カイ二乗分布表
この記事では、カイ二乗分布表と、この表を正しく使用するための手順について説明します。
カイ二乗分布表の値
以下に、カイ二乗分布確率テーブルの最もよく使用される値を示します。行はカイ二乗分布の自由度を表し、列は表にまとめられたカイ二乗値以上の値が見つかる確率を表します (右端)。
GL | 0.001 | 0.005 | 0.01 | 0.025 | 0.05 | 0.10 | 0.25 | 0.50 | 0.75 | 0.90 | 0.95 | 0.975 | 0.99 | 0.995 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 10,828 | 7,879 | 6,635 | 5,024 | 3,841 | 2,706 | 1,323 | 0.455 | 0.102 | 0.016 | 0.004 | 0.001 | 0.000 | 0.000 |
2 | 13,816 | 10,597 | 9,210 | 7,378 | 5,991 | 4,605 | 2,773 | 1,386 | 0.575 | 0.211 | 0.103 | 0.051 | 0.020 | 0.010 |
3 | 16,266 | 12,838 | 11,345 | 9,348 | 7,815 | 6,251 | 4,108 | 2,366 | 1,213 | 0.584 | 0.352 | 0.216 | 0.115 | 0.072 |
4 | 18,467 | 14,860 | 13,277 | 11,143 | 9,488 | 7,779 | 5,385 | 3,357 | 1,923 | 1,064 | 0.711 | 0.484 | 0.297 | 0.207 |
5 | 20,515 | 16,750 | 15,086 | 12,833 | 11,070 | 9,236 | 6,626 | 4,351 | 2,675 | 1,610 | 1,145 | 0.831 | 0.554 | 0.412 |
6 | 22,458 | 18,548 | 16,812 | 14,449 | 12,592 | 10,645 | 7,841 | 5,348 | 3,455 | 2,204 | 1,635 | 1,237 | 0.872 | 0.676 |
7 | 24,322 | 20,278 | 18,475 | 16,013 | 14,067 | 12,017 | 9,037 | 6,346 | 4,255 | 2,833 | 2,167 | 1,690 | 1,239 | 0.989 |
8 | 26,124 | 21,955 | 20,090 | 17,535 | 15,507 | 13,362 | 10,219 | 7,344 | 5,071 | 3,490 | 2,733 | 2,180 | 1,646 | 1,344 |
9 | 27,877 | 23,589 | 21,666 | 19,023 | 16,919 | 14,684 | 11,389 | 8,343 | 5,899 | 4,168 | 3,325 | 2,700 | 2,088 | 1,735 |
十 | 29,588 | 25,188 | 23,209 | 20,483 | 18,307 | 15,987 | 12,549 | 9,342 | 6,737 | 4,865 | 3,940 | 3,247 | 2,558 | 2,156 |
十一 | 31,264 | 26,757 | 24,725 | 21,920 | 19,675 | 17,275 | 13,701 | 10,341 | 7,584 | 5,578 | 4,575 | 3,816 | 3,053 | 2,603 |
12 | 32,909 | 28,300 | 26,217 | 23,337 | 21,026 | 18,549 | 14,845 | 11,340 | 8,438 | 6,304 | 5,226 | 4,404 | 3,571 | 3,074 |
13 | 34,528 | 29,819 | 27,688 | 24,736 | 22,362 | 19,812 | 15,984 | 12,340 | 9,299 | 7,042 | 5,892 | 5,009 | 4,107 | 3,565 |
14 | 36,123 | 31,319 | 29,141 | 26,119 | 23,685 | 21,064 | 17,117 | 13,339 | 10,165 | 7,790 | 6,571 | 5,629 | 4,660 | 4,075 |
15 | 37,697 | 32,801 | 30,578 | 27,488 | 24,996 | 22,307 | 18,245 | 14,339 | 11,037 | 8,547 | 7,261 | 6,262 | 5,229 | 4,601 |
16 | 39,252 | 34,267 | 32,000 | 28,845 | 26,296 | 23,542 | 19,369 | 15,338 | 11,912 | 9,312 | 7,962 | 6,908 | 5,812 | 5,142 |
17 | 40,790 | 35,718 | 33,409 | 30,191 | 27,587 | 24,769 | 20,489 | 16,338 | 12,792 | 10,085 | 8,672 | 7,564 | 6,408 | 5,697 |
18 | 42,312 | 37,156 | 34,805 | 31,526 | 28,869 | 25,989 | 21,605 | 17,338 | 13,675 | 10,865 | 9,390 | 8,231 | 7,015 | 6,265 |
19 | 43,820 | 38,582 | 36,191 | 32,852 | 30,144 | 27,204 | 22,718 | 18,338 | 14,562 | 11,651 | 10,117 | 8,907 | 7,633 | 6,844 |
二十 | 45,315 | 39,997 | 37,566 | 34,170 | 31,410 | 28,412 | 23,828 | 19,337 | 15,452 | 12,443 | 10,851 | 9,591 | 8,260 | 7,434 |
