Question

Montgomery gathered data on an experiment in paper production to determine the effects of
pulp cooking time (having two levels: 3 hours and 4 hours), 
vat pressure (having three levels:  400, 500, and 650), and
percent of hardwood concentration (having three levels: 2, 4, and 8) 
on the response variable: paper strength.

DO THE QUESTION IN SAS. PLEASE INCLUDE YOUR CODE TO GET THE ANSWER.

(a) Fit a three-way ANOVA, including ALL possible interaction terms.  
At a 5% significance level, is there a significant three-way interaction?
At a 5% significance level for each test, which of the two-way interactions are significant, if any?
(Give the test statistic values and P-values for the relevant tests.)

(b) Based on your answers to part (a), which of the three tests for MAIN effects is appropriate to examine here?
In other words, for which factor should we test about the main effects of that factor?  Explain.

DATA paper;
INPUT strength cooktime pressure concen;
cards;
196.6 3 400 2
196 3 400 2
198.5 3 400 4 
197.2 3 400 4
197.5 3 400 8
196.6 3 400 8
197.7 3 500 2 
196 3 500 2
196 3 500 4
196.9 3 500 4
195.6 3 500 8
196.2 3 500 8
199.8 3 650 2 
199.4 3 650 2
198.4 3 650 4
197.6 3 650 4
197.4 3 650 8
198.1 3 650 8
198.4 4 400 2
198.6 4 400 2
197.5 4 400 4
198.1 4 400 4
197.6 4 400 8
198.4 4 400 8
199.6 4 500 2
200.4 4 500 2
198.7 4 500 4
198 4 500 4
197 4 500 8
197.8 4 500 8
200.6 4 650 2
200.9 4 650 2
199.6 4 650 4
199 4 650 4
198.5 4 650 8
199.8 4 650 8
;
run;

Answer 1

Using SPSS:

Steps:

Analyze-->General Linear Model-->Univariate:

Then select the data and click ok:

Output:

(a):

At a 5% significance level, there is no significant three-way interaction.
Cooking_Time*Vat_Pressure*Concentration: F statistics = 1.350 and p-value = 0.290
At a 5% significance level for each test, the two-way interactions are significant is only Vat_Pressure*Concentration, F statistics = 4.166, p-value = 0.015.

(b):
The three tests for MAIN effects is appropriate to examine here is Vat_Pressure and Concentration.