Chapter 1
Design of Experiments Principles
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Continued...
Example: The use of unpaired observations
and the use of paired observations are the
experimental designs for two treatment
experiments.
Statistical design of experiments is the process of
planning the experiment so that appropriate data
can be obtained on the basis of which inferences
can be made in the best possible manner.
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To the statistician the experiment is the set of
rules used to draw the sample from the
population.
Two main aspects to any experimental
problem
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Design of the experiment.
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Statistical analysis of the data.
These two subjects are closely related since the
method of analysis depends directly on the
design employed.
Experimental design methods play an important
role in process development and process
improvement."
Planning Experiments

Important steps for planning experiments:
(1) Define the objective of the experiment:
Remark: Classify the objectives as major and
minor since certain experimental designs give
precision for some treatment comparison than
for others.
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Sources of variability
Remarks
(2) Identify all sources of variation:
In planning almost any experiment, we need to
decide

What measurement to make (the response)

What conditions to study (the treatments), and

What experimental material to use (the units or
subjects).
Planned, systematic variability - the kind we want

Chance-like variability - the kind we can live with,
and

Unplanned, systematic variability - the kind that
threatens disaster.
Variability due to the conditions of interest
(wanted)

Variability in the measurements process
(unwanted), and

Variability in the experimental material
(unwanted).
Basic Principles
Remarks
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(3) Choose a rule for assigning the
experimental units to the treatments:
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Replication: Which specifies the number of units
to be provided for each of the treatments.
Properties: (i) helps to estimate the error
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Randomization:
Properties Continue...
(ii) to improve the precision of an experiment by
reducing the standard deviation of a treatment
mean.

To avoid systematic and personal biases from being
introduced into the experiment by the
experimenter.
(iii) to increase the scope of inference of the
experiment by selection and appropriate use of
quite variable experiment units, and

Statistical methods require that the observations (or
errors) must be independently distributed random
variables.
(iv) to effect control of the error variance.
Blocking:
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A block is a portion of the experimental units
that should be more homogeneous than the
entire set of units.
Blocking involves making comparisons among
the conditions of interest in the experiment
within each block.
Planning continues
(iv) Selection of the response variable:
Most often, the average or standard deviation (or
both) of the measured characteristic will be the
response variable.
(v) Run a Pilot Study: A small-scale study
(involving only a few observations) of the
methods/model and procedures.
This increases the precision of an experiment.
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Continues…
Continue…
(vi) Choice of experimental design / Specify
the model:
(3)
(1) Whether the design is uni-factor or factorial.
(2) Whether to group the observation to
eliminate one, two or more causes of variation.
Example
Continues…
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Performing the experiment
Data Analysis:
Statistical methods should be used to analyze the
data so that results and conclusions are objective
rather than judgmental in nature.
Conclusions and Recommendations:
Follow-up runs and confirmation testing should
also be performed to validate the conclusions
from the experiment.
Whether the number of treatments or
treatment combinations is too large to allow a
full replication to be fitted conveniently into
one block. If so, the design is will referred to
as an “incomplete block design” and, if not, as a
“complete block design”.
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Consider the following enzyme concentrations
(mg/ml) in the hearts of eight hamsters.
Hamsters raised with long days:
1.49
1.53
1.56
1.79
Hamsters raised with short days:
1.39
1.49
1.25
1.38
Observations:
It looks that day length does affect the enzyme
concentration. The average for the long-day
hamsters is 1.59 mg/ml, which is higher than
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Example continues...
Example continues…
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the short-day average of 1.32 mg/ml.
The eight number show a lot of variability:
the long-day measurements range from 1.49 mg/ml to
1.79 mg/ml, and
 the difference of 0.30 mg/ml is bigger than the difference
between the long- and short-day averages.

The main important contents:
Treatments: To study the effect of day length.
Response: The concentration of enzyme.
Material: Hamsters.
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Sources of variability:
Variability in the conditions of interest:
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Objective: Need to estimate how much of the
difference between the averages is due to day
length and how much is due to other sources.
Example continues...
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Variability in the response:
measure the concentration of enzyme using a
spectrophotometer to measure the amount of
light absorbed by the suspended particles.

Variability in experimental material:
No two hamsters are biologically the same; some
just naturally have higher enzyme concentration
than others. We can also expect the hamsters’
environment and behavior to have some effect
on enzyme concentration.
The effects of day length---long versus short.
(main goal of the experiment)
Example continues..
Three sets of questions we want in this experiment
to answers.
(a) Long versus short days: Does day length
affect enzyme concentrations? If so, how big is
the effect?
(b) Hamsters: Is the variability from one hamster
to the next big enough to detect? If so, how much
variability is there?
(c) Measurement error: How big is the chance
error built into process of measuring enzyme
concentrations?
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Example continues...
Random assignment (Randomization):
Use a chance device to decide which hamsters
gets long days and which get short.
Randomization makes statistical analysis possible.
Example continues...
Randomized complete design: Random
assignment leads to the simplest experimental
plan: using a chance device, randomly assign a
day length (long or short) to each hamster. For
balance, make sure that half the hamsters get long
days and half get short.
Treatments: long and short days
Experimental units: hamsters (8 in all).
Design: RC design.
Continues...
Example continues...
Second principle (Blocking):
Randomized complete block design:
First sort (or subdivide) your experimental
material into groups (blocks) of similar units;
How to choose blocks:
then assign conditions to units separately within
each block.
Treatments: long and short days
Experimental units:
hamsters (8 in all).
Blocks: pairs of similar hamsters (4 pairs)
Design: RCB design.
(1) If our hamsters should actually happen to
come from four different litters, two hamsters
per litter, we could use pairs of littermates as
blocks.
The following three ways to choose blocks for
the hamster experiment.
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Computer Software
Example continues...
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(2) We could weigh the hamsters and then put
the two heaviest together in a pair, the next
together, and so on.
(3) Instead of weighing the hamsters, we could
measure how fast they use oxygen, and put the
two with the fastest rates together, and so on.
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R, SAS and SPSS (Used for this class),
R and S-PLUS (Graphic purpose)
Other Statistical Software etc.
Note: One can use any computer software
package, but make sure to know exactly the
capabilities of his/her package and also the likely
size of rounding errors.
Suggested Homework Exercises
Chapter 1
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Exercises: 2, 5, 12.
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