Kritischen Wert der Chi-Quadrat-Verteilung
Ihr habt zwei Möglichkeiten, an den kritischen Wert der Chi-Quadrat-Verteilung zu kommen. Zunächst mit einer direkten Berechnung oder klassisch über das Nutzen der Chi-Quadrat-Tabelle.
Direkte Berechnung
1) Ihr könnt folgendes Google Sheet verwenden und eure Freiheitsgrade und das Alpha eintragen. Der kritische Chi-Quadrat-Wert wird dann umgehend im grünen Kästchen berechnet.
Chi-Quadrat-Tabelle
2) Die nachfolgende Tabelle zeigt die kritischen Werte der Chi-Quadrat-Verteilung.
Anmerkung: In den Zeilen stehen die Freiheitsgrade (degrees of freedom – df) und in den Spalten steht das jeweilige Signifikanzniveau.
Signifikanzniveau (α) | ||||||||
---|---|---|---|---|---|---|---|---|
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
1 | 1,642 | 2,072 | 2,706 | 3,841 | 5,024 | 6,635 | 7,879 | 10,828 |
2 | 3,219 | 3,794 | 4,605 | 5,991 | 7,378 | 9,210 | 10,597 | 13,816 |
3 | 4,642 | 5,317 | 6,251 | 7,815 | 9,348 | 11,345 | 12,838 | 16,266 |
4 | 5,989 | 6,745 | 7,779 | 9,488 | 11,143 | 13,277 | 14,860 | 18,467 |
5 | 7,289 | 8,115 | 9,236 | 11,070 | 12,833 | 15,086 | 16,750 | 20,515 |
6 | 8,558 | 9,446 | 10,645 | 12,592 | 14,449 | 16,812 | 18,548 | 22,458 |
7 | 9,803 | 10,748 | 12,017 | 14,067 | 16,013 | 18,475 | 20,278 | 24,322 |
8 | 11,030 | 12,027 | 13,362 | 15,507 | 17,535 | 20,090 | 21,955 | 26,124 |
9 | 12,242 | 13,288 | 14,684 | 16,919 | 19,023 | 21,666 | 23,589 | 27,877 |
10 | 13,442 | 14,534 | 15,987 | 18,307 | 20,483 | 23,209 | 25,188 | 29,588 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
11 | 14,631 | 15,767 | 17,275 | 19,675 | 21,920 | 24,725 | 26,757 | 31,264 |
12 | 15,812 | 16,989 | 18,549 | 21,026 | 23,337 | 26,217 | 28,300 | 32,909 |
13 | 16,985 | 18,202 | 19,812 | 22,362 | 24,736 | 27,688 | 29,819 | 34,528 |
14 | 18,151 | 19,406 | 21,064 | 23,685 | 26,119 | 29,141 | 31,319 | 36,123 |
15 | 19,311 | 20,603 | 22,307 | 24,996 | 27,488 | 30,578 | 32,801 | 37,697 |
16 | 20,465 | 21,793 | 23,542 | 26,296 | 28,845 | 32,000 | 34,267 | 39,252 |
17 | 21,615 | 22,977 | 24,769 | 27,587 | 30,191 | 33,409 | 35,718 | 40,790 |
18 | 22,760 | 24,155 | 25,989 | 28,869 | 31,526 | 34,805 | 37,156 | 42,312 |
19 | 23,900 | 25,329 | 27,204 | 30,144 | 32,852 | 36,191 | 38,582 | 43,820 |
20 | 25,038 | 26,498 | 28,412 | 31,410 | 34,170 | 37,566 | 39,997 | 45,315 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
21 | 26,171 | 27,662 | 29,615 | 32,671 | 35,479 | 38,932 | 41,401 | 46,797 |
22 | 27,301 | 28,822 | 30,813 | 33,924 | 36,781 | 40,289 | 42,796 | 48,268 |
23 | 28,429 | 29,979 | 32,007 | 35,172 | 38,076 | 41,638 | 44,181 | 49,728 |
24 | 29,553 | 31,132 | 33,196 | 36,415 | 39,364 | 42,980 | 45,559 | 51,179 |
25 | 30,675 | 32,282 | 34,382 | 37,652 | 40,646 | 44,314 | 46,928 | 52,620 |
26 | 31,795 | 33,429 | 35,563 | 38,885 | 41,923 | 45,642 | 48,290 | 54,052 |
27 | 32,912 | 34,574 | 36,741 | 40,113 | 43,195 | 46,963 | 49,645 | 55,476 |
28 | 34,027 | 35,715 | 37,916 | 41,337 | 44,461 | 48,278 | 50,993 | 56,892 |
29 | 35,139 | 36,854 | 39,087 | 42,557 | 45,722 | 49,588 | 52,336 | 58,301 |
30 | 36,250 | 37,990 | 40,256 | 43,773 | 46,979 | 50,892 | 53,672 | 59,703 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
31 | 37,359 | 39,124 | 41,422 | 44,985 | 48,232 | 52,191 | 55,003 | 61,098 |
32 | 38,466 | 40,256 | 42,585 | 46,194 | 49,480 | 53,486 | 56,328 | 62,487 |
33 | 39,572 | 41,386 | 43,745 | 47,400 | 50,725 | 54,776 | 57,648 | 63,870 |
34 | 40,676 | 42,514 | 44,903 | 48,602 | 51,966 | 56,061 | 58,964 | 65,247 |
35 | 41,778 | 43,640 | 46,059 | 49,802 | 53,203 | 57,342 | 60,275 | 66,619 |
36 | 42,879 | 44,764 | 47,212 | 50,998 | 54,437 | 58,619 | 61,581 | 67,985 |
37 | 43,978 | 45,886 | 48,363 | 52,192 | 55,668 | 59,893 | 62,883 | 69,346 |
