Question

"Using data set 11-6; how many of the three factor interactions are stronger than the single factor ""B"""

11-6:

	Parameter				Reaction rate
	A	B	C	D	g/min
-1	-	-	-	-	46.9
a	+	-	-	-	71.1
b	-	+	-	-	49.9
c	-	-	+	-	70.4
d	-	-	-	+	44
ab	+	+	-	-	65.3
ac	+	-	+	-	62.4
ad	+	-	-	+	101.5
bc	-	+	+	-	81.8
bd	-	+	-	+	45.9
cd	-	-	+	+	76.4
abc	+	+	+	-	66.9
abd	+	+	-	+	105.8
acd	+	-	+	+	86.1
bcd	-	+	+	+	70.6
abcd	+	+	+	+	98.4

Answer 1

Solution:

By using minitab, (path is)

Go to Stat---DOE---Factorial---Create factorial design---select two level factorial (default generators)---no of factors=4---design=full factorial---option= uncheck randomized runs---click ok--make a responce column (y) and put the values of reaction rate on proper place.

you will get factorial design with 4 factors A,B,C and D

For analysis-

Go to Stat---DOE---Factorial---Analyze factorial design---select responce as y---graphs---tick in checkbox of pareto and normal---click ok.

ypu will get ANOVA and graph of all factor effects. From the pareto chart-

Only the three factor interaction ABD is stronger than single factor B.

ANOVA:-

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Model 15 5771.26 384.75 * *
Linear 4 3120.69 780.17 * *
A 1 1840.41 1840.41 * *
B 1 41.60 41.60 * *
C 1 426.42 426.42 * *
D 1 812.25 812.25 * *
2-Way Interactions 6 2497.32 416.22 * *
A*B 1 1.44 1.44 * *
A*C 1 1267.36 1267.36 * *
A*D 1 1193.70 1193.70 * *
B*C 1 22.56 22.56 * *
B*D 1 0.01 0.01 * *
C*D 1 12.25 12.25 * *
3-Way Interactions 4 141.34 35.34 * *
A*B*C 1 19.36 19.36 * *
A*B*D 1 81.90 81.90 * *
A*C*D 1 18.92 18.92 * *
B*C*D 1 21.16 21.16 * *
4-Way Interactions 1 11.90 11.90 * *
A*B*C*D 1 11.90 11.90 * *
Error 0 * *
Total 15 5771.26

Model Summary

S R-sq R-sq(adj) R-sq(pred)
* 100.00% * *

Coded Coefficients

SE
Term Effect Coef Coef T-Value P-Value VIF
Constant 71.46 * * *
A 21.45 10.72 * * * 1.00
B 3.225 1.613 * * * 1.00
C 10.325 5.163 * * * 1.00
D 14.250 7.125 * * * 1.00
A*B 0.6000 0.3000 * * * 1.00
A*C -17.800 -8.900 * * * 1.00
A*D 17.275 8.638 * * * 1.00
B*C 2.375 1.188 * * * 1.00
B*D -0.05000 -0.02500 * * * 1.00
C*D -1.7500 -0.8750 * * * 1.00
A*B*C 2.200 1.100 * * * 1.00
A*B*D 4.525 2.263 * * * 1.00
A*C*D -2.175 -1.087 * * * 1.00
B*C*D -2.300 -1.150 * * * 1.00
A*B*C*D 1.7250 0.8625 * * * 1.00

From above also we can say that only one three factor interaction effect ABD is stronger than single factor B.