
Chapter 12
468
Formulas for calculating SST (total sum of squares) and mean squares in a factorial design (two-way analysis of
variance)
SSC (sum of squares between columns) = nr
j
j
c
−
=
∑
2
1
where c is the number of column treatments, r the number of row treatments, n the number of observations in each cell, x
j
the sample mean of group j, and x the grand mean.
and MSC (mean square) =
SSC
c
where SSC is the sum of squares between columns and c – 1 the degrees of freedom (number of columns –1).
SSR (sum of squares between rows) = nc xx
i
i
r
\−
=
∑
2
1
where c is the number of column treatments, r the number of row treatments, n the number of observations ...