
-2.640 |
-2.189 |
-1.814 |
-1.395 |
1.157 |
1.465 |
1.722 |
2.010 |
2.199 |
800 |
-2.944 |
-2.630 |
-2.182 |
-1.809 |
-1.392 |
1.161 |
1.471 |
1.730 |
2.020 |
2.211 |
850 |
-2.933 |
-2.621 |
-2.176 |
-1.804 |
-1.389 |
1.165 |
1.476 |
1.737 |
2.029 |
2.221 |
900 |
-2.923 |
-2.613 |
-2.170 |
-1.800 |
-1.386 |
1.168 |
1.481 |
1.743 |
2.037 |
2.231 |
950 |
-2.914 |
-2.605 |
-2.164 |
-1.796 |
-1.383 |
1.171 |
1.485 |
1.749 |
2.045 |
2.241 |
1000 |
-2.906 |
-2.599 |
-2.159 |
-1.792 |
-1.381 |
1.174 |
1.489 |
1.754 |
2.052 |
2.249 |
2 Cabana-Cabana (1994, p. 1454)
Upper bound for the level |
Critical points for the general distribution |
Sharper critical points for product measures |
20% |
2.795 |
2.514 |
10% |
3.057 |
2.807 |
5% |
3.296 |
3.014 |
2.5% |
3.515 |
3.160 |
1% |
3.721 |
3.344 |
1.25% |
3.784 |
3.435 |
0.5% |
3.974 |
3.568 |
3 Chen-Shapiro (1995, p. 283)
N |
0.001 |
0.005 |
0.010 |
0.015 |
0.020 |
0.025 |
0.030 |
0.035 |
10 |
0.34896 |
0.22821 |
0.17690 |
0.14937 |
0.12967 |
0.11397 |
0.10124 |
0.09054 |
11 |
0.34140 |
0.22249 |
0.17236 |
0.14526 |
0.12598 |
0.11074 |
0.09839 |
0.08803 |
12 |
0.33406 |
0.21707 |
0.16805 |
0.14140 |
0.12252 |
0.10769 |
0.09570 |
0.08563 |
13 |
0.32697 |
0.21193 |
0.16397 |
0.13777 |
0.11928 |
0.10483 |
0.09316 |
0.08337 |
14 |
0.32017 |
0.20707 |
0.16012 |
0.13437 |
0.11625 |
0.10215 |
0.09076 |
0.08122 |
15 |
0.31367 |
0.20247 |
0.15648 |
0.13116 |
0.11339 |
0.09962 |
0.08850 |
0.07918 |
16 |
0.30744 |
0.19811 |
0.15303 |
0.12814 |
0.11071 |
0.09723 |
0.08636 |
0.07725 |
17 |
0.30150 |
0.19398 |
0.14977 |
0.12529 |
0.10818 |
0.09498 |
0.08434 |
0.07542 |
18 |
0.29582 |
0.19006 |
0.14667 |
0.12259 |
0.10578 |
0.09285 |
0.08242 |
0.07368 |
19 |
0.29039 |
0.18633 |
0.14373 |
0.12003 |
0.10352 |
0.09083 |
0.08059 |
0.07203 |
20 |
0.28519 |
0.18278 |
0.14093 |
0.11761 |
0.10137 |
0.08892 |
0.07886 |
0.07046 |
21 |
0.28022 |
0.17940 |
0.13827 |
0.11530 |
0.09933 |
0.08709 |
0.07722 |
0.06896 |
22 |
0.27545 |
0.17618 |
0.13572 |
0.11310 |
0.09738 |
0.08536 |
0.07564 |
0.06753 |
23 |
0.27088 |
0.17310 |
0.13329 |
0.11101 |
0.09553 |
0.08370 |
0.07414 |
0.06616 |
24 |
0.26650 |
0.17015 |
0.13097 |
0.10901 |
0.09376 |
0.08212 |
0.07271 |
0.06485 |
25 |
0.26229 |
0.16733 |
0.12875 |
0.10709 |
0.09207 |
0.08061 |
0.07134 |
0.06360 |
26 |
0.25824 |
0.16462 |
0.12661 |
0.10526 |
0.09046 |
0.07917 |
0.07002 |
0.06240 |
27 |
0.25434 |
0.16202 |
0.12457 |
0.10350 |
0.08891 |
0.07778 |
0.06876 |
0.06125 |
28 |
0.25059 |
0.15952 |
0.12260 |
0.10182 |
0.08742 |
0.07645 |
0.06755 |
0.06014 |
29 |
0.24697 |
0.15712 |
0.12071 |
0.10020 |
0.08599 |
0.07517 |
0.06639 |
0.05907 |
30 |
0.24348 |
0.15481 |
0.11889 |
0.09864 |
0.08462 |
0.07394 |
0.06527 |
0.05805 |
31 |
0.24011 |
0.15258 |
0.11713 |
0.09714 |
0.08330 |
0.07275 |
0.06419 |
0.05706 |
32 |
0.23686 |
0.15042 |
0.11544 |
0.09569 |
0.08202 |
0.07161 |
0.06315 |
0.05611 |
33 |
0.23371 |
0.14835 |
0.11381 |
0.09430 |
0.08079 |
0.07051 |
0.06215 |
0.05519 |
34 |
0.23067 |
0.14634 |
0.11223 |
0.09295 |
0.07961 |
0.06945 |
0.06118 |
0.05430 |
35 |
0.22772 |
0.14440 |
0.11070 |
0.09165 |
0.07846 |
0.06842 |
0.06024 |
0.05344 |
36 |
0.22486 |
0.14252 |
0.10923 |
0.09039 |
0.07736 |
0.06742 |
0.05934 |
0.05261 |
37 |
0.22209 |
0.14071 |
0.10780 |
0.08918 |
0.07629 |
0.06646 |
0.05846 |
0.05180 |
38 |
0.21941 |
0.13895 |
0.10641 |
0.08800 |
0.07525 |
0.06553 |
0.05761 |
0.05103 |
39 |
0.21680 |
0.13724 |
0.10507 |
0.08685 |
0.07424 |
0.06463 |
0.05679 |
0.05027 |
40 |
0.21427 |
0.13558 |
0.10377 |
0.08575 |
0.07327 |
0.06376 |
0.05599 |
0.04954 |
41 |
0.21181 |
0.13397 |
0.10250 |
0.08467 |
0.07233 |
0.06291 |
0.05521 |
0.04883 |
42 |
0.20942 |
0.13241 |
0.10127 |
0.08363 |
0.07141 |
0.06209 |
0.05446 |
0.04814 |
43 |
0.20710 |
0.13089 |
0.10008 |
0.08261 |
0.07052 |
0.06129 |
0.05373 |
0.04747 |
44 |
0.20483 |
0.12941 |
0.09892 |
0.08163 |
0.06965 |
0.06051 |
0.05302 |
0.04681 |
45 |
0.20263 |
0.12798 |
0.09779 |
0.08067 |
0.06881 |
0.05975 |
0.05233 |
0.04618 |
46 |
0.20048 |
0.12658 |
0.09669 |
0.07974 |
0.06799 |
0.05902 |
0.05166 |
0.04556 |
47 |
0.19839 |
0.12522 |
0.09562 |
0.07883 |
0.06719 |
0.05830 |
0.05101 |
0.04496 |
48 |
0.19635 |
0.12389 |
0.09458 |
0.07795 |
0.06642 |
0.05760 |
0.05037 |
0.04438 |
49 |
0.19436 |
0.12260 |
0.09356 |
0.07709 |
0.06566 |
0.05692 |
0.04975 |
0.04381 |
50 |
0.19242 |
0.12134 |
0.09257 |
0.07625 |
0.06492 |
0.05626 |
0.04914 |
0.04325 |
60 |
0.17531 |
0.11024 |
0.08385 |
0.06887 |
0.05845 |
0.05045 |
0.04383 |
0.03837 |
80 |
0.14995 |
0.09386 |
0.07100 |
0.05802 |
0.04894 |
0.04190 |
0.03603 |
0.03119 |
100 |
0.13183 |
0.08220 |
0.06184 |
0.05031 |
0.04219 |
0.03584 |
0.03050 |
0.02611 |
150 |
0.10269 |
0.06349 |
0.04715 |
0.03795 |
0.03138 |
0.02616 |
0.02168 |
0.01803 |
250 |
0.07326 |
0.04453 |
0.03227 |
0.02543 |
0.02045 |
0.01640 |
0.01287 |
0.01001 |
500 |
0.04601 |
0.02673 |
0.01828 |
0.01362 |
0.01015 |
0.00730 |
0.00481 |
0.00279 |
1000 |
0.03200 |
0.01709 |
0.01067 |
0.00709 |
0.00445 |
0.00244 |
0.00074 |
-0.00065 |
2000 |
0.02910 |
0.01424 |
0.00837 |
0.00492 |
0.00257 |
0.00106 |
-0.00004 |
-0.00097 |
N |
0.040 |
0.045 |
0.050 |
0.060 |
0.070 |
0.080 |
0.090 |
0.100 |
10 |
0.08178 |
0.07392 |
0.06668 |
0.05461 |
0.04433 |
0.03514 |
0.02694 |
0.01981 |
11 |
0.07945 |
0.07180 |
0.06476 |
0.05298 |
0.04297 |
0.03407 |
0.02614 |
0.01922 |
12 |
0.07723 |
0.06977 |
0.06292 |
0.05141 |
0.04165 |
0.03302 |
0.02531 |
