Таблицы критических значений статистических критериев
Стандартные нормальные вероятности
В таблице указаны значения площади под кривой единичного нормального распределения, находящиеся справа от Z. В крайнем левом столбце даны различные z-значения с точностью до одного десятичного знака. Значения вероятностей указаны для различных значений Z, включая второй знак после запятой (указан в верхнем ряду).
| z | 0,00 | 0,01 | 0,02 | 0,03 | 0,04 | 0,05 | 0,06 | 0,07 | 0,08 | 0,09 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0,0 | 0,5000 | 0,4960 | 0,4920 | 0,4880 | 0,4840 | 0,4801 | 0,4761 | 0,4721 | 0,4681 | 0,4641 |
| 0,1 | 0,4602 | 0,4562 | 0,4522 | 0,4483 | 0,4404 | 0,4404 | 0,4364 | 0,4325 | 0,4286 | 0,4247 |
| 0,2 | 0,4207 | 0,4168 | 0,4129 | 0,4090 | 0,4052 | 0,4013 | 0,3974 | 0,3936 | 0,3897 | 0,3859 |
| 0,3 | 0,3821 | 0,3783 | 0,3745 | 0,3707 | 0,3669 | 0,3632 | 0,3594 | 0,3557 | 0,3520 | 0,3483 |
| 0,4 | 0,3446 | 0,3409 | 0,3372 | 0,3336 | 0,3300 | 0,3264 | 0,3228 | 0,3192 | 0,3156 | 0,3121 |
| 0,5 | 0,3085 | 0,3050 | 0,3015 | 0,2981 | 0,2946 | 0,2912 | 0,2877 | 0,2843 | 0,2810 | 0,2776 |
| 0,6 | 0,2743 | 0,2709 | 0,2676 | 0,2643 | 0,2611 | 0,2578 | 0,2546 | 0,2514 | 0,2483 | 0,2451 |
| 0,7 | 0,2420 | 0,2389 | 0,2358 | 0,2327 | 0,2296 | 0,2266 | 0,2236 | 0,2206 | 0,2177 | 0,2148 |
| 0,8 | 0,2119 | 0,2090 | 0,2061 | 0,2033 | 0,2005 | 0,1977 | 0,1949 | 0,1922 | 0,1894 | 0,1867 |
| 0,9 | 0,1841 | 0,1814 | 0,1788 | 0,1762 | 0,1736 | 0,1711 | 0,1685 | 0,1660 | 0,1635 | 0,1611 |
| 1,0 | 0,1587 | 0,1562 | 0,1539 | 0,1515 | 0,1492 | 0,1469 | 0,1446 | 0,1423 | 0,1401 | 0,1379 |
| 1,1 | 0,1357 | 0,1335 | 0,1314 | 0,1292 | 0,1271 | 0,1251 | 0,1230 | 0,1210 | 0,1190 | 0,1170 |
| 1,2 | 0,1151 | 0,1131 | 0,1112 | 0,1093 | 0,1075 | 0,1056 | 0,1038 | 0,1020 | 0,1003 | 0,0985 |
| 1,3 | 0,0968 | 0,0951 | 0,0934 | 0,0918 | 0,0901 | 0,0885 | 0,0869 | 0,0853 | 0,0838 | 0,0823 |
| 1,4 | 0,0808 | 0,0793 | 0,0778 | 0,0764 | 0,0749 | 0,0735 | 0,0721 | 0,0708 | 0,0694 | 0,0681 |
| 1,5 | 0,0668 | 0,0655 | 0,0643 | 0,0630 | 0,0618 | 0,0606 | 0,0594 | 0,0582 | 0,0571 | 0,0559 |
| 1,6 | 0,0548 | 0,0537 | 0,0526 | 0,0516 | 0,0505 | 0,0495 | 0,0485 | 0,0475 | 0,0465 | 0,0455 |
| 1,7 | 0,0446 | 0,0436 | 0,0427 | 0,0418 | 0,0409 | 0,0401 | 0,0392 | 0,0384 | 0,0375 | 0,0367 |
| 1,8 | 0,0359 | 0,0351 | 0,0344 | 0,0336 | 0,0329 | 0,0322 | 0,0314 | 0,0307 | 0,0301 | 0,0294 |
| 1,9 | 0,0287 | 0,0281 | 0,0274 | 0,0268 | 0,0262 | 0,0256 | 0,0250 | 0,0244 | 0,0239 | 0,0233 |
| 2,0 | 0,0228 | 0,0222 | 0,0217 | 0,0212 | 0,0207 | 0,0202 | 0,0197 | 0,0192 | 0,0188 | 0,0183 |
| 2,1 | 0,0179 | 0,0174 | 0,0170 | 0,0166 | 0,0162 | 0,0158 | 0,0154 | 0,0150 | 0,0146 | 0,0143 |
| 2,2 | 0,0139 | 0,0136 | 0,0132 | 0,0129 | 0,0125 | 0,0122 | 0,0119 | 0,0116 | 0,0113 | 0,0110 |
| 2,3 | 0,0107 | 0,0104 | 0,0102 | 0,0099 | 0,0096 | 0,0094 | 0,0091 | 0,0089 | 0,0087 | 0,0084 |
| 2,4 | 0,0082 | 0,0080 | 0,0078 | 0,0075 | 0,0073 | 0,0071 | 0,0069 | 0,0068 | 0,0066 | 0,0064 |
| 2,5 | 0,0062 | 0,0060 | 0,0059 | 0,0057 | 0,0055 | 0,0054 | 0,0052 | 0,0051 | 0,0049 | 0,0048 |
