if we can reduce our desire, then all worries that bother us will disappear
TRANSCRIPT
If we can reduce our desire, then all worries that bother us will disappear.
Design of Experiments I
Topic: Introduction
Prof. Shenghua(Kelly) Fan
California State University
Representative Sample
• (Simple) random sample: Each group of units of the required size from the population has the same chance to be the selected sample.
Research studies
Observational studies
Randomized experiments
Sample surveys Case control studies
Case Study: Baldness and Heart Attacks
“A really bad hair day: Researchers link baldness and heart attack.” “Men with typical male pattern baldness … are anywhere from 30 to 300 % more likely to suffer a heart attach than men with little or no hair loss at all.” Newsweek, March 8, 1993.
Q: What type of study is it?
Which Type of Study?
• Ethical concerns
• Resource limitations
• Desired conclusion:– cause and effect– relationship
I want to slim down. Should I do exercise or limit my fat intake?
Problem: What are the factors affecting the taste of a soft drink beverage?
• Type of sweetener• Ratio of syrup to water• Carbonation level• Temperature• Others??
Iterative Nature of Experimentation
Conjecture
Experiment
Conjecture Conjecture
Experiment
Design Analysis Design Analysis Design
Increasing knowledge
Design = Analysis of conjecture & synthesis of experimentAnalysis = Interpretation of data & synthesis of new conjecture
The Phases/Objectives of Experimentation
Increase knowledge about process under study.
Phase Objective # of variables
Design type
Screening
(which)
•Identify key variables
•Estimate effects
2-15;
Numerical/
Categorical
Factorial design
Empirical
(how)
•Fit/test empirical model
•Determine local optimum
2-6;
Numerical
Response surface design
Theoretical
(why)
•Estimate parameters in mechanistic model
•Model testing
1-5;
Numerical/
Categorical
Optimal design
What Is an Experiment?
• An inquiry in which an investigator chooses the levels (values) of input or independent variables and observes the values of the output or dependent variable(s).
The Six Steps of Experimental Design
• Plan the experiment.
• Design the experiment.
• Perform the experiment.
• Analyze the data from the experiment.
• Confirm the results of the experiment.
• Evaluate the conclusions of the experiment.
Plan the Experiment
• Identify the dependent or output variable(s).• Translate output variables to measurable
quantities.• Determine the factors (input or independent
variables) that potentially affect the output variables that are to be studied.
• Identify potential combined actions between factors.
Problem (Cont.): soft drink beverage
• Type of sweetener• Ratio of syrup to
water• Carbonation level• Temperature
•What is the output variable?
Taste of the drink; score 1 to 10 (from poor to good)
•What factors and at which levels should we study?
A, B
Low, High
Design the Experiment
Determine the levels of independent variables (factors) and the number of experimental units at each combination of these levels according to the experimental goal.
Experimental unit: the unit we apply the factors on to get the response.
Problem (Cont.): soft drink beverage
•What combinations of factors should be studied?
All 2x2x2x2 combinations.
•How should we assign the studied combinations to experimental units?
Assign equal number of units to each combination.
(unit: the “null” beverage or say the plain water)
More on Experimental Design
• Randomizing the condition assigned to a unit– the type of treatments– the order of treatments
• Adding control groups– placebo; standard treatment; both
• Preventing bias: blinding– double blind; single blind
• Reducing the variability/ Increasing the accuracy– blocking; adding covariates (nuisance variables)
Complete Randomized Design (CRD)
The treatments are randomly assigned to (experimental) units.
Randomized Block Design (RBD)
Within each block, conduct CRD using an equal number of units.
Eg. Block factor: the age group
Basic Terminology
• Factors: the controlled variables;
must be categorical
• Treatments: conditions constructed from the factors
• Replications: observations or measurements in the observational study
Analysis of Variance (ANOVA)
Example: Y = battery life
X = battery brand
Objective: the impact of X on Y study how the value of Y changes according to X study how much of the variability in Y is due to the different levels of X
ANOVA: Analyze the variability in Y (output variable) to find the reasons of it (input factors).
Example: Y = LIFETIME (HOURS)
BRAND3 replications
per level 1 2 3 4 5 6 7 8
1.8 4.2 8.6 7.0 4.2 4.2 7.8 9.0
5.0 5.4 4.6 5.0 7.8 4.2 7.0 7.4
1.0 4.2 4.2 9.0 6.6 5.4 9.8 5.8
2.6 4.6 5.8 7.0 6.2 4.6 8.2 7.4 5.8
The total variability in life (Y)
How the variability in life is associated with brand (X):