0.01859 |
13 |
0.07513 |
0.06784 |
0.06116 |
0.04991 |
0.04037 |
0.03199 |
0.02449 |
0.01795 |
14 |
0.07314 |
0.06601 |
0.05950 |
0.04848 |
0.03916 |
0.03099 |
0.02368 |
0.01730 |
15 |
0.07126 |
0.06428 |
0.05791 |
0.04712 |
0.03799 |
0.03002 |
0.02290 |
0.01666 |
16 |
0.06947 |
0.06264 |
0.05641 |
0.04582 |
0.03688 |
0.02910 |
0.02214 |
0.01604 |
17 |
0.06778 |
0.06108 |
0.05498 |
0.04459 |
0.03583 |
0.02821 |
0.02140 |
0.01543 |
18 |
0.06618 |
0.05959 |
0.05362 |
0.04342 |
0.03482 |
0.02736 |
0.02069 |
0.01484 |
19 |
0.06465 |
0.05818 |
0.05232 |
0.04231 |
0.03386 |
0.02655 |
0.02001 |
0.01427 |
20 |
0.06320 |
0.05684 |
0.05109 |
0.04124 |
0.03294 |
0.02576 |
0.01935 |
0.01371 |
21 |
0.06181 |
0.05556 |
0.04991 |
0.04023 |
0.03206 |
0.02502 |
0.01872 |
0.01318 |
22 |
0.06049 |
0.05434 |
0.04879 |
0.03926 |
0.03122 |
0.02430 |
0.01811 |
0.01266 |
23 |
0.05923 |
0.05317 |
0.04771 |
0.03833 |
0.03042 |
0.02361 |
0.01752 |
0.01216 |
24 |
0.05802 |
0.05206 |
0.04668 |
0.03744 |
0.02965 |
0.02295 |
0.01696 |
0.01168 |
25 |
0.05687 |
0.05099 |
0.04569 |
0.03659 |
0.02891 |
0.02231 |
0.01641 |
0.01122 |
26 |
0.05576 |
0.04996 |
0.04475 |
0.03577 |
0.02820 |
0.02170 |
0.01589 |
0.01077 |
27 |
0.05470 |
0.04898 |
0.04384 |
0.03498 |
0.02752 |
0.02111 |
0.01539 |
0.01033 |
28 |
0.05367 |
0.04803 |
0.04297 |
0.03423 |
0.02687 |
0.02055 |
0.01490 |
0.00992 |
29 |
0.05269 |
0.04712 |
0.04213 |
0.03350 |
0.02624 |
0.02000 |
0.01443 |
0.00951 |
30 |
0.05175 |
0.04624 |
0.04132 |
0.03280 |
0.02563 |
0.01948 |
0.01398 |
0.00912 |
31 |
0.05084 |
0.04540 |
0.04054 |
0.03213 |
0.02504 |
0.01897 |
0.01354 |
0.00874 |
32 |
0.04996 |
0.04459 |
0.03979 |
0.03148 |
0.02448 |
0.01848 |
0.01312 |
0.00838 |
33 |
0.04911 |
0.04380 |
0.03906 |
0.03085 |
0.02393 |
0.01800 |
0.01271 |
0.00802 |
34 |
0.04829 |
0.04304 |
0.03836 |
0.03024 |
0.02341 |
0.01755 |
0.01231 |
0.00768 |
35 |
0.04750 |
0.04231 |
0.03768 |
0.02966 |
0.02290 |
0.01710 |
0.01193 |
0.00735 |
36 |
0.04674 |
0.04160 |
0.03703 |
0.02909 |
0.02241 |
0.01667 |
0.01156 |
0.00702 |
37 |
0.04599 |
0.04091 |
0.03639 |
0.02854 |
0.02193 |
0.01626 |
0.01120 |
0.00671 |
38 |
0.04528 |
0.04025 |
0.03578 |
0.02801 |
0.02147 |
0.01585 |
0.01085 |
0.00641 |
39 |
0.21680 |
0.13724 |
0.10507 |
0.08685 |
0.07424 |
0.06463 |
0.05679 |
0.05027 |
40 |
0.21427 |
0.13558 |
0.10377 |
0.08575 |
0.07327 |
0.06376 |
0.05599 |
0.04954 |
41 |
0.21181 |
0.13397 |
0.10250 |
0.08467 |
0.07233 |
0.06291 |
0.05521 |
0.04883 |
42 |
0.20942 |
0.13241 |
0.10127 |
0.08363 |
0.07141 |
0.06209 |
0.05446 |
0.04814 |
43 |
0.20710 |
0.13089 |
0.10008 |
0.08261 |
0.07052 |
0.06129 |
0.05373 |
0.04747 |
44 |
0.20483 |
0.12941 |
0.09892 |
0.08163 |
0.06965 |
0.06051 |
0.05302 |
0.04681 |
45 |
0.20263 |
0.12798 |
0.09779 |
0.08067 |
0.06881 |
0.05975 |
0.05233 |
0.04618 |
46 |
0.20048 |
0.12658 |
0.09669 |
0.07974 |
0.06799 |
0.05902 |
0.05166 |
0.04556 |
47 |
0.19839 |
0.12522 |
0.09562 |
0.07883 |
0.06719 |
0.05830 |
0.05101 |
0.04496 |
48 |
0.19635 |
0.12389 |
0.09458 |
0.07795 |
0.06642 |
0.05760 |
0.05037 |
0.04438 |
49 |
0.19436 |
0.12260 |
0.09356 |
0.07709 |
0.06566 |
0.05692 |
0.04975 |
0.04381 |
50 |
0.19242 |
0.12134 |
0.09257 |
0.07625 |
0.06492 |
0.05626 |
0.04914 |
0.04325 |
60 |
0.17531 |
0.11024 |
0.08385 |
0.06887 |
0.05845 |
0.05045 |
0.04383 |
0.03837 |
80 |
0.14995 |
0.09386 |
0.07100 |
0.05802 |
0.04894 |
0.04190 |
0.03603 |
0.03119 |
100 |
0.13183 |
0.08220 |
0.06184 |
0.05031 |
0.04219 |
0.03584 |
0.03050 |
0.02611 |
150 |
0.10269 |
0.06349 |
0.04715 |
0.03795 |
0.03138 |
0.02616 |
0.02168 |
0.01803 |
250 |
0.07326 |
0.04453 |
0.03227 |
0.02543 |
0.02045 |
0.01640 |
0.01287 |
0.01001 |
500 |
0.04601 |
0.02673 |
0.01828 |
0.01362 |
0.01015 |
0.00730 |
0.00481 |
0.00279 |
1000 |
0.03200 |
0.01709 |
0.01067 |
0.00709 |
0.00445 |
0.00244 |
0.00074 |
-0.00065 |
2000 |
0.02910 |
0.01424 |
0.00837 |
0.00492 |
0.00257 |
0.00106 |
-0.00004 |
-0.00097 |
4 Coin (2008, p. 2188)
N |
0.9 |
0.95 |
0.99 |
0.995 |
0.999 |
10 |
0.069253 |
0.096065 |
0.155307 |
0.192290 |
0.258412 |
20 |
0.017407 |
0.024703 |
0.042435 |
0.050970 |
0.077089 |
30 |
0.009008 |
0.012618 |
0.022509 |
0.027305 |
0.038290 |
40 |
0.005861 |
0.008326 |
0.014124 |
0.017144 |
0.023908 |
50 |
0.004307 |
0.006316 |
0.010719 |
0.013013 |
0.019142 |
60 |
0.003331 |
0.004690 |
0.008182 |
0.010084 |
0.013719 |
70 |
0.002662 |
0.003768 |
0.006582 |
0.007972 |
0.011837 |
80 |
0.002234 |
0.003134 |
0.005332 |
0.006340 |
0.009136 |
90 |
0.001932 |
0.002723 |
0.004816 |
0.005684 |
0.008162 |
100 |
0.001706 |
0.002453 |
0.004280 |
0.005131 |
0.007455 |
150 |
0.001015 |
0.001447 |
0.002495 |
0.003047 |
0.004483 |
200 |
0.000732 |
0.001033 |
0.001836 |
0.002257 |
0.003017 |
250 |
0.000578 |
0.000806 |
0.001400 |
0.001677 |
0.002330 |
300 |
0.000446 |
0.000628 |
0.001102 |
0.001312 |
0.002005 |
350 |
0.000386 |
0.000543 |
0.000904 |
0.001087 |
0.001592 |
400 |
0.000327 |
0.000467 |
0.000848 |
0.000993 |
0.001406 |
450 |
0.000286 |
0.000411 |
0.000712 |
0.000851 |
0.001130 |
500 |
0.000260 |
0.000365 |
0.000644 |
0.000768 |
0.001081 |
600 |
0.000213 |
0.000303 |
0.000525 |
0.000617 |
0.000837 |
700 |
0.000180 |
0.000258 |
0.000445 |
0.000517 |
0.000762 |
800 |
0.000154 |
0.000217 |
0.000375 |
0.000443 |
0.000614 |
900 |
0.000138 |
0.000194 |
0.000335 |
0.000403 |
0.000562 |
1000 |
0.000125 |
0.000178 |
0.000302 |
0.000368 |
0.000489 |
5 Epps-Pulley (1983, p. 725)
α = 0.7??
