Question

solve number 3 only

3. The following sample data stem from two-factor factorial study. a) b) c) Give the ANOVA model for the study. Prepare an estimated treatment means plot. Does it appear that the factors interact? Set up the ANOVA table, and carry out all appropriate tests for factor effects. In each case state the null and alternative hypotheses, the decision rule and the conclusion. Use a=.01. Factor B 1 Factor A 1 2 ,6,5 10.12.11 12,13,117.7.8 4 EEEY 7038 Use SAS to help answer the following questions You will be using PRO GIM for this question is it allows you to find is for general contrasts PROCANOVA only dos pais comparisons 4 American americana 0 e . 9 # ** + > ? É pause mouse

Answer 1

solution:

Given data:

3.

a)

The ANOVA model is:

Data = 8.833 - 0.333 Factor A_1 + 0.333 Factor A_2 - 0.833 Factor B_1 + 0.833 Factor B_2

b)

The plots are:

Interaction Plot by Factor 1 Cell Mean Factor A2 Factor A 1 o-Factor B1 * Factor B 2

Interaction Plot by Factor 2 Cell Mean Factor B 2 Factor B 1 -Factor A1 * Factor A 2

Yes, the factors interact.

c)

The ANOVA table is:

Source	SS	df	MS	F	p-value
Factor 1	1.33	1	1.333	1.60	.2415
Factor 2	8.33	1	8.333	10.00	.0133
Interaction	85.33	1	85.333	102.40	7.77E-06
Error	6.67	8	0.833
Total	101.67	11

The hypothesis being tested is:

H₀: There is no main effect of Factor A

H_a: There is a main effect of Factor A

The p-value is 0.2415.

Since the p-value (0.2415) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a main effect of Factor A.

The hypothesis being tested is:

H₀: There is no main effect of Factor B

H_a: There is a main effect of Factor B

The p-value is 0.0133.

Since the p-value (0.0133) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a main effect of Factor B.

The hypothesis being tested is:

H₀: There is no interaction effect

H_a: There is an interaction effect

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction effect.

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