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 = 272, SSA = 25, SSB = 24, SSAB = 165. Set up the ANOVA table and test for significance using  = .05. Show entries to 2 decimals, if necessary. Round p-value to four decimal places. If your 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 The p-value for Factor A is Select: less than .01, between .01 and .02, between .02 and .05, between .05 and .10, greater than .10 What is your conclusion with respect to Factor A? Select: Factor A is significant, Factor A is not significant The p-value for Factor B is Select; less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10 What is your conclusion with respect to Factor B? Select; Factor B is significant, Factor B is not significant The p-value for the interaction of factors A and B is Select; less than .0, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10 What is your conclusion with respect to the interaction of Factors A and B? Select; The interaction of factors A and B is significant, The interaction of factors A and B is not significant

Answer 1

a.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A	25	3	8.33	3.44	0.0327
Factor B	24	2	12	4.95	0.0159
Interaction	165	6	27.5	11.36	0
Error	58	24	2.42
Total	272	35

SS Error - SS Total - (SSA + SSB + SSAB) = 272 - (25 + 24 + 165) = 58

Given a = 4, b = 3, r = 3

DFA = a - 1 = 4 - 1 = 3

DFB = b - 1 = 3 - 1 = 2

DFAB = (a-1) * (b-1) = 3 * 2 = 6

DF Error = ab(r - 1) = 4 * 3 * (3 - 1) = 24

F = MS / MS for Error

DFT = abr-1 = 4 * 3 * 3 - 1 = 35

Mean Square = Sum of Squares / DF

P-value for A for df = 3, 24 is 0.0327

P-value for B for df = 2, 24 is 0.0159

P-value for A for df = 6, 24 is 0

b.

The p-value for Factor A is between .02 and .05

Since p-value is less than 0.05, Factor A is significant

c.

The p-value for Factor B is between .01 and .025

Since p-value is less than 0.05, Factor B is significant

d.

The p-value for the interaction of factors A and B is less than .01

Since p-value is less than 0.05, The interaction of factors A and B is significant.