N |
0.025 |
0.050 |
0.950 |
0.975 |
4 |
2.90 |
2.76 |
0.42 |
0.33 |
6 |
3.07 |
2.79 |
0.39 |
0.24 |
8 |
3.16 |
2.91 |
0.38 |
0.22 |
10 |
3.24 |
2.96 |
0.37 |
0.19 |
12 |
3.29 |
2.98 |
0.36 |
0.17 |
>12 |
3.30 |
3.00 |
0.35 |
0.17 |
α = 1.0??
N |
0.025 |
0.050 |
0.950 |
0.975 |
4 |
4.22 |
3.91 |
1.23 |
1.15 |
6 |
4.34 |
4.00 |
1.13 |
0.90 |
8 |
4.39 |
4.03 |
1.09 |
0.86 |
10 |
4.43 |
4.08 |
1.06 |
0.84 |
12 |
4.44 |
4.09 |
1.03 |
0.82 |
>12 |
4.45 |
4.10 |
1.00 |
0.79 |
6 Filliben (1973, p. 113)
N |
0.000 |
0.005 |
0.010 |
0.025 |
0.050 |
0.100 |
0.250 |
0.500 |
0.750 |
0.900 |
0.950 |
0.975 |
0.990 |
0.995 |
3 |
0.866 |
0.867 |
0.869 |
0.872 |
0.879 |
0.891 |
0.924 |
0.966 |
0.991 |
0.999 |
1.000 |
1.000 |
1.000 |
1.000 |
4 |
0.784 |
0.813 |
0.822 |
0.845 |
0.868 |
0.894 |
0.931 |
0.958 |
0.979 |
0.992 |
0.996 |
0.998 |
0.999 |
1.000 |
5 |
0.726 |
0.803 |
0.822 |
0.855 |
0.879 |
0.902 |
0.935 |
0.960 |
0.977 |
0.988 |
0.992 |
0.995 |
0.997 |
0.998 |
6 |
0.683 |
0.818 |
0.835 |
0.868 |
0.890 |
0.911 |
0.940 |
0.962 |
0.977 |
0.986 |
0.990 |
0.993 |
0.996 |
0.997 |
7 |
0.648 |
0.828 |
0.847 |
0.876 |
0.899 |
0.916 |
0.944 |
0.965 |
0.978 |
0.986 |
0.990 |
0.992 |
0.995 |
0.996 |
8 |
0.619 |
0.841 |
0.859 |
0.886 |
0.905 |
0.924 |
0.948 |
0.967 |
0.979 |
0.986 |
0.990 |
0.992 |
0.995 |
0.996 |
9 |
0.595 |
0.851 |
0.868 |
0.893 |
0.912 |
0.929 |
0.951 |
0.968 |
0.980 |
0.987 |
0.990 |
0.992 |
0.994 |
0.995 |
10 |
0.574 |
0.860 |
0.876 |
0.900 |
0.917 |
0.934 |
0.954 |
0.970 |
0.981 |
0.987 |
0.990 |
0.992 |
0.994 |
0.995 |
11 |
0.556 |
0.868 |
0.883 |
0.906 |
0.922 |
0.938 |
0.957 |
0.972 |
0.982 |
0.988 |
0.990 |
0.992 |
0.994 |
0.995 |
12 |
0.539 |
0.875 |
0.889 |
0.912 |
0.926 |
0.941 |
0.959 |
0.973 |
0.982 |
0.988 |
0.990 |
0.992 |
0.994 |
0.995 |
13 |
0.525 |
0.882 |
0.895 |
0.917 |
0.931 |
0.944 |
0.962 |
0.975 |
0.983 |
0.988 |
0.991 |
0.993 |
0.994 |
0.995 |
14 |
0.512 |
0.888 |
0.901 |
0.921 |
0.934 |
0.947 |
0.964 |
0.976 |
0.984 |
0.989 |
0.991 |
0.993 |
0.994 |
0.995 |
15 |
0.500 |
0.894 |
0.907 |
0.925 |
0.937 |
0.950 |
0.965 |
0.977 |
0.984 |
0.989 |
0.991 |
0.993 |
0.994 |
0.995 |
16 |
0.489 |
0.899 |
0.912 |
0.928 |
0.940 |
0.952 |
0.967 |
0.978 |
0.985 |
0.989 |
0.991 |
0.993 |
0.994 |
0.995 |
17 |
0.478 |
0.903 |
0.916 |
0.931 |
0.942 |
0.954 |
0.968 |
0.979 |
0.986 |
0.990 |
0.992 |
0.993 |
0.994 |
0.995 |
18 |
0.469 |
0.907 |
0.919 |
0.934 |
0.945 |
0.956 |
0.969 |
0.979 |
0.986 |
0.990 |
0.992 |
0.993 |
0.995 |
0.995 |
19 |
0.460 |
0.909 |
0.923 |
0.937 |
0.947 |
0.958 |
0.971 |
0.980 |
0.987 |
0.990 |
0.992 |
0.993 |
0.995 |
0.995 |
20 |
0.452 |
0.912 |
0.925 |
0.939 |
0.950 |
0.960 |
0.972 |
0.981 |
0.987 |
0.991 |
0.992 |
0.994 |
0.995 |
0.995 |
21 |
0.445 |
0.914 |
0.928 |
0.942 |
0.952 |
0.961 |
0.973 |
0.981 |
0.987 |
0.991 |
0.993 |
0.994 |
0.995 |
0.996 |
22 |
0.437 |
0.918 |
0.930 |
0.944 |
0.954 |
0.962 |
0.974 |
0.982 |
0.988 |
0.991 |
0.993 |
0.994 |
0.995 |
0.996 |
23 |
0.431 |
0.922 |
0.933 |
0.947 |
0.955 |
0.964 |
0.975 |
0.983 |
0.988 |
0.991 |
0.993 |
0.994 |
0.995 |
0.996 |
24 |
0.424 |
0.926 |
0.936 |
0.949 |
0.957 |
0.965 |
0.975 |
0.983 |
0.988 |
0.992 |
0.993 |
0.994 |
0.995 |
0.996 |
25 |
0.418 |
0.928 |
0.937 |
0.950 |
0.958 |
0.966 |
0.976 |
0.984 |
0.989 |
0.992 |
0.993 |
0.994 |
0.995 |
0.996 |
26 |
0.412 |
0.930 |
0.939 |
0.952 |
0.959 |
0.967 |
0.977 |
0.984 |
0.989 |
0.992 |
0.993 |
0.994 |
0.995 |
0.996 |
27 |
0.407 |
0.932 |
0.941 |
0.953 |
0.960 |
0.968 |
0.977 |
0.984 |
0.989 |
0.992 |
0.994 |
0.995 |
0.995 |
0.996 |
28 |
0.402 |
0.934 |
0.943 |
0.955 |
0.962 |
0.969 |
0.978 |
0.985 |
0.990 |
0.992 |
0.994 |
0.995 |
0.995 |
0.996 |
29 |
0.397 |
0.937 |
0.945 |
0.956 |
0.962 |
0.969 |
0.979 |
0.985 |
0.990 |
0.992 |
0.994 |
0.995 |
0.995 |
0.996 |
30 |
0.392 |
0.938 |
0.947 |
0.957 |
0.964 |
0.970 |
0.979 |
0.986 |
0.990 |
0.993 |
0.994 |
0.995 |
0.996 |
0.996 |
31 |
0.388 |
0.939 |
0.948 |
0.958 |
0.965 |
0.971 |
0.980 |
0.980 |
0.986 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
32 |
0.383 |
0.939 |
0.949 |
0.959 |
0.966 |
0.972 |
0.980 |
0.980 |
0.986 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
33 |
0.379 |
0.940 |
0.950 |
0.960 |
0.967 |
0.973 |
0.981 |
0.981 |
0.987 |
0.991 |
0.993 |
0.995 |
0.996 |
0.996 |
34 |
0.375 |
0.941 |
0.951 |
0.960 |
0.967 |
0.973 |
0.981 |
0.981 |
0.987 |
0.991 |
0.993 |
0.995 |
0.996 |
0.996 |
35 |
0.371 |
0.943 |
0.952 |
0.961 |
0.968 |
0.974 |
0.982 |
0.982 |
0.987 |
0.991 |
0.993 |
0.995 |
0.996 |
0.997 |
36 |
0.367 |
0.945 |
0.953 |
0.962 |
0.968 |
0.974 |
0.982 |
0.987 |
