A curve defining the distribution of values for chi-square. There is a chi-square curve for each number of degrees of freedom. The degrees of freedom of a chi-square curve is the number of terms in chi-square minus one.

The formula for a chi-square distribution curve is C x(n / 2 - 1) e(-x / 2), where n is the degrees of freedom and C is a constant equal to 1 over the integral of x(n / 2 - 1)e(-x / 2) from 0 to infinity.

Here is a table of some approximate C values for the above formula:

n    1    2    3    4    5    6    7    8     9    10
C 0.40 0.50 0.40 0.25 0.13 .063 .027 .010 .0038 .0013

Here is a table of integrals from the given P-values to infinity of chi-square curves between 1 and 20 degrees of freedom:

P=  .99     .95    .90   .70   .50   .30   .10   .05   .01
----------------------------------------------------------
 1 0.00016 0.0039 0.016 0.15  0.46  1.07  2.71  3.84  6.64
 2 0.020   0.10   0.21  0.71  1.39  2.41  4.60  5.99  9.21
 3 0.12    0.35   0.58  1.42  2.37  3.67  6.25  7.82 11.34
 4 0.30    0.71   1.06  1.61  3.36  4.88  7.78  9.49 13.28
 5 0.55    1.14   1.61  2.20  4.35  6.06  9.24 11.07 15.09
 6 0.87    1.64   2.20  3.00  5.35  7.23 10.65 12.59 16.81
 7 1.24    2.17   2.83  3.83  6.35  8.38 12.02 14.07 18.48
 8 1.65    2.73   3.49  4.67  7.34  9.52 13.36 15.51 20.09
 9 2.09    3.33   4.17  6.39  8.34 10.66 14.68 16.92 21.67
10 2.56    3.94   4.86  7.27  9.34 11.78 15.99 18.31 23.21
11 3.05    4.58   5.58  8.15 10.34 12.90 17.28 19.68 24.73
12 3.57    5.23   6.30  9.03 11.34 14.01 18.55 21.03 26.22
13 4.11    5.89   7.04  9.93 12.34 15.12 19.81 22.36 27.69
14 4.66    6.57   7.79 10.82 13.34 16.22 21.06 23.69 29.14
15 5.23    7.26   8.55 11.72 14.34 17.32 22.31 25.00 30.58
16 5.81    7.96   9.31 12.62 15.34 18.42 23.54 26.30 32.00
17 6.41    8.67  10.09 13.53 16.34 19.51 24.77 27.59 33.41
18 7.00    9.39  10.87 14.44 17.34 20.60 25.99 28.87 34.81
19 7.63   10.12  11.65 15.35 18.34 21.69 27.20 30.14 36.19
20 8.26   10.85  12.44 16.27 19.34 22.78 28.41 31.41 37.57

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