Lecture 1 - SFU Mathematics and Statistics Web Serverpeople.stat.sfu.ca/~jtg3/unit0.pdf ·...
Transcript of Lecture 1 - SFU Mathematics and Statistics Web Serverpeople.stat.sfu.ca/~jtg3/unit0.pdf ·...
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Lecture 1Joslin Goh
Simon Fraser University
Lecture 1 – p. 1/20
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Outline
What you want to know
What you might want to know
What you have to know
Lecture 1 – p. 2/20
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What you want to know
Office Hour: Tuesday 1-2pm; Thursday 3.30-4.30pm
Office:K 10564
5 assignments; 2 midterms (Oct 13 & Nov 18); Final(Dec 14)
Grading: Assignment 20%, Midterm 30%, Final 50%;
Http://www.people.stat.sfu.ca/∼jtg3/stat430.html
Lecture 1 – p. 3/20
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A few more things:
Reference books:Design and Analysis of Experiments — Douglas C.MontgomeryDesign and analysis of experiments — Angela DeanStatistics for Experimenters: An Introduction toDesign, Data Analysis, and Model BuildingGeorge E.P.Box, William G. Hunter, J. Stuart Hunter,William Gordon HunterExperiments: Planning, Analysis, and ParameterDesign OptimizationJeff Wu and Michael Hamada
Away between Nov 15 and Nov 18.
Replacement lectures: TBD
Lecture 1 – p. 4/20
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What you might not want to know
Lecture 1 – p. 5/20
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Ronald.A.Fisher
Introduce three basic principles, analysis of variance
Lecture 1 – p. 6/20
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Frank Yates
Lecture 1 – p. 7/20
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David John Finney
Lecture 1 – p. 8/20
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R.C. Bose
Combinatorial Designs
Lecture 1 – p. 9/20
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George E.P. Box
Industrial Era: process modelling, optimization,response surface methodology.
Lecture 1 – p. 10/20
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G. Taguchi
Quality improvement, Robust parameter designs
Lecture 1 – p. 11/20
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Current Trend
Computer modelling and experiment
Application to other fields such as biotechnology
Large designs
Lecture 1 – p. 12/20
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What you have to know
The formulation of a problem is often more essential thanits solution which may be merely a matter of mathematicalor experimental skill.
————— Albert Einstein
Formulation;1. Understand the physical background2. Understand the objective3. Make sure you know what the clients want4. Put the problem into statistical terms
Data Collection
Lecture 1 – p. 13/20
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Overview
Design ⇋ Analysis
Design: the way that the experiment is performed
Analysis: including model fitting, assessment of themodel assumption, drawing the conclusion
Relationship between design and analysis
The choice of the design is often linked to aparticular modelImpact of the design on the analysis-> criterion
Lecture 1 – p. 14/20
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Definition
Factor: variables whose influence upon a responsevariable is being studied
Factor level: Setting of a factor{
Quantitative, e.g., Time, pressure, temperature;Qualitative, e.g., Methods, suppliers, gender.
Trial (Run): application of a treatment to anexperimental unit;
Treatment: a combination of factor level setting;
Experimental units: object to which a treatment isapplied.
Lecture 1 – p. 15/20
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An Example
Goal: to compare two headache remedies to determinewhich is more effective at alleviating the symptoms.
Procedure: 20 volunteers are randomly divided into twogroups. One group takes Drug 1 and the other takes Drug2. Within each group the dosage levels are randomlyassigned to each patient. One hour after taking the drug,the rate of blood flow to the brain of each patient ismeasured.
Lecture 1 – p. 16/20
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Systematic Approach to Experimentation
State the objective of the study
Choose the response variable
Choose factors and levels
Choose experimental design
Perform the experiment
Analyze data
Draw conclusions
Lecture 1 – p. 17/20
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Three Basic Principles
Definition Purpose
Randomization Randomizing the allocation • Prevent the unknown variables;and order • Ensure the valid estimate of
experimental error.
Replication Repeat the treatment • Estimate the variance of experiment error
Blocking A group of homogeneous units • Eliminate the block effects
Lecture 1 – p. 18/20
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Categories of experimental problems
Treatment comparison
Variable selection, screening design
Response surface methodology
System optimization
System Robustness
Lecture 1 – p. 19/20
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Outline
Basic principles and simple comparative experiments
Experiments with a single factor, analysis of variance,random effects model
Experiments with more than one factor, blocking, Latinsquares, analysis of variance and covariance, split-plotexperiments, other analysis techniques
Factorial experiments at two levels, comparison with“one-factor-at-a-time” plans, analysis of location anddispersion
Fractional factorial experiments at two levels, maximumresolution and minimum aberration for choosing optimaldesigns
A brief introduction to response surface methodology.
Variation reductionLecture 1 – p. 20/20