0.991 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
37 |
0.364 |
0.947 |
0.955 |
0.962 |
0.969 |
0.975 |
0.982 |
0.988 |
0.991 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
38 |
0.360 |
0.948 |
0.956 |
0.964 |
0.970 |
0.975 |
0.983 |
0.988 |
0.992 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
39 |
0.357 |
0.949 |
0.957 |
0.965 |
0.971 |
0.976 |
0.983 |
0.988 |
0.992 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
40 |
0.354 |
0.949 |
0.958 |
0.966 |
0.972 |
0.977 |
0.983 |
0.988 |
0.992 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
41 |
0.351 |
0.950 |
0.958 |
0.967 |
0.972 |
0.977 |
0.984 |
0.989 |
0.992 |
0.994 |
0.995 |
0.996 |
0.996 |
0.997 |
42 |
0.348 |
0.951 |
0.959 |
0.967 |
0.973 |
0.978 |
0.984 |
0.989 |
0.992 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
43 |
0.345 |
0.953 |
0.959 |
0.967 |
0.973 |
0.978 |
0.984 |
0.989 |
0.992 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
44 |
0.342 |
0.954 |
0.960 |
0.968 |
0.973 |
0.978 |
0.984 |
0.989 |
0.992 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
45 |
0.339 |
0.955 |
0.961 |
0.969 |
0.974 |
0.978 |
0.985 |
0.989 |
0.993 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
46 |
0.336 |
0.956 |
0.962 |
0.969 |
0.974 |
0.979 |
0.985 |
0.990 |
0.993 |
0.995 |
0.995 |
0.996 |
0.997 |
0.997 |
47 |
0.334 |
0.956 |
0.963 |
0.970 |
0.974 |
0.979 |
0.985 |
0.990 |
0.993 |
0.995 |
0.995 |
0.996 |
0.997 |
0.997 |
48 |
0.331 |
0.957 |
0.963 |
0.970 |
0.975 |
0.980 |
0.985 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
0.997 |
0.997 |
49 |
0.329 |
0.957 |
0.964 |
0.971 |
0.975 |
0.980 |
0.986 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
0.997 |
0.997 |
50 |
0.326 |
0.959 |
0.965 |
0.972 |
0.977 |
0.981 |
0.986 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
0.997 |
0.997 |
55 |
0.315 |
0.962 |
0.967 |
0.974 |
0.978 |
0.982 |
0.987 |
0.991 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
0.997 |
60 |
0.305 |
0.965 |
0.970 |
0.976 |
0.980 |
0.983 |
0.988 |
0.991 |
0.994 |
0.995 |
0.996 |
0.997 |
0.997 |
0.998 |
65 |
0.296 |
0.967 |
0.972 |
0.977 |
0.981 |
0.984 |
0.989 |
0.992 |
0.994 |
0.996 |
0.996 |
0.997 |
0.997 |
0.998 |
70 |
0.288 |
0.969 |
0.974 |
0.978 |
0.982 |
0.985 |
0.989 |
0.993 |
0.995 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
75 |
0.281 |
0.971 |
0.975 |
0.979 |
0.983 |
0.986 |
0.990 |
0.993 |
0.995 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
80 |
0.274 |
0.973 |
0.976 |
0.980 |
0.984 |
0.987 |
0.991 |
0.993 |
0.995 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
85 |
0.268 |
0.974 |
0.977 |
0.981 |
0.985 |
0.987 |
0.991 |
0.994 |
0.995 |
0.997 |
0.997 |
0.997 |
0.998 |
0.998 |
90 |
0.263 |
0.976 |
0.978 |
0.982 |
0.985 |
0.988 |
0.991 |
0.994 |
0.996 |
0.997 |
0.997 |
0.997 |
0.998 |
0.998 |
95 |
0.257 |
0.977 |
0.979 |
0.983 |
0.986 |
0.989 |
0.992 |
0.994 |
0.996 |
0.997 |
0.997 |
0.997 |
0.998 |
0.998 |
100 |
0.252 |
0.979 |
0.981 |
0.984 |
0.987 |
0.989 |
0.992 |
0.994 |
0.996 |
0.997 |
0.998 |
0.998 |
0.998 |
0.998 |
7 Glen-Leemis-Barr (2001, p. 212)
N |
α = 0.10 |
α = 0.05 |
α = 0.01 |
2 |
4.9 |
6.1 |
8.9 |
3 |
7.6 |
9.1 |
13.4 |
4 |
10.1 |
12.1 |
17.0 |
5 |
12.6 |
15.3 |
21.5 |
6 |
15.1 |
18.1 |
24.4 |
7 |
17.7 |
21.1 |
28.2 |
8 |
20.4 |
23.9 |
32.0 |
9 |
22.7 |
26.8 |
36.5 |
10 |
24.9 |
29.4 |
39.5 |
11 |
27.9 |
32.2 |
43.7 |
12 |
30.0 |
35.2 |
48.0 |
15 |
37.5 |
44.0 |
59.6 |
20 |
50.7 |
58.7 |
81.1 |
25 |
63.2 |
76.2 |
116.5 |
30 |
80.0 |
107.1 |
218.4 |
40 |
445.0 |
576.5 |
776.8 |
50 |
1025.4 |
1108.8 |
1231.6 |
8 Martinez-Iglewicz (1981, p. 332)
N |
90.0 |
95.0 |
97.5 |
99.0 |
10 |
1.448 |
1.969 |
2.917 |
5.273 |
15 |
1.283 |
1.516 |
1.858 |
2.502 |
20 |
1.210 |
1.351 |
1.540 |
1.878 |
25 |
1.173 |
1.280 |
1.405 |
1.639 |
30 |
1.145 |
1.232 |
1.334 |
1.487 |
35 |
1.129 |
1.200 |
1.290 |
1.405 |
40 |
1.113 |
1.174 |
1.244 |
1.352 |
45 |
1.103 |
1.160 |
1.221 |
1.308 |
50 |
1.093 |
1.145 |
1.199 |
1.276 |
60 |
1.080 |
1.122 |
1.168 |
1.233 |
70 |
1.071 |
1.109 |
1.147 |
1.197 |
80 |
1.064 |
1.097 |
1.132 |
1.180 |
90 |
1.058 |
1.087 |
1.117 |
1.159 |
100 |
1.052 |
1.079 |
1.109 |
1.146 |
150 |
1.037 |
1.056 |
1.075 |
1.101 |
200 |
1.027 |
1.043 |
1.060 |
1.080 |
300 |
1.017 |
1.030 |
1.042 |
1.058 |
9 Rahman-Govindarajulu (1997, p. 226)
N |
α = 0.01 |
0.02 |
0.05 |
0.10 |
0.50 |
0.90 |
0.95 |
0.98 |
0.99 |
3 |
0.754 |
0.758 |
0.771 |
0.793 |
0.933 |
0.997 |
0.999 |
0.999 |
1.000 |
4 |
0.703 |
0.722 |
0.760 |
0.795 |
0.911 |
0.983 |
0.992 |
0.996 |
0.998 |
5 |
0.702 |
0.728 |
0.770 |
0.803 |
0.906 |
0.975 |
0.984 |
0.991 |
0.994 |
6 |
0.722 |
0.748 |