| 2,6 | 0,0047 | 0,0045 | 0,0044 | 0,0043 | 0,0041 | 0,0040 | 0,0039 | 0,0038 | 0,0037 | 0,0036 |
| 2,7 | 0,0035 | 0,0034 | 0,0033 | 0,0032 | 0,0031 | 0,0030 | 0,0029 | 0,0028 | 0,0027 | 0,0026 |
| 2,8 | 0,0026 | 0,0025 | 0,0024 | 0,0023 | 0,0023 | 0,0022 | 0,0021 | 0,0021 | 0,0020 | 0,0019 |
| 2,9 | 0,0019 | 0,0018 | 0,0018 | 0,0017 | 0,0016 | 0,0016 | 0,0015 | 0,0015 | 0,0014 | 0,0014 |
| 3,0 | 0,0013 | 0,0013 | 0,0013 | 0,0012 | 0,0012 | 0,0011 | 0,0011 | 0,0011 | 0,0010 | 0,0010 |
| 3,1 | 0,0010 | 0,0009 | 0,0009 | 0,0009 | 0,0008 | 0,0008 | 0,0008 | 0,0008 | 0,0007 | 0,0007 |
| 3,2 | 0,0007 | |||||||||
| 3,3 | 0,0005 | |||||||||
| 3,4 | 0,0003 | |||||||||
| 3,5 | 0,00023 | |||||||||
| 3,6 | 0,00016 | |||||||||
| 3,7 | 0,00011 | |||||||||
| 3,8 | 0,00007 | |||||||||
| 3,9 | 0,00005 | |||||||||
| 4,0 | 0,00003 |
Критические значения критерия t-Стьюдента
(для проверки ненаправленных альтернатив — двусторонний критерий)
| df | Р | df | Р | df | Р | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | |||
| 1 | 6,314 | 12,70 | 63,65 | 636,61 | 31 | 1,696 | 2,040 | 2,744 | 3,633 | 61 | 1,670 | 2,000 | 2,659 | 3,457 |
| 2 | 2,920 | 4,303 | 9,925 | 31,602 | 32 | 1,694 | 2,037 | 2,738 | 3,622 | 62 | 1,670 | 1,999 | 2,657 | 3,454 |
| 3 | 2,353 | 3,182 | 5,841 | 12,923 | 33 | 1,692 | 2,035 | 2,733 | 3,611 | 63 | 1,669 | 1,998 | 2,656 | 3,452 |
| 4 | 2,132 | 2,776 | 4,604 | 8,610 | 34 | 1,691 | 2,032 | 2,728 | 3,601 | 64 | 1,669 | 1,998 | 2,655 | 3,449 |
| 5 | 2,015 | 2,571 | 4,032 | 6,869 | 35 | 1,690 | 2,030 | 2,724 | 3,591 | 65 | 1,669 | 1,997 | 2,654 | 3,447 |
| 6 | 1,943 | 2,447 | 3,707 | 5,959 | 36 | 1,688 | 2,028 | 2,719 | 3,582 | 66 | 1,668 | 1,997 | 2,652 | 3,444 |
| 7 | 1,895 | 2,365 | 3,499 | 5,408 | 37 | 1,687 | 2,026 | 2,715 | 3,574 | 67 | 1,668 | 1,996 | 2,651 | 3,442 |
| 8 | 1,860 | 2,306 | 3,355 | 5,041 | 38 | 1,686 | 2,024 | 2,712 | 3,566 | 68 | 1,668 | 1,995 | 2,650 | 3,439 |
| 9 | 1,833 | 2,262 | 3,250 | 4,781 | 39 | 1,685 | 2,023 | 2,708 | 3,558 | 69 | 1,667 | 1,995 | 2,649 | 3,437 |
| 10 | 1,812 | 2,228 | 3,169 | 4,587 | 40 | 1,684 | 2,021 | 2,704 | 3,551 | 70 | 1,667 | 1,994 | 2,648 | 3,435 |
| 11 | 1,796 | 2,201 | 3,106 | 4,437 | 41 | 1,683 | 2,020 | 2,701 | 3,544 | 71 | 1,667 | 1,994 | 2,647 | 3,433 |
| 12 | 1,782 | 2,179 | 3,055 | 4,318 | 42 | 1,682 | 2,018 | 2,698 | 3,538 | 72 | 1,666 | 1,993 | 2,646 | 3,431 |
| 13 | 1,771 | 2,160 | 3,012 | 4,221 | 43 | 1,681 | 2,017 | 2,695 | 3,532 | 73 | 1,666 | 1,993 | 2,645 | 3,429 |
| 14 | 1,761 | 2,145 | 2,977 | 4,140 | 44 | 1,680 | 2,015 | 2,692 | 3,526 | 74 | 1,666 | 1,993 | 2,644 | 3,427 |
| 15 | 1,753 | 2,131 | 2,947 | 4,073 | 45 | 1,679 | 2,014 | 2,690 | 3,520 | 75 | 1,665 | 1,992 | 2,643 | 3,425 |
| 16 | 1,746 | 2,120 | 2,921 | 4,015 | 46 | 1,679 | 2,013 | 2,687 | 3,515 | 76 | 1,665 | 1,992 | 2,642 | 3,423 |
| 17 | 1,740 | 2,110 | 2,898 | 3,965 | 47 | 1,678 | 2,012 | 2,685 | 3,510 | 78 | 1,665 | 1,991 | 2,640 | 3,420 |
