Graeco Latin Square Design (GLSD) is an experimental design used to eliminate three nuisance sources of variability. It merges two p X p Latin squares, with one using Latin letters for treatments and the other using Greek letters, such that each Greek letter appears once with each Latin letter. This allows blocking out of three nuisance factors. Statistical analysis of a GLSD involves analyzing the variance components and performing an ANOVA. Model adequacy is checked using plots of residuals against fitted values and other variables. An example is given of a rocket propellant experiment using a GLSD.

1. Graeco Latin Square
Design
ARIF RAHMAN
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2. Experiments
Hypothesis/
Conjecture
Design of
Experiment
Conduct
Experiment
Analysis of
Data
Discussion &
Conclusion
Refine
the Model
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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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4. P Diagram
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Signal
Factors
(m)
Noise
Factors
(x)
Control
Factors
(z)
Scaling
Factors
(r)
Response
Variables
(y)
F(x,m,z,r)
Inputs
Controllable Factors
(x)
Uncontrollable Factors
(z)
Output
(y)
F(x,z)

5. Blocking Principles and Nuisance
Factors
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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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8. Graeco Latin Square Design
(GLSD)
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9. Graeco Latin Square Design
(GLSD)
Graeco Latin Square Design is a type of
experimental design to eliminate three
nuisance sources of variability by merging two
p X p latin square. Consider a first p X p Latin
square in which the treatments are denoted
by Latin letters, and superimpose on it a
second p X p Latin square in which the
treatments are denoted by Greek letters.
Each Greek letter appears once and only
once with each Latin letter.
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10. Graeco Latin Square Design
(GLSD)
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11. Statistical Analysis of the GLSD
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12. Statistical Analysis of the GLSD
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13. 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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14. an Example: The Rocket
Propellant Experiment
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15. an Example: The Rocket
Propellant Experiment
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16. an Example: The Rocket
Propellant Experiment
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17. an Example: The Rocket
Propellant Experiment
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18. an Example: The Rocket
Propellant Experiment
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19. 19
That’s all
... Any Questions ???