The definition of a chi-square distribution is given. Chi-square is defined as the sum of random normally distributed variables (mean=0, variance=s.d.=1). The number of added squared variables is equal to the degrees of freedom. With more degrees of freedom the probability of larger chi-square values is increased.

The chi-square distribution is used to test a hypothesis. Therefore, expected values are related to observed values using a chi-square distribution. Then using p-value tables the hypothesis is tested at a 5% significance level.