Question

Please show your work

The following table summarizes the results of a two-factor ANOVA evaluating an independent- measures experiment with two levels of factor A three levels of factor B, and n= 5 subjects in each separate sample. a. Fill in all missing values in the table. (Hint: Start with the df column.) Source SS df MS Between Treatments 60 Fbtw = Factor A FA= 5 Factor B FB= Ах В 30 FAB= I Within Treatments Total

Answer 1

Level of Factor A, a = 2

Level of Factor B, b = 3

Number of repetition, r = 5

df(A) = a-1 = 1

df(B) = b-1 = 2

df(AB) = (a-1)*(b-1) = 2

df(error) = ab(r-1) = 24

df(total) = abr-1 = 29

df(Between) = 1+2+2 = 5

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SS(Within) = df(within) *MS(within) = 24*2 = 48

SS(Total) = 60+48 = 108

MSA = 5*2 = 10

SSA = 10*1 = 10

SSB = 60-30-10 = 20

MSB = 20/2 = 10

MSAxB = 30/2 = 15

F for Factor B = MSB/MS(within) = 10/2 = 5

F for interaction = MSAxB/MS(within) = 15/2 = 7.5

ANOVA
Source of Variation	SS	df	MS	F
Between Treatments	60	5
Factor A	10	1	10	5
Factor B	20	2	10	5
A x B	30	2	15	7.5
Within Treatments	48	24	2
Total	108	29