| 18 | 1,734 | 2,101 | 2,878 | 3,922 | 48 | 1,677 | 2,011 | 2,682 | 3,505 | 79 | 1,664 | 1,990 | 2,639 | 3,418 |
| 19 | 1,729 | 2,093 | 2,861 | 3,883 | 49 | 1,677 | 2,010 | 2,680 | 3,500 | 80 | 1,664 | 1,990 | 2,639 | 3,416 |
| 20 | 1,725 | 2,086 | 2,845 | 3,850 | 50 | 1,676 | 2,009 | 2,678 | 3,496 | 90 | 1,662 | 1,987 | 2,632 | 3,402 |
| 21 | 1,721 | 2,080 | 2,831 | 3,819 | 51 | 1,675 | 2,008 | 2,676 | 3,492 | 100 | 1,660 | 1,984 | 2,626 | 3,390 |
| 22 | 1,717 | 2,074 | 2,819 | 3,792 | 52 | 1,675 | 2,007 | 2,674 | 3,488 | 110 | 1,659 | 1,982 | 2,621 | 3,381 |
| 23 | 1,714 | 2,069 | 2,807 | 3,768 | 53 | 1,674 | 2,006 | 2,672 | 3,484 | 120 | 1,658 | 1,980 | 2,617 | 3,373 |
| 24 | 1,711 | 2,064 | 2,797 | 3,745 | 54 | 1,674 | 2,005 | 2,670 | 3,480 | 130 | 1,657 | 1,978 | 2,614 | 3,367 |
| 25 | 1,708 | 2,060 | 2,787 | 3,725 | 55 | 1,673 | 2,004 | 2,668 | 3,476 | 140 | 1,656 | 1,977 | 2,611 | 3,361 |
| 26 | 1,706 | 2,056 | 2,779 | 3,707 | 56 | 1,673 | 2,003 | 2,667 | 3,473 | 150 | 1,655 | 1,976 | 2,609 | 3,357 |
| 27 | 1,703 | 2,052 | 2,771 | 3,690 | 57 | 1,672 | 2,002 | 2,665 | 3,470 | 200 | 1,653 | 1,972 | 2,601 | 3,340 |
| 28 | 1,701 | 2,049 | 2,763 | 3,674 | 58 | 1,672 | 2,002 | 2,663 | 3,466 | 250 | 1,651 | 1,969 | 2,596 | 3,330 |
| 29 | 1,699 | 2,045 | 2,756 | 3,659 | 59 | 1,671 | 2,001 | 2,662 | 3,463 | 300 | 1,650 | 1,968 | 2,592 | 3,323 |
| 30 | 1,697 | 2,042 | 2,750 | 3,646 | 60 | 1,671 | 2,000 | 2,660 | 3,460 | 350 | 1,649 | 1,967 | 2,590 | 3,319 |
Критические значения критерия χ2
| df | Р | df | Р | df | Р | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | |||
| 1 | 2,706 | 3,842 | 6,635 | 10,829 | 31 | 41,422 | 44,993 | 52,203 | 61,118 | 61 | 75,514 | 80,232 | 89,591 | 100,887 |
| 2 | 4,605 | 5,992 | 9,211 | 13,817 | 32 | 42,585 | 46,202 | 53,498 | 62,508 | 62 | 76,630 | 81,381 | 90,802 | 102,165 |
| 3 | 6,251 | 7,815 | 11,346 | 16,269 | 33 | 43.745 | 47.408 | 54.789 | 63.891 | 63 | 77,745 | 82,529 | 92,010 | 103,442 |
| 4 | 7,779 | 9,488 | 13,278 | 18,470 | 34 | 44.903 | 48.610 | 56.074 | 65.269 | 64 | 78,860 | 83,675 | 93,217 | 104,717 |
| 5 | 9,236 | 11,071 | 15,088 | 20,519 | 35 | 46.059 | 49.810 | 57.356 | 66.641 | 65 | 79,973 | 84,821 | 94,422 | 105,988 |
| 6 | 10,645 | 12,593 | 16,814 | 22,462 | 36 | 47.212 | 51.007 | 58.634 | 68.008 | 66 | 81,085 | 85,965 | 95,626 | 107,257 |
| 7 | 12,017 | 14,068 | 18,478 | 24,327 | 37 | 48.363 | 52.201 | 59.907 | 69.370 | 67 | 82,197 | 87,108 | 96,828 | 108,525 |
| 8 | 13,362 | 15,509 | 20,093 | 26,130 | 38 | 49.513 | 53.393 | 61.177 | 70.728 | 68 | 83,308 | 88,250 | 98,028 | 109,793 |
| 9 | 14,684 | 16,921 | 21,669 | 27,883 | 39 | 50.660 | 54.582 | 62.444 | 72.080 | 69 | 84,418 | 89,391 | 99,227 | 111,055 |
| 10 | 15,987 | 18,309 | 23,213 | 29,594 | 40 | 51.805 | 55.768 | 63.707 | 73.428 | 70 | 85,527 | 90,531 | 100,425 | 112,317 |
| 11 | 17,275 | 19,677 | 24,729 | 31,271 | 41 | 52.494 | 56.953 | 64.967 | 74.772 | 71 | 86,635 | 91,670 | 101,621 | 113,577 |
| 12 | 18,549 | 21,028 | 26,221 | 32,917 | 42 | 54.090 | 58.135 | 66.224 | 76.111 | 72 | 87,743 | 92,808 | 102,816 | 114,834 |
