Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Analysis of Variance – ANOVA 423

Source

of Vari-

ation

SS df MS E(MS)

Cells SS

Cells

ab − 1 MS

Cells

σ

2

+ n

P

i

P

j

(µ

ij.

−µ

...

)

2

ab−1

A fac tors SS

A

a − 1 M S

A

σ

2

+ nb

P

i

(µ

i..

−µ

...

)

2

a−1

B factors SS

B

b − 1 MS

B

σ

2

+ na

P

j

(µ

.j.

−µ

...

)

2

b−1

A × B SS

A×B

(a − 1)(b − 1) M S

A×B

σ

2

+ n

P

i

P

j

(αβ)

2

ij

(a−1)(b−1)

Erro r SS

Error

ab(n − 1) M S

A×B

σ

2

Total SS

T otal

abn − 1

TABLE 13.1: The main quantities involved in a factorial design ANOVA:

sums of squares, degrees of freedom and mean squa res. The table also shows

the e xpected va lue s for each mean square MS.

13.3.6 Reference formulae for fact orial design ANOVA

The various sums of squares involved can be calculated as follows:

SS

T otal

=

X

i

X

j

X

k



X