A First Course in Quality Engineering, 2nd Edition

352 A First Course in Quality Engineering

We can write:

SS (Total) = SS (Factor A) + SS (Factor B) + SS (AB interaction) + SS (Error)�

Using abbreviations, the equation can be rewritten as:

SS

T

= SS

A

+ SS

B

+ SS

AB

+ SS

E

Each of the sums of squares in the above equation has associated with

it a certain number of degrees of freedom (df) equal to the number of inde-

pendent squared terms that are summed to produce the sum of squares�

Take, for example,

SS

E

= ∑ ∑ ∑ −

( )

= = =i

a

j

b

k

n

ijk ij

y y

1 1 1

2

.

� Although abn number of

squared terms go into this sum of squares, there are only ab(n − 1) indepen-

dent terms in this sum� In each cell, even