| 13 | 19,812 | 22,365 | 27,693 | 34,536 | 43 | 55.230 | 59.314 | 67.477 | 77.447 | 73 | 88,850 | 93,945 | 104,010 | 116,092 |
| 14 | 21,064 | 23,688 | 29,146 | 36,132 | 44 | 56.369 | 60.492 | 68.728 | 78.779 | 74 | 89,956 | 95,081 | 105,202 | 117,347 |
| 15 | 22,307 | 24,999 | 30,583 | 37,706 | 45 | 57.505 | 61.668 | 69.976 | 80.107 | 75 | 91,061 | 96,217 | 106,393 | 118,599 |
| 16 | 23,542 | 26,299 | 32,006 | 39,262 | 46 | 58,641 | 62,841 | 71,221 | 81,431 | 76 | 92,166 | 97,351 | 107,582 | 119,850 |
| 17 | 24,769 | 27,591 | 33,415 | 40,801 | 47 | 59,774 | 64,013 | 72,463 | 82,752 | 78 | 94,374 | 99,617 | 109,958 | 122,347 |
| 18 | 25,989 | 28,873 | 34,812 | 42,323 | 48 | 60,907 | 65,183 | 73,703 | 84,069 | 79 | 95.476 | 100.749 | 111.144 | 123.595 |
| 19 | 27,204 | 30,147 | 36,198 | 43,832 | 49 | 62,038 | 66,351 | 74,940 | 85,384 | 80 | 96.578 | 101.879 | 112.329 | 124.839 |
| 20 | 28,412 | 31,415 | 37,574 | 45,327 | 50 | 63,167 | 67,518 | 76,175 | 86,694 | 90 | 107.565 | 113.145 | 124.116 | 137.208 |
| 21 | 29,615 | 32,675 | 38,940 | 46,810 | 51 | 64,295 | 68,683 | 77,408 | 88,003 | 100 | 118.498 | 124.342 | 135.807 | 149.449 |
| 22 | 30,813 | 33,929 | 40,298 | 48,281 | 52 | 65,422 | 69,846 | 78,638 | 89,308 | 110 | 129.385 | 135.480 | 147.414 | 161.582 |
| 23 | 32,007 | 35,177 | 41,647 | 49,742 | 53 | 66,548 | 71,008 | 79,866 | 90,609 | 120 | 140.233 | 146.567 | 158.950 | 173.618 |
| 24 | 33,196 | 36,420 | 42,989 | 51,194 | 54 | 67,673 | 72,168 | 81,092 | 91,909 | 130 | 151.045 | 157.610 | 170.423 | 185.573 |
| 25 | 34,382 | 37,658 | 44,324 | 52,635 | 55 | 68,796 | 73,326 | 82,316 | 93,205 | 140 | 161.827 | 138.613 | 181.841 | 197.450 |
| 26 | 35,563 | 38,891 | 45,652 | 54,068 | 56 | 69,919 | 74,484 | 83,538 | 94,499 | 150 | 172.581 | 179.581 | 193.207 | 209.265 |
| 27 | 36,741 | 40,119 | 46,973 | 55,493 | 57 | 71,040 | 75,639 | 84,758 | 95,790 | 200 | 226.021 | 233.994 | 249.445 | 267.539 |
| 28 | 37,916 | 41,343 | 48,289 | 56,910 | 58 | 72,160 | 76,794 | 85,976 | 97,078 | 250 | 279.050 | 287.882 | 304.939 | 324.831 |
| 29 | 39,087 | 42,564 | 49,599 | 58,320 | 59 | 73,279 | 77,947 | 87,192 | 98,365 | 300 | 331.788 | 341.395 | 359.906 | 381.424 |
| 30 | 40,256 | 43,780 | 50,904 | 59,722 | 60 | 74,397 | 79,099 | 88,406 | 99,649 | 350 | 384.306 | 394.626 | 414.474 | 437.487 |
Критические значения коэффициентов корреляции r-Пирсона (r-Спирмена)
(для проверки ненаправленных альтернатив, n — объем выборки)
| n | Р | n | Р | n | Р | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | 0,10 | 0,05 | 0,01 | 0,001 | |||
| 5 | 0,805 | 0,878 | 0,959 | 0,991 | 33 | 0,291 | 0,344 | 0,442 | 0,547 | 61 | 0,213 | 0,252 | 0,327 | 0,411 |
| 6 | 0,729 | 0,811 | 0,917 | 0,974 | 34 | 0,287 | 0,339 | 0,436 | 0,539 | 62 | 0,211 | 0,250 | 0,325 | 0,408 |
| 7 | 0,669 | 0,754 | 0,875 | 0,951 | 35 | 0,283 | 0,334 | 0,430 | 0,532 | 63 | 0,209 | 0,248 | 0,322 | 0,405 |
| 8 | 0,621 | 0,707 | 0,834 | 0,925 | 36 | 0,279 | 0,329 | 0,424 | 0,525 | 64 | 0,207 | 0,246 | 0,320 | 0,402 |