0.784 |
0.816 |
0.909 |
0.971 |
0.980 |
0.988 |
0.991 |
7 |
0.737 |
0.763 |
0.799 |
0.829 |
0.911 |
0.968 |
0.978 |
0.985 |
0.989 |
8 |
0.755 |
0.775 |
0.809 |
0.836 |
0.915 |
0.967 |
0.976 |
0.984 |
0.987 |
9 |
0.768 |
0.790 |
0.819 |
0.843 |
0.917 |
0.967 |
0.975 |
0.983 |
0.987 |
10 |
0.779 |
0.800 |
0.828 |
0.852 |
0.920 |
0.967 |
0.975 |
0.982 |
0.986 |
11 |
0.794 |
0.814 |
0.839 |
0.859 |
0.923 |
0.966 |
0.975 |
0.982 |
0.986 |
12 |
0.805 |
0.823 |
0.846 |
0.866 |
0.926 |
0.967 |
0.975 |
0.982 |
0.986 |
13 |
0.814 |
0.830 |
0.852 |
0.871 |
0.928 |
0.968 |
0.975 |
0.982 |
0.986 |
14 |
0.817 |
0.834 |
0.856 |
0.875 |
0.930 |
0.968 |
0.975 |
0.982 |
0.985 |
15 |
0.827 |
0.842 |
0.863 |
0.881 |
0.932 |
0.968 |
0.975 |
0.982 |
0.985 |
16 |
0.834 |
0.848 |
0.868 |
0.886 |
0.935 |
0.969 |
0.976 |
0.982 |
0.985 |
17 |
0.839 |
0.853 |
0.872 |
0.889 |
0.936 |
0.969 |
0.976 |
0.982 |
0.985 |
18 |
0.842 |
0.857 |
0.878 |
0.893 |
0.938 |
0.969 |
0.976 |
0.982 |
0.985 |
19 |
0.848 |
0.862 |
0.881 |
0.896 |
0.940 |
0.970 |
0.977 |
0.982 |
0.985 |
20 |
0.853 |
0.867 |
0.884 |
0.899 |
0.941 |
0.971 |
0.977 |
0.983 |
0.986 |
21 |
0.857 |
0.870 |
0.888 |
0.902 |
0.943 |
0.971 |
0.977 |
0.983 |
0.986 |
22 |
0.863 |
0.875 |
0.891 |
0.904 |
0.944 |
0.971 |
0.977 |
0.983 |
0.986 |
23 |
0.865 |
0.877 |
0.893 |
0.907 |
0.945 |
0.972 |
0.978 |
0.983 |
0.986 |
24 |
0.869 |
0.880 |
0.895 |
0.909 |
0.946 |
0.972 |
0.978 |
0.983 |
0.986 |
25 |
0.873 |
0.884 |
0.899 |
0.911 |
0.947 |
0.973 |
0.978 |
0.983 |
0.986 |
26 |
0.875 |
0.887 |
0.902 |
0.914 |
0.949 |
0.974 |
0.979 |
0.984 |
0.986 |
27 |
0.880 |
0.890 |
0.904 |
0.916 |
0.950 |
0.974 |
0.979 |
0.984 |
0.986 |
28 |
0.883 |
0.892 |
0.906 |
0.917 |
0.950 |
0.974 |
0.979 |
0.984 |
0.986 |
29 |
0.885 |
0.896 |
0.909 |
0.920 |
0.952 |
0.974 |
0.980 |
0.984 |
0.987 |
30 |
0.887 |
0.897 |
0.911 |
0.921 |
0.952 |
0.975 |
0.980 |
0.984 |
0.987 |
31 |
0.890 |
0.900 |
0.913 |
0.923 |
0.953 |
0.975 |
0.980 |
0.984 |
0.987 |
32 |
0.891 |
0.901 |
0.913 |
0.924 |
0.954 |
0.976 |
0.980 |
0.985 |
0.987 |
33 |
0.894 |
0.904 |
0.916 |
0.926 |
0.955 |
0.976 |
0.980 |
0.985 |
0.987 |
34 |
0.897 |
0.906 |
0.917 |
0.927 |
0.956 |
0.976 |
0.981 |
0.985 |
0.987 |
35 |
0.899 |
0.907 |
0.919 |
0.928 |
0.956 |
0.976 |
0.981 |
0.985 |
0.988 |
36 |
0.901 |
0.909 |
0.921 |
0.930 |
0.957 |
0.977 |
0.981 |
0.985 |
0.988 |
37 |
0.902 |
0.910 |
0.922 |
0.931 |
0.958 |
0.977 |
0.981 |
0.985 |
0.988 |
38 |
0.905 |
0.913 |
0.924 |
0.933 |
0.958 |
0.977 |
0.982 |
0.986 |
0.988 |
39 |
0.906 |
0.913 |
0.925 |
0.934 |
0.959 |
0.977 |
0.982 |
0.986 |
0.988 |
40 |
0.908 |
0.916 |
0.925 |
0.934 |
0.960 |
0.978 |
0.982 |
0.986 |
0.988 |
41 |
0.909 |
0.916 |
0.927 |
0.935 |
0.960 |
0.978 |
0.982 |
0.986 |
0.988 |
42 |
0.912 |
0.918 |
0.928 |
0.936 |
0.961 |
0.978 |
0.982 |
0.986 |
0.988 |
43 |
0.913 |
0.920 |
0.930 |
0.938 |
0.961 |
0.979 |
0.982 |
0.986 |
0.988 |
44 |
0.914 |
0.921 |
0.931 |
0.939 |
0.962 |
0.979 |
0.982 |
0.986 |
0.988 |
45 |
0.915 |
0.923 |
0.932 |
0.939 |
0.962 |
0.979 |
0.983 |
0.986 |
0.988 |
46 |
0.917 |
0.923 |
0.933 |
0.940 |
0.963 |
0.979 |
0.983 |
0.987 |
0.988 |
47 |
0.918 |
0.924 |
0.934 |
0.942 |
0.963 |
0.979 |
0.983 |
0.987 |
0.989 |
48 |
0.919 |
0.926 |
0.934 |
0.942 |
0.964 |
0.980 |
0.983 |
0.987 |
0.989 |
49 |
0.921 |
0.927 |
0.936 |
0.943 |
0.964 |
0.980 |
0.983 |
0.987 |
0.989 |
50 |
0.921 |
0.928 |
0.937 |
0.944 |
0.965 |
0.980 |
0.984 |
0.987 |
0.989 |
51 |
0.922 |
0.928 |
0.937 |
0.944 |
0.965 |
0.980 |
0.984 |
0.987 |
0.989 |
52 |
0.923 |
0.930 |
0.938 |
0.945 |
0.966 |
0.981 |
0.984 |
0.987 |
0.989 |
53 |
0.925 |
0.930 |
0.939 |
0.946 |
0.966 |
0.981 |
0.984 |
0.987 |
0.989 |
54 |
0.925 |
0.932 |
0.940 |
0.947 |
0.966 |
0.981 |
0.984 |
0.987 |
0.989 |
55 |
0.927 |
0.933 |
0.941 |
0.947 |
0.967 |
0.981 |
0.984 |
0.988 |
0.989 |
56 |
0.928 |
0.934 |
0.942 |
0.948 |
0.967 |
0.981 |
0.985 |
0.988 |
0.989 |
57 |
0.928 |
0.934 |
0.942 |
0.949 |
0.967 |
0.982 |
0.985 |
0.988 |
0.990 |
58 |
0.929 |
0.935 |
0.942 |
0.949 |
0.968 |
0.982 |
0.985 |
0.988 |
0.990 |
59 |
0.930 |
0.936 |
0.943 |
0.950 |
0.968 |
0.982 |
0.985 |
0.988 |
0.990 |
60 |
0.931 |
0.936 |
0.944 |
0.950 |
0.968 |
0.982 |
0.985 |
0.988 |
0.990 |
61 |
0.932 |
0.937 |
0.945 |
0.951 |
0.969 |
0.982 |
0.985 |
0.988 |
0.990 |
62 |
0.933 |
0.938 |
0.946 |
0.952 |
0.969 |
0.982 |
0.985 |
0.988 |
0.990 |
63 |
0.934 |
0.939 |
0.946 |
0.952 |
0.969 |
0.982 |
0.985 |
0.988 |
0.990 |
64 |
0.934 |
0.939 |
0.946 |
0.952 |
0.970 |
0.983 |
0.986 |
0.989 |
0.990 |
65 |
0.935 |
0.941 |
0.947 |
0.953 |
0.970 |
0.983 |
0.986 |
0.989 |
