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

 

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