| 9 | 0,582 | 0,666 | 0,798 | 0,898 | 37 | 0,275 | 0,325 | 0,418 | 0,519 | 65 | 0,206 | 0,244 | 0,317 | 0,399 |
| 10 | 0,549 | 0,632 | 0,765 | 0,872 | 38 | 0,271 | 0,320 | 0,413 | 0,513 | 66 | 0,204 | 0,242 | 0,315 | 0,396 |
| 11 | 0,521 | 0,602 | 0,735 | 0,847 | 39 | 0,267 | 0,316 | 0,408 | 0,507 | 67 | 0,203 | 0,240 | 0,313 | 0,393 |
| 12 | 0,497 | 0,576 | 0,708 | 0,823 | 40 | 0,264 | 0,312 | 0,403 | 0,501 | 68 | 0,201 | 0,239 | 0,310 | 0,390 |
| 13 | 0,476 | 0,553 | 0,684 | 0,801 | 4! | 0,260 | 0,308 | 0,398 | 0,495 | 69 | 0,200 | 0,237 | 0,308 | 0,388 |
| 14 | 0,458 | 0,532 | 0,661 | 0,780 | 42 | 0,257 | 0,304 | 0,393 | 0,490 | 70 | 0,198 | 0,235 | 0,306 | 0,385 |
| 15 | 0,441 | 0,514 | 0,641 | 0,760 | 43 | 0,254 | 0,301 | 0,389 | 0,484 | 80 | 0,185 | 0,220 | 0,286 | 0,361 |
| 16 | 0,426 | 0,497 | 0,623 | 0,742 | 44 | 0,251 | 0,297 | 0,384 | 0,479 | 90 | 0,174 | 0,207 | 0,270 | 0,341 |
| 17 | 0,412 | 0,482 | 0,606 | 0,725 | 45 | 0,248 | 0,294 | 0,380 | 0,474 | 100 | 0,165 | 0,197 | 0,256 | 0,324 |
| 18 | 0,400 | 0,468 | 0,590 | 0,708 | 46 | 0,246 | 0,291 | 0,376 | 0,469 | 110 | 0,158 | 0,187 | 0,245 | 0,310 |
| 19 | 0,389 | 0,456 | 0,575 | 0,693 | 47 | 0,243 | 0,288 | 0,372 | 0,465 | 120 | 0,151 | 0,179 | 0,234 | 0,297 |
| 20 | 0,378 | 0,444 | 0,561 | 0,679 | 48 | 0,240 | 0,285 | 0,368 | 0,460 | 130 | 0,145 | 0,172 | 0,225 | 0,285 |
| 21 | 0,369 | 0,433 | 0,549 | 0,665 | 49 | 0,238 | 0,282 | 0,365 | 0,456 | 140 | 0,140 | 0,166 | 0,217 | 0,275 |
| 22 | 0,360 | 0,423 | 0,537 | 0,652 | 50 | 0,235 | 0,279 | 0,361 | 0,451 | 150 | 0,135 | 0,160 | 0,210 | 0,266 |
| 23 | 0,352 | 0,413 | 0,526 | 0,640 | 51 | 0,233 | 0,276 | 0,358 | 0,447 | 200 | 0,117 | 0,139 | 0,182 | 0,231 |
| 24 | 0,344 | 0,404 | 0,515 | 0,629 | 52 | 0,231 | 0,273 | 0,354 | 0,443 | 250 | 0,104 | 0,124 | 0,163 | 0,207 |
| 25 | 0,337 | 0,396 | 0,505 | 0,618 | 53 | 0,228 | 0,271 | 0,351 | 0,439 | 300 | 0,095 | 0,113 | 0,149 | 0,189 |
| 26 | 0,330 | 0,388 | 0,496 | 0,607 | 54 | 0,226 | 0,268 | 0,348 | 0,435 | 350 | 0,088 | 0,105 | 0,138 | 0,175 |
| 27 | 0,323 | 0,381 | 0,487 | 0,597 | 55 | 0,224 | 0,266 | 0,345 | 0,432 | 400 | 0,082 | 0,098 | 0,129 | 0,164 |
| 28 | 0,317 | 0,374 | 0,479 | 0,588 | 56 | 0,222 | 0,263 | 0,341 | 0,428 | 450 | 0,078 | 0,092 | 0,121 | 0,155 |
| 29 | 0,311 | 0,367 | 0,471 | 0,579 | 57 | 0,220 | 0,261 | 0,339 | 0,424 | 500 | 0,074 | 0,088 | 0,115 | 0,147 |
| 30 | 0,306 | 0,361 | 0,463 | 0,570 | 58 | 0,218 | 0,259 | 0,336 | 0,421 | 600 | 0,067 | 0,080 | 0,105 | 0,134 |
| 31 | 0,301 | 0,355 | 0,456 | 0,562 | 59 | 0,216 | 0,256 | 0,333 | 0,418 |
| ||||
| 32 | 0,296 | 0,349 | 0,449 | 0,554 | 60 | 0,214 | 0,254 | 0,330 | 0,414 |
| ||||
Критические значения критерия U Манна-Уитни
(для проверки ненаправленных альтернатив)
Р=0,05
|
N2 | N1 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
| 3 | I | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 |
| 4 | 3 | 4 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 11 | 12 | 13 | 13 |
| 5 | 5 | 6 | 7 | 8 | 9 | 11 | 12 | 13 | 14 | 15 | 17 | 18 | 19 | 20 |