21 | 46,797 | 41,401 | 38,932 | 35,479 | 32,671 | 29,615 | 24,935 | 20,337 | 16,344 | 13,240 | 11,591 | 10,283 | 8,897 | 8,034 |
22 | 48,268 | 42,796 | 40,289 | 36,781 | 33,924 | 30,813 | 26,039 | 21,337 | 17,240 | 14,041 | 12,338 | 10,982 | 9,542 | 8,643 |
23 | 49,728 | 44,181 | 41,638 | 38,076 | 35,172 | 32,007 | 27,141 | 22,337 | 18,137 | 14,848 | 13,091 | 11,689 | 10,196 | 9,260 |
24 | 51,179 | 45,559 | 42,980 | 39,364 | 36,415 | 33,196 | 28,241 | 23,337 | 19,037 | 15,659 | 13,848 | 12,401 | 10,856 | 9,886 |
25 | 52,620 | 46,928 | 44,314 | 40,646 | 37,652 | 34,382 | 29,339 | 24,337 | 19,939 | 16,473 | 14,611 | 13,120 | 11,524 | 10,520 |
26 | 54,052 | 48,290 | 45,642 | 41,923 | 38,885 | 35,563 | 30,435 | 25,336 | 20,843 | 17,292 | 15,379 | 13,844 | 12,198 | 11,160 |
27 | 55,476 | 49,645 | 46,963 | 43,195 | 40,113 | 36,741 | 31,528 | 26,336 | 21,749 | 18,114 | 16,151 | 14,573 | 12,879 | 11,808 |
28 | 56,892 | 50,993 | 48,278 | 44,461 | 41,337 | 37,916 | 32,620 | 27,336 | 22,657 | 18,939 | 16,928 | 15,308 | 13,565 | 12,461 |
29 | 58,301 | 52,336 | 49,588 | 45,722 | 42,557 | 39,087 | 33,711 | 28,336 | 23,567 | 19,768 | 17,708 | 16,047 | 14,256 | 13,121 |
30 | 59,703 | 53,672 | 50,892 | 46,979 | 43,773 | 40,256 | 34,800 | 29,336 | 24,478 | 20,599 | 18,493 | 16,791 | 14,953 | 13,787 |
35 | 66,619 | 60,275 | 57,342 | 53,203 | 49,802 | 46,059 | 40,223 | 34,336 | 29,054 | 24,797 | 22,465 | 20,569 | 18,509 | 17,192 |
40 | 73,402 | 66,766 | 63,691 | 59,342 | 55,758 | 51,805 | 45,616 | 39,335 | 33,660 | 29,051 | 26,509 | 24,433 | 22,164 | 20,707 |
四五 | 80,078 | 73,166 | 69,957 | 65,410 | 61,656 | 57,505 | 50,985 | 44,335 | 38,291 | 33,350 | 30,612 | 28,366 | 25,901 | 24,311 |
50 | 86,660 | 79,450 | 76,154 | 71,420 | 67,505 | 63,167 | 56,334 | 49,335 | 42,942 | 37,689 | 34,764 | 32,357 | 29,707 | 27,991 |
60 | 99,607 | 91,952 | 88,379 | 83,298 | 79,082 | 74,397 | 66,981 | 59,335 | 52,294 | 46,459 | 43,188 | 40,482 | 37,485 | 35,534 |
70 | 112,317 | 104 215 | 100 425 | 95,023 | 90,531 | 85,527 | 77,577 | 69,335 | 61,698 | 55,329 | 51,739 | 48,758 | 45,442 | 43,275 |
80 | 124,839 | 116,321 | 112,329 | 106,629 | 101,879 | 96,578 | 88 130 | 79,334 | 71,145 | 64,278 | 60,391 | 57,153 | 53,540 | 51,172 |
90 | 137 208 | 128,299 | 124 116 | 118 136 | 113 145 | 107,565 | 98,650 | 89,334 | 80,625 | 73,291 | 69,126 | 65,647 | 61,754 | 59,196 |
100 | 149,449 | 140 169 | 135,807 | 129,561 | 124,342 | 118,498 | 109 141 | 99,334 | 90 133 | 82,358 | 77,929 | 74,222 | 70,065 | 67,328 |
カイ二乗分布表の使い方
カイ二乗分布図を使用するには、次の 3 つの簡単な手順に従う必要があります。
- カイ二乗分布に対応する自由度の行をテーブルに入力します。
- 対応する確率列ごとにテーブルを挿入します。
- カイ二乗分布の値は、前の手順の行と列が交わる場所で見つかった値です。
たとえば、自由度が 4 で、これ以上の値が見つかる確率が 1% のカイ二乗分布の値は 13.277 です。これは、4 自由度の行と 1% の確率 (0.01) の列にある値であるためです。