Question

A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data.

		Factor B
		Level 1	Level 2	Level 3
Factor A	Level 1	137	88	75
		167	64	93
	Level 2	123	129	120
		93	107	136

a) Test for any significant main effects and any interaction. Use α = 0.05.

Find the value of the test statistic for factor A. (Round your answer to two decimal places.)

Find the p-value for factor A. (Round your answer to three decimal places.)

p-value =

b) Find the value of the test statistic for factor B. (Round your answer to two decimal places.)

Find the p-value for factor B. (Round your answer to three decimal places.)

p-value =

c) Find the value of the test statistic for the interaction between factors A and B. (Round your answer to two decimal places.)

Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)

p-value =

Answer 1

from excel: data-data analysis: 2 way ANOVA with replication

Source	SS	df	MS	F	p value
factor A	588.00	1	588.00	2.05	0.2021
factor B	2328.00	2	1164.00	4.06	0.0767
interaction	5048.00	2	2524.00	8.80	0.0164
error	1720.00	6	286.67
total	9684.00	11

a) value of the test statistic for factor A =2.05
p-value =0.202
Because the p-value ≥ α = 0.05, factor A is not significant.
b) value of the test statistic for factor B =4.06
p-value =0.077
Because the p-value ≥ α = 0.05, factor B is not significant.
value of the test statistic for interaction =8.8
p-value = 0.016
Because the p-value < α = 0.05, interaction is significant.