Question

3. (20 points) A partially completed ANOVA table for a two-factor factorial experiment is shown here: Source df SS 3 1 0.95 MS F 0.75 0.30 AB Error Total 23 6.5 a Give the number of levels for each factor. b How many observations were collected for each factor-level combination? c Complete the ANOVA table above. d Test to determine whether the treatment means differ using a = 0.10?

Answer 1

a) number of levels of factor A =df(A)+1 =3+1 =4

number of levels of factor B =df(B)+1 =1+1 =2

b)

number of observation for each combination =(total df+1)/(level of factor A*level of factor B) =24/(4*2)=3

c)

Source	df	SS	MS	F
A	3	2.25	0.75	5.00
B	1	0.95	0.95	6.33
A*B	3	0.9	0.30	2.00
error	16	2.4	0.15
total	23	6.5

d)

for 0.1 level and (3,16) df , crtiical value =2.46

since test statistic F=5 is higher than critical value, factor A is significant

for 0.1 level and (1,16) df , crtiical value =3.05

since test statistic F=6.33 is higher than critical value, factor B is significant

for 0.1 level and (3,16) df , crtiical value =2.46

since test statistic F=2 is not higher than critical value, interaction is not significant