Chi Square Distribution

The chi-square statistic can be calculated from a sample of size $n$ drawn from a population, which is normal, using the following equation.

$$\chi^2 = \frac{(n - 1)s^2}{\sigma^2}$$

When sampling is done for an infinite number of times, and by calculating the chi-square statistic for each sample, the sampling distribution for the chi-square statistic can be obtained. It is then called the chi-square distribution.

Properties

Mean

The mean is $\mu = \nu$.

Variance

The variance is $\sigma^2 = 2\nu$.

Degrees of Freedom

The degrees of freedom is $\nu = n - 1$.

As $\nu$ increases, the chi-square distribution approaches a normal distribution.