0.990 |
66 |
0.936 |
0.941 |
0.947 |
0.953 |
0.970 |
0.983 |
0.986 |
0.989 |
0.990 |
67 |
0.937 |
0.941 |
0.948 |
0.954 |
0.971 |
0.983 |
0.986 |
0.989 |
0.990 |
68 |
0.937 |
0.942 |
0.949 |
0.954 |
0.971 |
0.983 |
0.986 |
0.989 |
0.990 |
69 |
0.937 |
0.942 |
0.949 |
0.955 |
0.971 |
0.983 |
0.986 |
0.989 |
0.990 |
70 |
0.939 |
0.944 |
0.950 |
0.955 |
0.971 |
0.983 |
0.986 |
0.989 |
0.990 |
71 |
0.940 |
0.944 |
0.950 |
0.956 |
0.972 |
0.984 |
0.986 |
0.989 |
0.991 |
72 |
0.939 |
0.944 |
0.951 |
0.956 |
0.972 |
0.984 |
0.986 |
0.989 |
0.991 |
73 |
0.940 |
0.945 |
0.951 |
0.956 |
0.972 |
0.984 |
0.986 |
0.989 |
0.991 |
74 |
0.940 |
0.945 |
0.952 |
0.957 |
0.972 |
0.984 |
0.987 |
0.989 |
0.991 |
75 |
0.940 |
0.945 |
0.952 |
0.957 |
0.973 |
0.984 |
0.987 |
0.989 |
0.991 |
16 |
0.942 |
0.946 |
0.953 |
0.958 |
0.973 |
0.984 |
0.987 |
0.989 |
0.991 |
77 |
0.942 |
0.948 |
0.953 |
0.958 |
0.973 |
0.984 |
0.987 |
0.990 |
0.991 |
78 |
0.943 |
0.947 |
0.954 |
0.959 |
0.973 |
0.984 |
0.987 |
0.990 |
0.991 |
79 |
0.944 |
0.948 |
0.954 |
0.959 |
0.974 |
0.984 |
0.987 |
0.990 |
0.991 |
80 |
0.944 |
0.948 |
0.954 |
0.959 |
0.974 |
0.985 |
0.987 |
0.990 |
0.991 |
81 |
0.945 |
0.949 |
0.955 |
0.960 |
0.974 |
0.985 |
0.987 |
0.990 |
0.991 |
82 |
0.945 |
0.950 |
0.955 |
0.960 |
0.974 |
0.985 |
0.987 |
0.990 |
0.991 |
83 |
0.946 |
0.950 |
0.956 |
0.960 |
0.974 |
0.985 |
0.987 |
0.990 |
0.991 |
84 |
0.946 |
0.950 |
0.956 |
0.961 |
0.975 |
0.985 |
0.987 |
0.990 |
0.991 |
85 |
0.947 |
0.951 |
0.957 |
0.961 |
0.975 |
0.985 |
0.988 |
0.990 |
0.991 |
86 |
0.947 |
0.952 |
0.957 |
0.962 |
0.975 |
0.985 |
0.988 |
0.990 |
0.991 |
87 |
0.947 |
0.952 |
0.957 |
0.962 |
0.975 |
0.985 |
0.988 |
0.990 |
0.991 |
88 |
0.948 |
0.953 |
0.958 |
0.962 |
0.975 |
0.985 |
0.988 |
0.990 |
0.991 |
89 |
0.948 |
0.952 |
0.958 |
0.962 |
0.976 |
0.986 |
0.988 |
0.990 |
0.992 |
90 |
0.948 |
0.953 |
0.958 |
0.963 |
0.976 |
0.986 |
0.988 |
0.990 |
0.992 |
91 |
0.949 |
0.954 |
0.959 |
0.963 |
0.976 |
0.986 |
0.988 |
0.990 |
0.992 |
92 |
0.950 |
0.953 |
0.959 |
0.963 |
0.976 |
0.986 |
0.988 |
0.990 |
0.992 |
93 |
0.951 |
0.954 |
0.959 |
0.963 |
0.976 |
0.986 |
0.988 |
0.990 |
0.992 |
94 |
0.951 |
0.955 |
0.960 |
0.964 |
0.976 |
0.986 |
0.988 |
0.991 |
0.992 |
95 |
0.951 |
0.955 |
0.960 |
0.964 |
0.977 |
0.986 |
0.988 |
0.990 |
0.992 |
96 |
0.951 |
0.955 |
0.960 |
0.965 |
0.977 |
0.986 |
0.988 |
0.991 |
0.992 |
97 |
0.951 |
0.955 |
0.961 |
0.965 |
0.977 |
0.986 |
0.988 |
0.991 |
0.992 |
98 |
0.952 |
0.956 |
0.961 |
0.965 |
0.977 |
0.986 |
0.988 |
0.991 |
0.992 |
99 |
0.952 |
0.956 |
0.961 |
0.965 |
0.977 |
0.986 |
0.989 |
0.991 |
0.992 |
100 |
0.953 |
0.956 |
0.961 |
0.965 |
0.977 |
0.987 |
0.989 |
0.991 |
0.992 |
110 |
0.957 |
0.960 |
0.964 |
0.968 |
0.979 |
0.987 |
0.989 |
0.991 |
0.992 |
120 |
0.959 |
0.962 |
0.966 |
0.970 |
0.980 |
0.988 |
0.990 |
0.992 |
0.993 |
130 |
0.962 |
0.964 |
0.968 |
0.972 |
0.981 |
0.988 |
0.990 |
0.992 |
0.993 |
140 |
0.964 |
0.966 |
0.970 |
0.973 |
0.982 |
0.989 |
0.991 |
0.992 |
0.993 |
150 |
0.966 |
0.968 |
0.972 |
0.975 |
0.983 |
0.989 |
0.991 |
0.993 |
0.993 |
160 |
0.968 |
0.970 |
0.973 |
0.976 |
0.984 |
0.990 |
0.991 |
0.993 |
0.994 |
170 |
0.969 |
0.971 |
0.974 |
0.977 |
0.984 |
0.990 |
0.992 |
0.993 |
0.994 |
180 |
0.970 |
0.972 |
0.975 |
0.978 |
0.985 |
0.991 |
0.992 |
0.993 |
0.994 |
190 |
0.971 |
0.973 |
0.976 |
0.979 |
0.986 |
0.991 |
0.992 |
0.994 |
0.994 |
200 |
0.973 |
0.975 |
0.977 |
0.979 |
0.986 |
0.991 |
0.993 |
0.994 |
0.995 |
250 |
0.977 |
0.979 |
0.981 |
0.983 |
0.988 |
0.992 |
0.993 |
0.994 |
0.995 |
300 |
0.981 |
0.982 |
0.984 |
0.985 |
0.990 |
0.993 |
0.994 |
0.995 |
0.996 |
350 |
0.983 |
0.984 |
0.985 |
0.987 |
0.991 |
0.994 |
0.995 |
0.996 |
0.996 |
400 |
0.984 |
0.985 |
0.987 |
0.988 |
0.992 |
0.994 |
0.995 |
0.996 |
0.996 |
450 |
0.986 |
0.987 |
0.988 |
0.989 |
0.992 |
0.995 |
0.996 |
0.996 |
0.997 |
500 |
0.987 |
0.988 |
0.989 |
0.990 |
0.993 |
0.995 |
0.996 |
0.996 |
0.997 |
550 |
0.988 |
0.989 |
0.990 |
0.991 |
0.993 |
0.995 |
0.996 |
0.997 |
0.997 |
600 |
0.989 |
0.990 |
0.991 |
0.991 |
0.994 |
0.996 |
0.996 |
0.997 |
0.997 |
650 |
0.990 |
0.990 |
0.991 |
0.992 |
0.994 |
0.996 |
0.996 |
0.997 |
0.997 |
700 |
0.990 |
0.991 |
0.992 |
0.992 |
0.994 |
0.996 |
0.997 |
0.997 |
0.997 |
750 |
0.991 |
0.991 |
0.992 |
0.993 |
0.995 |
0.996 |
0.997 |
0.997 |
0.997 |
800 |
0.991 |
0.992 |
0.992 |
0.993 |
0.995 |
0.997 |
0.997 |
0.997 |
0.998 |
850 |
0.992 |
0.992 |
0.993 |
0.993 |
0.995 |
0.997 |
0.997 |
0.997 |
0.998 |
900 |
0.992 |
0.993 |
0.993 |
0.994 |
0.995 |
0.997 |
0.997 |
0.997 |
0.998 |
950 |
0.992 |
0.993 |
