What exactly is a chi-square distribution

2-Distribution

The following table shows selected values ​​of the inverse distribution function of the 2-Distribution: 2(1- | df). For selected degrees of freedom (df) and probabilities (1-) the corresponding 2-Values ​​(2-Quantile), for which the following applies: W (X22| df) = (1-). (1-) corresponds to the red (dark) area in the following figure (i.e. the integral of the density function from 0 to 2). An exact calculation is possible with the statistical internet calculator.

Reading example: He is wanted 2-Value, below which 95% of all possible values ​​of one with df = 17 degrees of freedom 2-distributed random variables X2 lie. In the line for df = 17 you will find the value you are looking for in column (1 -) = 0.95 2=27,59.

df(red / dark) area (1-)
0,70,750,80,850,90,950,9750,990,995
11,071,321,642,072,713,845,026,637,88
22,412,773,223,794,615,997,389,2110,60
33,664,114,645,326,257,819,3511,3412,84
44,885,395,996,747,789,4911,1413,2814,86
56,066,637,298,129,2411,0712,8315,0916,75
67,237,848,569,4510,6412,5914,4516,8118,55
78,389,049,8010,7512,0214,0716,0118,4820,28
89,5210,2211,0312,0313,3615,5117,5320,0921,95
910,6611,3912,2413,2914,6816,9219,0221,6723,59
1011,7812,5513,4414,5315,9918,3120,4823,2125,19
1112,9013,7014,6315,7717,2819,6821,9224,7326,76
1214,0114,8515,8116,9918,5521,0323,3426,2228,30
1315,1215,9816,9818,2019,8122,3624,7427,6929,82
1416,2217,1218,1519,4121,0623,6826,1229,1431,32
1517,3218,2519,3120,6022,3125,0027,4930,5832,80
1618,4219,3720,4721,7923,5426,3028,8532,0034,27
1719,5120,4921,6122,9824,7727,5930,1933,4135,72
1820,6021,6022,7624,1625,9928,8731,5334,8137,16
1921,6922,7223,9025,3327,2030,1432,8536,1938,58
2022,7723,8325,0426,5028,4131,4134,1737,5740,00
2123,8624,9326,1727,6629,6232,6735,4838,9341,40
2224,9426,0427,3028,8230,8133,9236,7840,2942,80
2326,0227,1428,4329,9832,0135,1738,0841,6444,18
2427,1028,2429,5531,1333,2036,4239,3642,9845,56
2528,1729,3430,6832,2834,3837,6540,6544,3146,93
3033,5334,8036,2537,9940,2643,7746,9850,8953,67
4044,1645,6247,2749,2451,8155,7659,3463,6966,77
5054,7256,3358,1660,3563,1767,5071,4276,1579,49
6065,2366,9868,9771,3474,4079,0883,3088,3891,95
7075,6977,5879,7182,2685,5390,5395,02100,43104,21
8086,1288,1390,4193,1196,58101,88106,63112,33116,32
9096,5298,65101,05103,90107,57113,15118,14124,12128,30
100106,91109,14111,67114,66118,50124,34129,56135,81140,17
150158,58161,29164,35167,96172,58179,58185,80193,21198,36
200209,99213,10216,61220,74226,02233,99241,06249,45255,26
500516,09520,95526,40532,80540,93553,13563,85576,49585,21