| 6 | 6 | 8 | 10 | 11 | 13 | 14 | 16 | 17 | 19 | 21 | 22 | 24 | 25 | 27 |
| 7 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 |
| 8 | 10 | 13 | 15 | 17 | 19 | 22 | 24 | 26 | 29 | 31 | 34 | 36 | 38 | 41 |
| 9 | 12 | 15 | 17 | 20 | 23 | 26 | 28 | 31 | 34 | 37 | 39 | 42 | 45 | 48 |
| 10 | 14 | 17 | 20 | 23 | 26 | 29 | 33 | 36 | 39 | 42 | 45 | 48 | 52 | 55 |
| 11 | 16 | 19 | 23 | 26 | 30 | 33 | 37 | 40 | 44 | 47 | 51 | 55 | 58 | 62 |
| 12 | 18 | 22 | 26 | 29 | 33 | 37 | 41 | 45 | 49 | 53 | 57 | 61 | 65 | 69 |
| 13 | 20 | 24 | 28 | 33 | 37 | 41 | 45 | 50 | 54 | 59 | 63 | 67 | 72 | 76 |
| 14 | 22 | 26 | 31 | 36 | 40 | 45 | 50 | 55 | 59 | 64 | 67 | 74 | 78 | 83 |
| 15 | 24 | 29 | 34 | 39 | 44 | 49 | 54 | 59 | 64 | 70 | 75 | 80 | 85 | 90 |
| 16 | 26 | 31 | 37 | 42 | 47 | 53 | 59 | 64 | 70 | 75 | 81 | 86 | 92 | 98 |
| 17 | 28 | 34 | 39 | 45 | 51 | 57 | 63 | 67 | 75 | 81 | 87 | 93 | 99 | 105 |
| 18 | 30 | 36 | 42 | 48 | 55 | 61 | 67 | 74 | 80 | 86 | 93 | 99 | 106 | 112 |
| 19 | 32 | 38 | 45 | 52 | 58 | 65 | 72 | 78 | 85 | 92 | 99 | 106 | 113 | 119 |
| 20 | 34 | 41 | 48 | 55 | 62 | 69 | 76 | 83 | 90 | 98 | 105 | 112 | 119 | 127 |
Р=0,01
| N2 | N1 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
| 3 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | ||
| 4 | 0 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 5 | 5 | 6 | 6 | 7 | 8 |
| 5 | 1 | 2 | 3 | 4 | 4 | 6 | 7 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 6 | 3 | 4 | 5 | 6 | 6 | 9 | 10 | 11 | 12 | 13 | 15 | 16 | 17 | 18 |
| 7 | 4 | 6 | 7 | 9 | 9 | 12 | 13 | 15 | 16 | 18 | 19 | 21 | 22 | 24 |
| 8 | 6 | 7 | 9 | 11 | 11 | 15 | 17 | 18 | 20 | 22 | 24 | 26 | 28 | 30 |
| 9 | 7 | 9 | 11 | 13 | 13 | 18 | 20 | 22 | 24 | 27 | 29 | 31 | 33 | 36 |
| 10 | 9 | 11 | 13 | 16 | 16 | 21 | 24 | 26 | 29 | 31 | 34 | 37 | 39 | 42 |
| 11 | 10 | 13 | 16 | 18 | 18 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 |
| 12 | 12 | 15 | 18 | 21 | 21 | 27 | 31 | 34 | 37 | 41 | 44 | 47 | 51 | 54 |
| 13 | 13 | 17 | 20 | 24 | 24 | 31 | 34 | 38 | 42 | 45 | 49 | 53 | 56 . | 60 |
| 14 | 15 | 18 | 22 | 26 | 26 | 34 | 38 | 42 | 46 | 50 | 54 | 58 | 63 | 67 |
| 15 | 16 | 20 | 24 | 29 | 29 | 37 | 42 | 46 | 51 | 55 | 60 | 64 | 69 | 73 |
| 16 | 18 | 22 | 27 | 31 | 31 | 41 | 45 | 50 | 55 | 60 | 65 | 70 | 74 | 79 |
| 17 | 19 | 24 | 29 | 34 | 34 | 44 | 49 | 54 | 60 | 65 | 70 | 75 | 81 | 86 |
| 18 | 21 | 26 | 31 | 37 | 37 | 47 | 53 | 58 | 64 | 70 | 75 | 81 | 87 | 92 |
| 19 | 22 | 28 | 33 | 39 | 39 | 51 | 56 | 63 | 69 | 74 | 81 | 87 | 93 | 99 |
| 20 | 24 | 30 | 36 | 42 | 42 | 54 | 60 | 67 | 73 | 79 | 86 | 92 | 99 | 105 |
Критические значения критерия F-Фишера
(Для ненаправленных альтернатив)
Р=0,05
|
| Степени свободы для числителя | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 24 | ? | ||
|
| 3 | 10,128 | 9,552 | 9,277 | 9,117 | 9,013 | 8,941 | 8,887 | 8,845 | 8,785 | 8,745 | 8,638 | 8,527 |
| 5 | 6,608 | 5,786 | 5,409 | 5,192 | 5,050 | 4,950 | 4,876 | 4,818 | 4,735 | 4,678 | 4,527 | 4,366 | |