0.993 |
0.994 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
1000 |
0.993 |
0.993 |
0.994 |
0.994 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
1500 |
0.995 |
0.995 |
0.995 |
0.996 |
0.997 |
0.998 |
0.998 |
0.998 |
0.998 |
2000 |
0.996 |
0.996 |
0.996 |
0.997 |
0.997 |
0.998 |
0.998 |
0.998 |
0.999 |
2500 |
0.996 |
0.997 |
0.997 |
0.997 |
0.998 |
0.998 |
0.998 |
0.999 |
0.999 |
3000 |
0.997 |
0.997 |
0.997 |
0.997 |
0.998 |
0.998 |
0.999 |
0.999 |
0.999 |
3500 |
0.997 |
0.997 |
0.998 |
0.998 |
0.998 |
0.999 |
0.999 |
0.999 |
0.999 |
4000 |
0.998 |
0.998 |
0.998 |
0.998 |
0.998 |
0.999 |
0.999 |
0.999 |
0.999 |
4500 |
0.998 |
0.998 |
0.998 |
0.998 |
0.998 |
0.999 |
0.999 |
0.999 |
0.999 |
5000 |
0.998 |
0.998 |
0.998 |
0.998 |
0.999 |
0.999 |
0.999 |
0.999 |
0.999 |
10 Spiegelhalter (1977, p. 417)
Table 1: Estimated significance points for \(T^\prime\)
N |
cN |
5% |
10% |
5 |
0.3310 |
1.532 |
1.512 |
10 |
0.2678 |
1.453 |
1.417 |
15 |
0.2445 |
1.423 |
1.387 |
20 |
0.2321 |
1.403 |
1.369 |
50 |
0.2070 |
1.337 |
1.317 |
100 |
0.1971 |
1.308 |
1.295 |
11 Zhang (1999, p. 523)
Table 2: Empirical percentage points of \(Q\) compared with Cornish-Fisher percentage points
N |
0.025 |
0.05 |
0.10 |
0.25 |
0.50 |
0.75 |
0.90 |
0.95 |
0.975 |
10 |
0.028 |
0.054 |
0.104 |
0.255 |
0.502 |
0.745 |
0.891 |
0.946 |
0.972 |
20 |
0.025 |
0.045 |
0.099 |
0.249 |
0.498 |
0.744 |
0.892 |
0.947 |
0.970 |
30 |
0.024 |
0.050 |
0.101 |
0.249 |
0.502 |
0.745 |
0.889 |
0.940 |
0.968 |
40 |
0.025 |
0.048 |
0.098 |
0.249 |
0.507 |
0.756 |
0.904 |
0.950 |
0.974 |
50 |
0.025 |
0.049 |
0.100 |
0.256 |
0.505 |
0.757 |
0.902 |
0.947 |
0.972 |
100 |
0.027 |
0.051 |
0.103 |
0.258 |
0.510 |
0.756 |
0.905 |
0.948 |
0.973 |
500 |
0.025 |
0.054 |
0.104 |
0.248 |
0.505 |
0.747 |
0.892 |
0.940 |
0.969 |
1000 |
0.024 |
0.050 |
0.091 |
0.239 |
0.493 |
0.749 |
0.901 |
0.951 |
0.977 |
1500 |
0.020 |
0.041 |
0.086 |
0.239 |
0.501 |
0.768 |
0.912 |
0.954 |
0.975 |
2000 |
0.015 |
0.030 |
0.075 |
0.223 |
0.496 |
0.763 |
0.904 |
0.955 |
0.980 |
Procedure:
- Calculate \(Q\) and \(Q^*\) as already defined
- Conduct the hypothesis test based on \(Q\) and \(Q^*\) separately at the level of \(\alpha/2\)
- Accept the null hypothesis of normality only when both \(Q\) and \(Q^*\) are non-signicant.
12 Zhang-Wu (2005, p. 712)
Table 3: Percentage points of \(10 \times Z_{A} - 32\) for testing normality
N |
0.001 |
0.01 |
0.05 |
0.10 |
0.20 |
0.30 |
0.40 |
0.50 |
0.60 |
0.70 |
0.80 |
0.90 |
0.95 |
0.99 |
0.999 |
5 |
-0.351 |
-0.303 |
-0.186 |
-0.080 |
0.093 |
0.262 |
0.435 |
0.613 |
0.817 |
1.083 |
1.457 |
2.093 |
2.720 |
4.188 |
5.568 |
6 |
-0.133 |
-0.063 |
0.066 |
0.170 |
0.344 |
0.503 |
0.660 |
0.832 |
1.038 |
1.299 |
1.658 |
2.278 |
2.923 |
4.431 |
6.231 |
7 |
0.032 |
0.111 |
0.242 |
0.344 |
0.510 |
0.658 |
0.809 |
0.976 |
1.173 |
1.420 |
1.765 |
2.374 |
2.994 |
4.503 |
6.472 |
8 |
0.158 |
0.241 |
0.369 |
0.468 |
0.625 |
0.766 |
0.912 |
1.073 |
1.261 |
1.499 |
1.831 |
2.414 |
3.020 |
4.484 |
6.540 |
9 |
0.258 |
0.339 |
0.465 |
0.561 |
0.710 |
0.845 |
0.985 |
1.139 |
1.319 |
1.545 |
1.864 |
2.419 |
2.993 |
4.409 |
6.442 |
10 |
0.335 |
0.416 |
0.538 |
0.632 |
0.774 |
0.904 |
1.038 |
1.184 |
1.356 |
1.575 |
1.879 |
2.414 |
2.970 |
4.318 |
6.265 |
12 |
0.453 |
0.530 |
0.645 |
0.730 |
0.862 |
0.983 |
1.106 |
1.242 |
1.401 |
1.602 |
1.885 |
2.375 |
2.882 |
4.117 |
5.978 |
14 |
0.533 |
0.607 |
0.716 |
0.795 |
0.918 |
1.029 |
1.144 |
1.272 |
1.420 |
1.607 |
1.866 |
2.316 |
2.783 |
3.939 |
5.641 |
16 |
0.592 |
0.663 |
0.766 |
0.840 |
0.954 |
1.059 |
1.166 |
1.285 |
1.423 |
1.596 |
1.838 |
2.256 |
2.689 |
3.740 |
5.287 |
18 |
0.639 |
0.707 |
0.803 |
0.873 |
0.981 |
1.079 |
1.180 |
1.291 |
1.419 |
1.582 |
1.810 |
2.199 |
2.601 |
3.568 |
5.031 |
20 |
0.674 |
0.739 |
0.831 |
0.897 |
0.999 |
1.092 |
1.187 |
1.291 |
1.414 |
1.567 |
1.780 |
2.146 |
2.521 |
3.427 |
4.780 |
25 |
0.737 |
0.796 |
0.876 |
0.935 |
1.025 |
1.106 |
1.190 |
1.282 |
1.389 |
1.524 |
1.710 |
2.029 |
2.353 |
3.126 |
4.246 |
30 |
0.776 |
0.829 |
0.902 |
0.955 |
1.036 |
1.109 |
1.184 |
1.266 |
1.362 |
1.482 |
1.648 |
1.931 |
2.217 |
2.902 |
3.914 |
40 |
0.823 |
0.868 |
0.929 |
0.973 |
1.041 |
1.102 |
1.165 |
1.233 |
1.313 |
1.413 |
1.550 |
1.783 |
2.015 |
2.564 |
3.380 |
50 |
0.847 |
0.887 |
0.941 |
0.979 |
1.038 |
1.091 |
1.145 |
1.204 |
1.273 |
1.358 |
1.475 |
1.674 |
1.873 |
2.342 |
3.028 |
70 |
0.874 |
0.906 |
0.949 |
0.979 |
1.026 |
1.068 |
1.111 |
1.157 |
1.212 |
1.279 |
1.371 |
1.526 |
1.682 |
2.046 |
2.567 |
100 |
0.890 |
0.915 |
0.949 |
0.973 |
1.009 |
1.042 |
1.075 |
1.111 |
1.152 |
