Lecture 1Joslin Goh

Simon Fraser University

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Outline

What you want to know

What you might want to know

What you have to know

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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

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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

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What you might not want to know

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Ronald.A.Fisher

Introduce three basic principles, analysis of variance

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Frank Yates

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David John Finney

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R.C. Bose

Combinatorial Designs

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George E.P. Box

Industrial Era: process modelling, optimization,response surface methodology.

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G. Taguchi

Quality improvement, Robust parameter designs

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Current Trend

Computer modelling and experiment

Application to other fields such as biotechnology

Large designs

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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

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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

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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.

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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.

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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

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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

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Categories of experimental problems

Treatment comparison

Variable selection, screening design

Response surface methodology

System optimization

System Robustness

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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