3. Elements of Design of
Experiments
1. Conjecture or hypothesis
2. Response variable
3. Factors, levels and ranges
4. Treatments of factors
5. Blockings
6. Tools and methods for experiments and
measurements
7. Effect models (independent or interaction factors)
8. Replication, randomization and local factor
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6. Blocking Principles and Nuisance
Factors
Blocking is a technique for dealing with nuisance factors
A nuisance factor is a factor that probably has some
effect on the response, but it’s of no interest to the
experimenter…however, the variability it transmits to the
response needs to be minimized
Typical nuisance factors include batches of raw material,
operators, pieces of test equipment, time (shifts, days,
etc.), different experimental units
Many industrial experiments involve blocking (or should)
Failure to block is a common flaw in designing an
experiment (consequences?)
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7. Blocking Principles and Nuisance
Factors
If the nuisance variable is known and controllable, we
use blocking
If the nuisance factor is known and uncontrollable,
sometimes we can use the analysis of covariance to
remove the effect of the nuisance factor from the analysis
If the nuisance factor is unknown and uncontrollable (a
“lurking” variable), we hope that randomization
balances out its impact across the experiment
Sometimes several sources of variability are combined in
a block, so the block becomes an aggregate variable
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11. Latin Square Design (LSD)
Latin Square Design is a type of
experimental design to eliminate two nuisance
sources of variability by systematically
allowing blocking in two directions. The rows
and columns actually represent two
restrictions on randomization. A p X p latin
square is a square containing p rows and p
columns. There are p Latin letters that
correspond to the treatments and occur once
in each row and column.
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14. Latin Square Design (LSD)
14
Random Order Experimental Units
1 2 3 4 5 6 7 8 9 10 11 12
A A A A A A B B B B B B
B B C C D D A A C C D D
C D B D B C C D A D A C
D C D B C B D C D A C A
Randomization Alternatives of four Experimental Units
24
!
4
4
4
P
Random Order Experimental Units
13 14 15 16 17 18 19 20 21 22 23 24
C C C C C C D D D D D D
A A B B D D A A B B C C
B D A D A B B C A C A B
D B D A B A C B C A B A
15. Latin Square Design (LSD)
15
Standard Latin Square
A B C D
B C D A
C D A B
D A B C
A B C D
B A D C
C D B A
D C A B
A B C D
B D A C
C A D B
D C B A
A B C D
B A D C
C D A B
D C B A
20. Model Adequacy Checking
Normal Probability Plot of the Residuals
Plot of Residuals in Time Sequence
Plot of Residuals versus Fitted Values
Plot of Residuals versus Other Variables
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