Question

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST= 248, SSA= 22, SSB= 21, SSAB= 155.

Set up the ANOVA table and test for significance using alpha= .05 . Show entries to 2 decimals, if necessary. If the answer is zero enter “0”.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A
Factor B
Interaction
Error
Total

Answer 1

Level of factor A, a = 4

Level of factor B,b = 3

Replications, r = 3

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A	22	a-1 = 3	22/3 = 7.3333	7.333/2.0833 = 3.52	F.DIST.RT(3.52, 3, 24) = 0.0303
Factor B	21	b-1 = 2	21/2 = 10.5	10.5/2.0833 = 5.04	F.DIST.RT(5.04, 2, 24) = 0.0149
Interaction	155	(a-1)*(b-1) = 6	155/6 = 25.8333	25.8333/2.0833 = 12.4	F.DIST.RT(12.4, 6, 24) = 0.0000
Error	248 -22-21-155 = 50	ab(r-1) = 24	50/24 = 2.0833
Total	248	abr -1 = 35