| 7 | 5,591 | 4,737 | 4,347 | 4,120 | 3,972 | 3,866 | 3,787 | 3,726 | 3,637 | 3,575 | 3,410 | 3,231 | |
| 10 | 4,965 | 4,103 | 3,708 | 3,478 | 3,326 | 3,217 | 3,135 | 3,072 | 2,978 | 2,913 | 2,737 | 2,539 | |
| 11 | 4,844 | 3,982 | 3,587 | 3,357 | 3,204 | 3,095 | 3,012 | 2,948 | 2,854 | 2,788 | 2,609 | 2,406 | |
| 12 | 4,747 | 3,885 | 3,490 | 3,259 | 3,106 | 2,996 | 2,913 | 2,849 | 2,753 | 2,687 | 2,505 | 2,297 | |
| 13 | 4,667 | 3,806 | 3,411 | 3,179 | 3,025 | 2,915 | 2,832 | 2,767 | 2,671 | 2,604 | 2,420 | 2,208 | |
| 14 | 4,600 | 3,739 | 3,344 | 3,112 | 2,958 | 2,848 | 2,764 | 2,699 | 2,602 | 2,534 | 2,349 | 2,132 | |
| 15 | 4,543 | 3,682 | 3,287 | 3,056 | 2,901 | 2,790 | 2,707 | 2,641 | 2,544 | 2,475 | 2,288 | 2,067 | |
| 16 | 4,494 | 3,634 | 3,239 | 3,007 | 2,852 | 2,741 | 2,657 | 2,591 | 2,494 | 2,425 | 2,235 | 2,011 | |
| 18 | 4,414 | 3,555 | 3,160 | 2,928 | 2,773 | 2,661 | 2,577 | 2,510 | 2,412 | 2,342 | 2,150 | 1,918 | |
| 20 | 4,351 | 3,493 | 3,098 | 2,866 | 2,711 | 2,599 | 2,514 | 2,447 | 2,348 | 2,278 | 2,082 | 1,844 | |
| 30 | 4,171 | 3,316 | 2,922 | 2,690 | 2,534 | 2,421 | 2,334 | 2,266 | 2,165 | 2,092 | 1,887 | 1,624 | |
| 40 | 4,085 | 3,232 | 2,839 | 2,606 | 2,449 | 2,336 | 2,249 | 2,180 | 2,077 | 2,003 | 1,793 | 1,511 | |
| 50 | 4,034 | 3,183 | 2,790 | 2,557 | 2,400 | 2,286 | 2,199 | 2,130 | 2,026 | 1,952 | 1,737 | 1,440 | |
| 70 | 3,978 | 3,128 | 2,736 | 2,503 | 2,346 | 2,231 | 2,143 | 2,074 | 1,969 | 1,893 | 1,674 | 1,355 | |
| 100 | 3,936 | 3,087 | 2,696 | 2,463 | 2,305 | 2,191 | 2,103 | 2,032 | 1,927 | 1,850 | 1,627 | 1,286 | |
| 200 | 3,888 | 3,041 | 2,650 | 2,417 | 2,259 | 2,144 | 2,056 | 1,985 | 1,878 | 1,801 | 1,572 | 1,192 | |
| оо | 3,843 | 2,998 | 2,607 | 2,374 | 2,216 | 2,100 | 2,011 | 1,940 | 1,833 | 1,754 | 1,519 | ||
P> = 0,01
|
| Степени свободы для числителя | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 24 | ? | ||
|
| 3 | 34,116 | 30,816 | 29,457 | 28,710 | 28,237 | 27,911 | 27,671 | 27,489 | 27,228 | 27,052 | 26,597 | 26,126 |
| 5 | 16,258 | 13,274 | 12,060 | 11,392 | 10,967 | 10,672 | 10,456 | 10,289 | 10,051 | 9,888 | 9,466 | 9,022 | |
| 7 | 12,246 | 9,547 | 8,451 | 7,847 | 7,460 | 7,191 | 6,993 | 6,840 | 6,620 | 6,469 | 6,074 | 5,651 | |
| 10 | 10,044 | 7,559 | 6,552 | 5,994 | 5,636 | 5,386 | 5,200 | 5,057 | 4,849 | 4,706 | 4,327 | 3,910 | |
| 11 | 9,646 | 7,206 | 6,217 | 5,668 | 5,316 | 5,069 | 4,886 | 4,744 | 4,539 | 4,397 | 4,021 | 3,604 | |
| 12 | 9,330 | 6,927 | 5,953 | 5,412 | 5,064 | 4,821 | 4,640 | 4,499 | 4,296 | 4,155 | 3,780 | 3,362 | |
| 13 | 9,074 | 6,701 | 5,739 | 5,205 | 4,862 | 4,620 | 4,441 | 4,302 | 4,100 | 3,960 | 3,587 | 3,166 | |
| 14 | 8,862 | 6,515 | 5,564 | 5,035 | 4,695 | 4,456 | 4,278 | 4,140 | 3,939 | 3,800 | 3,427 | 3,005 | |
| 15 | 8,683 | 6,359 | 5,417 | 4,893 | 4,556 | 4,318 | 4,142 | 4,004 | 3,805 | 3,666 | 3,294 | 2,870 | |
| 16 | 8,531 | 6,226 | 5,292 | 4,773 | 4,437 | 4,202 | 4,026 | 3,890 | 3,691 | 3,553 | 3,181 | 2,754 | |
| 18 | 8,285 | 6,013 | 5,092 | 4,579 | 4,248 | 4,015 | 3,841 | 3,705 | 3,508 | 3,371 | 2,999 | 2,567 | |