38 | 45,076 | 47,007 | 49,513 | 53,384 | 56,896 | 61,162 | 64,181 | 70,703 |
39 | 46,173 | 48,126 | 50,660 | 54,572 | 58,120 | 62,428 | 65,476 | 72,055 |
40 | 47,269 | 49,244 | 51,805 | 55,758 | 59,342 | 63,691 | 66,766 | 73,402 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
41 | 48,363 | 50,360 | 52,949 | 56,942 | 60,561 | 64,950 | 68,053 | 74,745 |
42 | 49,456 | 51,475 | 54,090 | 58,124 | 61,777 | 66,206 | 69,336 | 76,084 |
43 | 50,548 | 52,588 | 55,230 | 59,304 | 62,990 | 67,459 | 70,616 | 77,419 |
44 | 51,639 | 53,700 | 56,369 | 60,481 | 64,201 | 68,710 | 71,893 | 78,750 |
45 | 52,729 | 54,810 | 57,505 | 61,656 | 65,410 | 69,957 | 73,166 | 80,077 |
46 | 53,818 | 55,920 | 58,641 | 62,830 | 66,617 | 71,201 | 74,437 | 81,400 |
47 | 54,906 | 57,028 | 59,774 | 64,001 | 67,821 | 72,443 | 75,704 | 82,720 |
48 | 55,993 | 58,135 | 60,907 | 65,171 | 69,023 | 73,683 | 76,969 | 84,037 |
49 | 57,079 | 59,241 | 62,038 | 66,339 | 70,222 | 74,919 | 78,231 | 85,351 |
50 | 58,164 | 60,346 | 63,167 | 67,505 | 71,420 | 76,154 | 79,490 | 86,661 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
60 | 68,972 | 71,341 | 74,397 | 79,082 | 83,298 | 88,379 | 91,952 | 99,607 |
70 | 79,715 | 82,255 | 85,527 | 90,531 | 95,023 | 100,425 | 104,215 | 112,317 |
80 | 90,405 | 93,106 | 96,578 | 101,879 | 106,629 | 112,329 | 116,321 | 124,839 |
90 | 101,054 | 103,904 | 107,565 | 113,145 | 118,136 | 124,116 | 128,299 | 137,208 |
100 | 111,667 | 114,659 | 118,498 | 124,342 | 129,561 | 135,807 | 140,169 | 149,449 |
110 | 122,250 | 125,376 | 129,385 | 135,480 | 140,917 | 147,414 | 151,948 | 161,581 |
120 | 132,806 | 136,062 | 140,233 | 146,567 | 152,211 | 158,950 | 163,648 | 173,617 |
130 | 143,340 | 146,719 | 151,045 | 157,610 | 163,453 | 170,423 | 175,278 | 185,571 |
140 | 153,854 | 157,352 | 161,827 | 168,613 | 174,648 | 181,840 | 186,847 | 197,451 |
150 | 164,349 | 167,962 | 172,581 | 179,581 | 185,800 | 193,208 | 198,360 | 209,265 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
160 | 174,828 | 178,552 | 183,311 | 190,516 | 196,915 | 204,530 | 209,824 | 221,019 |
170 | 185,293 | 189,123 | 194,017 | 201,423 | 207,995 | 215,812 | 221,242 | 232,719 |
180 | 195,743 | 199,679 | 204,704 | 212,304 | 219,044 | 227,056 | 232,620 | 244,370 |
190 | 206,182 | 210,218 | 215,371 | 223,160 | 230,064 | 238,266 | 243,959 | 255,976 |
200 | 216,609 | 220,744 | 226,021 | 233,994 | 241,058 | 249,445 | 255,264 | 267,541 |
250 | 268,599 | 273,194 | 279,050 | 287,882 | 295,689 | 304,940 | 311,346 | 324,832 |
300 | 320,397 | 325,409 | 331,789 | 341,395 | 349,874 | 359,906 | 366,844 | 381,425 |
350 | 372,051 | 377,445 | 384,306 | 394,626 | 403,723 | 414,474 | 421,900 | 437,488 |
400 | 423,590 | 429,340 | 436,649 | 447,632 | 457,305 | 468,724 | 476,606 | 493,132 |
450 | 475,035 | 481,120 | 488,849 | 500,456 | 510,670 | 522,717 | 531,026 | 548,432 |
Signifikanzniveau (α) | ||||||||
Freiheits- grade (df) | 0,2 | 0,15 | 0,1 | 0,05 | 0,025 | 0,01 | 0,005 | 0,001 |
500 | 526,401 | 532,803 | 540,930 | 553,127 | 563,852 | 576,493 | 585,207 | 603,446 |
600 | 628,943 | 635,933 | 644,800 | 658,094 | 669,769 | 683,516 | 692,982 | 712,771 |
700 | 731,280 | 738,811 | 748,359 | 762,661 | 775,211 | 789,974 | 800,131 | 821,347 |
800 | 833,456 | 841,490 | 851,671 | 866,911 | 880,275 | 895,984 | 906,786 | 929,329 |
900 | 935,499 | 944,006 | 954,782 | 970,904 | 985,032 | 1001,630 | 1013,036 | 1036,826 |
1000 | 1037,431 | 1046,385 | 1057,724 | 1074,679 | 1089,531 | 1106,969 | 1118,948 | 1143,917 |
5000 | 5083,962 | 5103,686 | 5128,576 | 5165,615 | 5197,884 | 5235,572 | 5261,338 | 5314,731 |
10000 | 10118,82 | 10146,62 | 10181,66 | 10233,75 | 10279,07 | 10331,93 | 10368,03 | 10442,73 |