First the global mean is calculated from a matrix of three sets each containing three observations. Then the sum of squares is calculated. Lastly, the concept of degree of freedom is explained.

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.