| 20 | 8,096 | 5,849 | 4,938 | 4,431 | 4,103 | 3,871 | 3,699 | 3,564 | 3,368 | 3,231 | 2,859 | 2,422 | |
| 30 | 7,562 | 5,390 | 4,510 | 4,018 | 3,699 | 3,473 | 3,305 | 3,173 | 2,979 | 2,843 | 2,469 | 2,008 | |
| 40 | 7,314 | 5,178 | 4,313 | 3,828 | 3,514 | 3,291 | 3,124 | 2,993 | 2,801 | 2,665 | 2,288 | 1,806 | |
| 50 | 7,171 | 5,057 | 4,199 | 3,720 | 3,408 | 3,186 | 3,020 | 2,890 | 2,698 | 2,563 | 2,183 | 1,685 | |
| 70 | 7,011 | 4,922 | 4,074 | 3,600 | 3,291 | 3,071 | 2,906 | 2,777 | 2,585 | 2,450 | 2,067 | 1,542 | |
| 100 | 6,895 | 4,824 | 3,984 | 3,513 | 3,206 | 2,988 | 2,823 | 2,694 | 2,503 | 2,368 | 1,983 | 1,429 | |
| 200 | 6,763 | 4,713 | 3,881 | 3,414 | 3,110 | 2,893 | 2,730 | 2,601 | 2,411 | 2,275 | 1,886 | 1,281 | |
| оо | 6,637 | 4,607 | 3,784 | 3,321 | 3,019 | 2,804 | 2,641 | 2,513 | 2,323 | 2,187 | 1,793 | ||
Критические значения λα распределения Колмогорова: Р(λ > λα) = α
| λ | 0.20 | 0.10 | 0.05 | 0.02 | 0.01 | 0.001 |
|---|---|---|---|---|---|---|
| λα | 1.073 | 1.224 | 1.358 | 1.520 | 1.627 | 1.950 |
Критические значения критерия T-Вилкоксона
(для проверки ненаправленных альтернатив)
| n | Уровень значимости для
одностороннего критерия | n | Уровень значимости для
одностороннего критерия | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 0,05 | 0,025 | 0,01 | 0,005 | 0,05 | 0,025 | 0,01 | 0,005 | ||
| Уровень значимости для
двустороннего критерия | Уровень значимости для
двустороннего критерия | ||||||||
| 0,10 | 0,05 | 0,02 | 0,01 | 0,10 | 0,05 | 0,02 | 0,01 | ||
| 5 | 0 | 28 | 130 | 116 | 101 | 91 | |||
| 6 | 2 | 0 | — | — | 29 | 140 | 126 | ПО | 100 |
| 7 | 3 | 2 | 0 | — | 30 | 153 | 137 | 120 | 109 |
| 8 | 5 | 3 | 1 | 0 | 31 | 163 | 147 | 130 | 118 |
| 9 | 8 | 5 | 3 | 1 | 32 | 175 | 159 | 140 | 128 |
| 10 | 10 | 8 | 5 | 3 | 33 | 187 | 170 | 151 | 138 |
| 11 | 13 | 10 | 7 | 5 | 34 | 200 | 182 | 162 | 148 |
| 12 | 17 | 13 | 9 | 7 | 35 | 213 | 195 | 173 | 159 |
| 13 | 21 | 17 | 12 | 9 | 36 | 227 | 208 | 185 | 171 |
| 14 | 25 | 21 | 15 | 12 | 37 | 241 | 221 | 198 | 182 |
| 15 | 30 | 25 | 19 | 15 | 38 | 256 | 235 | 211 | 194 |
| 16 | 35 | 29 | 23 | 19 | 39 | 271 | 249 | 224 | 207 |
| 17 | 41 | 34 | 27 | 23 | 40 | 286 | 264 | 238 | 220 |
| 18 | 47 | 40 | 32 | 27 | 41 | 302 | 279 | 252 | 233 |
| 19 | 53 | 46 | 37 | 32 | 42 | 319 | 294 | 266 | 247 |
| 20 | 60 | 52 | 43 | 37 | 43 | 336 | 310 | 281 | 261 |
| 21 | 67 | 58 | 49 | 42 | 44 | 353 | 327 | 296 | 276 |
| 22 | 75 | 65 | 55 | 48 | 45 | 371 | 343 | 312 | 291 |
| 23 | 83 | 73 | 62 | 54 | 46 | 389 | 361 | 328 | 307 |
| 24 | 91 | 81 | 69 | 61 | 47 | 407 | 378 | 345 | 322 |
| 25 | 100 | 89 | 76 | 68 | 48 | 426 | 396 | 362 | 339 |
| 26 | ПО | 98 | 84 | 75 | 49 | 446 | 415 | 379 | 355 |
| 27 | 119 | 107 | 92 | 83 | 50 | 466 | 434 | 397 | 373 |
Источники:
- Наследов А.Д. Математические методы психологического исследования. Анализ и интерпретация данных. – СПб.:Речь, 2004.
- Сидоренко Е.В. Методы математической обработки в психологии. – СПб.:Речь, 2003.
- Мартин Д. Психологические эксперименты. - СПб.,2002.