1.204 |
1.275 |
1.394 |
1.514 |
1.791 |
2.193 |
150 |
0.900 |
0.919 |
0.944 |
0.962 |
0.989 |
1.013 |
1.038 |
1.064 |
1.095 |
1.133 |
1.184 |
1.271 |
1.359 |
1.562 |
1.856 |
200 |
0.904 |
0.919 |
0.939 |
0.954 |
0.976 |
0.995 |
1.014 |
1.036 |
1.060 |
1.090 |
1.132 |
1.202 |
1.272 |
1.435 |
1.670 |
300 |
0.906 |
0.918 |
0.932 |
0.943 |
0.959 |
0.973 |
0.987 |
1.002 |
1.020 |
1.042 |
1.072 |
1.122 |
1.172 |
1.289 |
1.465 |
500 |
0.906 |
0.914 |
0.924 |
0.931 |
0.942 |
0.951 |
0.960 |
0.970 |
0.982 |
0.996 |
1.016 |
1.048 |
1.081 |
1.159 |
1.275 |
1000 |
0.905 |
0.909 |
0.915 |
0.919 |
0.925 |
0.930 |
0.935 |
0.941 |
0.947 |
0.955 |
0.966 |
0.984 |
1.002 |
1.046 |
1.111 |
Table 4: Percentage points of \(Z_{C}\) for testing normality
N |
0.001 |
0.01 |
0.05 |
0.10 |
0.20 |
0.30 |
0.40 |
0.50 |
0.60 |
0.70 |
0.80 |
0.90 |
0.95 |
0.99 |
0.999 |
5 |
0.664 |
0.724 |
0.874 |
1.007 |
1.252 |
1.501 |
1.749 |
2.002 |
2.261 |
2.577 |
3.002 |
3.639 |
4.213 |
5.460 |
6.757 |
6 |
0.704 |
0.808 |
1.003 |
1.176 |
1.475 |
1.756 |
2.028 |
2.298 |
2.602 |
2.967 |
3.433 |
4.158 |
4.849 |
6.382 |
8.280 |
7 |
0.745 |
0.881 |
1.120 |
1.322 |
1.662 |
1.966 |
2.255 |
2.555 |
2.891 |
3.288 |
3.797 |
4.610 |
5.385 |
7.196 |
9.635 |
8 |
0.781 |
0.945 |
1.218 |
1.446 |
1.819 |
2.144 |
2.453 |
2.778 |
3.141 |
3.567 |
4.123 |
5.007 |
5.864 |
7.908 |
10.954 |
9 |
0.813 |
0.997 |
1.306 |
1.556 |
1.955 |
2.299 |
2.631 |
2.979 |
3.362 |
3.810 |
4.404 |
5.350 |
6.267 |
8.545 |
12.102 |
10 |
0.842 |
1.049 |
1.388 |
1.658 |
2.079 |
2.438 |
2.789 |
3.155 |
3.559 |
4.035 |
4.659 |
5.663 |
6.650 |
9.138 |
13.115 |
12 |
0.895 |
1.138 |
1.526 |
1.831 |
2.290 |
2.682 |
3.065 |
3.463 |
3.902 |
4.424 |
5.105 |
6.209 |
7.304 |
10.156 |
15.147 |
14 |
0.935 |
1.212 |
1.645 |
1.972 |
2.464 |
2.888 |
3.298 |
3.723 |
4.195 |
4.755 |
5.486 |
6.669 |
7.862 |
11.103 |
16.969 |
16 |
0.976 |
1.277 |
1.746 |
2.096 |
2.616 |
3.064 |
3.495 |
3.944 |
4.443 |
5.036 |
5.808 |
7.065 |
8.352 |
11.838 |
18.474 |
18 |
1.014 |
1.334 |
1.838 |
2.207 |
2.754 |
3.222 |
3.675 |
4.147 |
4.669 |
5.287 |
6.099 |
7.422 |
8.767 |
12.493 |
19.899 |
20 |
1.046 |
1.396 |
1.924 |
2.309 |
2.875 |
3.361 |
3.835 |
4.328 |
4.869 |
5.511 |
6.362 |
7.752 |
9.157 |
13.150 |
21.149 |
25 |
1.120 |
1.519 |
2.103 |
2.519 |
3.137 |
3.664 |
4.176 |
4.707 |
5.298 |
5.994 |
6.918 |
8.438 |
9.984 |
14.432 |
23.753 |
30 |
1.170 |
1.618 |
2.246 |
2.693 |
3.349 |
3.910 |
4.456 |
5.023 |
5.649 |
6.391 |
7.375 |
8.998 |
10.662 |
15.580 |
26.091 |
40 |
1.285 |
1.783 |
2.483 |
2.972 |
3.693 |
4.307 |
4.901 |
5.521 |
6.209 |
7.031 |
8.109 |
9.888 |
11.733 |
17.223 |
29.333 |
50 |
1.366 |
1.912 |
2.674 |
3.193 |
3.957 |
4.612 |
5.248 |
5.913 |
6.648 |
7.522 |
8.683 |
10.594 |
12.583 |
18.480 |
31.707 |
70 |
1.512 |
2.131 |
2.963 |
3.535 |
4.367 |
5.079 |
5.771 |
6.499 |
7.302 |
8.262 |
9.540 |
11.640 |
13.835 |
20.399 |
35.532 |
100 |
1.693 |
2.369 |
3.279 |
3.902 |
4.810 |
5.590 |
6.344 |
7.132 |
8.011 |
9.059 |
10.452 |
12.758 |
15.171 |
22.242 |
39.126 |
150 |
1.891 |
2.653 |
3.655 |
4.339 |
5.327 |
6.175 |
6.999 |
7.862 |
8.818 |
9.970 |
11.488 |
14.027 |
16.628 |
24.405 |
42.354 |
200 |
2.043 |
2.867 |
3.923 |
4.649 |
5.696 |
6.593 |
7.464 |
8.376 |
9.391 |
10.613 |
12.244 |
14.934 |
17.714 |
25.839 |
44.611 |
300 |
2.298 |
3.196 |
4.338 |
5.118 |
6.245 |
7.209 |
8.149 |
9.123 |
10.220 |
11.530 |
13.276 |
16.179 |
19.139 |
27.523 |
46.663 |
500 |
2.609 |
3.596 |
4.861 |
5.702 |
6.932 |
7.977 |
8.990 |
10.055 |
11.246 |
12.674 |
14.567 |
17.717 |
20.927 |
29.760 |
49.888 |
1000 |
3.072 |
4.191 |
5.588 |
6.526 |
7.885 |
9.045 |
10.169 |
11.346 |
12.654 |
14.224 |
16.322 |
19.796 |
23.301 |
32.811 |
53.458 |
n
|
|
|
E
p
|
20%
|
10%
|
5%
|
1%
|
20%
|
10%
|
5%
|
1%
|
20%
|
10%
|
5%
|
1%
|
10 |
0.033 |
0.017 |
0.010 |
0.002 |
0.158 |
0.093 |
0.057 |
0.024 |
0.204 |
0.101 |
0.048 |
0.007 |
20 |
0.062 |
0.036 |
0.022 |
0.010 |
0.165 |
0.091 |
0.055 |
0.018 |
0.185 |
0.092 |
0.046 |
0.011 |
50 |
0.094 |
0.055 |
0.035 |
0.012 |
0.177 |
0.095 |
0.055 |
0.017 |
0.178 |
0.088 |
0.046 |
0.011 |
150 |
0.138 |
0.070 |
0.044 |
0.018 |
0.191 |
0.098 |
0.055 |
0.016 |
0.182 |
0.092 |
0.047 |
0.012 |
MCSE |
0.004 |
0.003 |
0.002 |
0.001 |
0.004 |
0.003 |
0.002 |
0.001 |
0.004 |
0.003 |
0.002 |
0.001 |
This tool provides a web interface for several diagnostic test of distributional shape, normality, and homogeneity of variances.
The About tab is under development to provide description of the some of the functions and requirements (e.g., data.csv file) for use of this tool.
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