Question

An experiment was conducted as a one-way factorial design with K sample means, each based on n scores. What is the number of degrees of freedom for the between mean squares

Answer 1

The mean squares has d.f (n-1)

Explanation:

The total number of degrees of freedom is n-1 as there is only one restriction of computing the grand mean. The d.f for k samples is k-1 beacuase the mean of the sample means must equal the grand mean. Similarly , the d.f for within SS is n-k , due to the k restrictions of computing the k sample means. Hence we find that

Total df= Within df + Between df

n-1= (n-k)+(k-1)

Between SS has (k-1) d.f

Within SS has (n-k) d.f

These two quantities are known as mean squares and has d.f (n-1)