1. Design and Analysis of Multi-Factored Experiments
Part IV
Analysis with Blocking : More examples
L. M. Lye
DOE Course

2. Analysis of 2k factorial experiments with blocking
Method for obtaining estimates of effects and sum-squares is exactly the same as without blocking.
The only difference is in the ANOVA table.
An additional line for variation due to “Blocks” must be added.
L. M. Lye
DOE Course

3. Example 1
Consider a 24 experiment in two blocks with effect ABCD confounded. Using the method discussed, the two blocks are as follows with the responses given.
Block 1 Block 2
(1) = 3 a = 7
ab = 7 b = 5
ac =6 c = 6
bc = 8 d = 4
ad = 10 abc = 6
bd = 4 bcd = 7
cd = 8 acd = 9
abcd = 9 abd = 12
L. M. Lye
DOE Course

4. L. M. Lye
DOE Course

5. L. M. Lye
DOE Course

6. Regression Equation
Effects and sum-squares are obtained by Yate’s algorithm in the usual way.
Final Equation in Terms of Coded Factors: Y = A C D AC AD
R2 = 0.917
L. M. Lye
DOE Course

7. L. M. Lye
DOE Course

8. L. M. Lye
DOE Course

9. L. M. Lye
DOE Course

10. Example 2
Consider a 25 experiment that were conducted in 4 blocks. Effects ABCD, BCDE, and AE are confounded with blocks.
L. M. Lye
DOE Course

11. ANOVA Table
L. M. Lye
DOE Course

12. Summary
ANOVA table with blocking has an extra line – SS due to Blocking
Other steps are the same as without blocking
Examples shown here were done using Design-Ease
Fractional design uses similar concepts are blocking – next topic
L. M. Lye
DOE Course