ANOVA Table Please show all work Given the partially filled

ANOVA Table, Please show all work

Given the partially filled ANOVA table below please determine the following: Fill out the rest of the ANOVA table. Test which factors are significant at an alpha level of .05

Solution

The Complete ANOVA table is wriiten down here.

Now , MS(B) = SS(B) / DF(B)

DF(B)= SS(B) / MS(B)

=> DF(B) = 4 .

## DF(error) = SS(error)/MS(error) = 30 .

## We know , DF(A) +DF(B)+DF(INTERACTION)+DF(ERROR)=DF(TOTAL)

=> 2 + 4 + DF(IN..) + 30 = 44

=> DF(Interaction) = 8.

## MS(Interaction) = SS(interaction)/DF(interaction) = 7000/8 = 875 .

## F(A) = MS(A)/MS(error) = 30

MS(A) = MS(error)*30 = 30*33.33333 = 1000 .

## SS(A) = MS(A)*DF(A) = 2000

## F(INteraction)=MS(interaction)/MS(error) = 875/33.33333=26.25

## F(B) = MS(B)/MS(error)= 1250/33.3333= 37.5

TOTAL(SS)= SS(A)+SS(B)+SS(INTERACTION)+SS(ERROR) = 2000+5000+7000+1000 = 15000 .

B. Now at level 0.05 ,

A factor is significant iff p-value(of the factor) < 0.05

## Now, p-value(Interaction) = 0.000 < 0.05

Hence Interaction effect is significant.

## P-value(B) = 0.000

## P-value(A) = 0.000

Hence all the factors are significant at 0.05 level .

Where p-value(factor) is defined as , P(F_{DF(factor) , DF(error)} > F(factor)) , F_{DF(factor) , DF(error)} is the F-distribution with degrees of freedom DF(factor) ,DF(Error) .

Souece	SS	DF	MS	F
Factor A	2000	2	1000	30
Factor B	5000	4	1250	37.5
Interaction	7000	8	875	26.25
Error	1000	30	33.3333
Total	15000	44