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