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 sum of squares and degree of freedom calculation from the previous videos are put into a ratio to calculate the F Value, on whose basis the null hypothesis is confirmed or rejected. If variance is higher between samples than within the null hypothesis is more likely to be rejected. The results of a numerical example are interpreted more abstractly and then tested with regards to a confidence interval and the corresponding F table.
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 total sum of squares and the total degrees of freedoms are disaggregated by calculating in sample variance and "between" sample variance and their respective degrees of freedoms. It is demonstrated numerically that both these measures add up to the total sum of squares and the total degrees of freedom.