Transcript ST5204 Experimental Design II

ST5204 Experimental Design II
Introduction
By Shenghua Kelly Fan
What is a statistical experimental
design?
• Determine the used levels of predictors and
the proportion of experimental units in each
selected level according to the experimental
goal.
Design topics vs. variable types
Response
Continuous
Categorical
Predictor
Continuous
Categorical
•Standard ANOVA
•Response
designs (eg.
surfaces
factorial designs)
•Uniform
designs
•Optimal
designs
Beyond the course
Prior experimental information
The model is known but
the parameters are not:
Optimal designs
The shape of the model is
somewhat clear:
Response surfaces
The model is completely
unknown:
Uniform designs
What I wish you to achieve
• Learn the basic standard ANOVA designs
and also standard design techniques such as
“randomization”, “blocking”, so you can
create new designs based on your own.
• Be able to provide a good design to locate
the maximum (or minimum) precisely.
• Be able to provide a good design where
there is no prior information at all.
Example 1: A new drug for
reducing the blood pressure:
1. You are asked to provide a good design to
explore the association between blood
pressure and the dosage of the new drug.
2. You are asked to provide a good design to
identify the dosage at which the blood
pressure is reduced the most.
Three conditions:
You only have budget for four subjects and
(0,1) as the possible range of dosage.
•Totally no idea.
•Linear association.
•Nonlinear with a minimum inside.
Example 2: Two drugs to reduce
the blood pressure:
1. You are asked to provide a good design to
explore the association between blood
pressure and the dosages of the two drugs.
2. You are asked to provide a good design to
identify the dosages of the two drugs at
which the blood pressure is reduced the
most.
Three conditions:
You only have budget for four subjects
and (0,1)X(0,1) as the possible domain of
dosages of the two drugs.
•Totally no idea.
•Linear association.
•Nonlinear with a minimum inside.