S.V

d.f

SS

MS

Expected mean square

f-ratio

A

2

144.9638

72.4819

$\frac{{\displaystyle \sum _i^a{N}_i{A}_i^2}}{a-1}+7.7153{\sigma }_{AC}^2+1.2531{\sigma }_{ABC}^2+{\sigma }_e^2$

0.7373

B

2

101.0706

50.5353

$\frac{{\displaystyle \sum _j^b{N}_j{B}_j^2}}{b-1}+6.8274{\sigma }_{BC}^2+1.2531{\sigma }_{ABC}^2+{\sigma }_e^2$

0.9649

C

3

201.1734

67.0578

$26.963{\sigma }_C^2+1.7325{\sigma }_{AC}^2+2.2840{\sigma }_{BC}^2+0.8354{\sigma }_{ABC}^2+{\sigma }_e^2$

1.4645

AB

4

213.6512

53.4128

$\frac{{\displaystyle \sum _{ij}^{ab}{n}_{ij.}E{\left(AB\right)}_{ij}^2}}{\left(a-1\right)\left(b-1\right)}+8.6482{\sigma }_{ABC}^2+{\sigma }_e^2$

0.2757

AC

6

152.5572

86.2273

$11.2040{\sigma }_{AC}^2+0.4177{\sigma }_{ABC}^2+{\sigma }_e^2$

1

BC

6

517.3638

25.3261

$0.4177{\sigma }_{BC}^2+67.3453{\sigma }_{ABC}^2+{\sigma }_e^2$

1

ABC

12

2324.8692

193.7391

$4.8323{\sigma }_{ABC}^2+{\sigma }_e^2$

99.4911

Error

54

87.6285

1.9473

${\sigma }_e^2$

Total

80