Question

The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.

Click here for the Excel Data File

					Factor A
Factor B				1				2				3				4				X¯¯¯jX¯j for Factor B
	1				3				4				3				5				3.750
	2				8				10				9				8				8.750
	3				12				16				14				13				13.750
X−iX−i for Factor A				7.667					10.000				8.667			8.667				X¯¯¯¯¯¯¯ = 8.7500X¯¯⁢ = 8.7500

a. Calculate SST, SSA, SSB, and SSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

b. Calculate MSA, MSB, and MSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

c. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS" to 2 decimal places, "F" 3 decimal places.)

d. At the 1% significance level, do the levels of Factor B differ?

• Yes, since we reject the null hypothesis.

• No , since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

e. At the 1% significance level, do the levels of Factor A differ?

• Yes, since we reject the null hypothesis.

• No, since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

Answer 1

Applying 2 way ANOVA(without replication):

Source of Variation	SS	df	MS	F	P-value
B	200	2	100	100	0.0000
A	8.25	3	2.75	2.75	0.1348
Error	6	6	1
Total	214.25	11

a)

SST =214.25

SSA=8.25

, SSB=200,

and SSE=6

b)

MSA=2.75

, MSB=100

, and MSE=1

c)

Source of Variation	SS	df	MS	F
A	8.25	3	2.75	2.750
B	200.00	2	100.00	100.000
Error	6.00	6	1.00
Total	214.25	11

d)

Yes, since we reject the null hypothesis.

e)

No, since we do not reject the null hypothesis.