Statistics of Experimental Design

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# Statistics of Experimental Design - PowerPoint PPT Presentation

Ludolf E. Meester, Statistics Dept. Peter J.T. Verheijen, Chemical Eng. Dept. Statistics of Experimental Design. wi2144st. Aim. Introduction probability and statistics Familiarise engineering students with the jargon of the statisticians Model-based analysis of experimental data

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Ludolf E. Meester, Statistics Dept.

Peter J.T. Verheijen, Chemical Eng. Dept.

Statistics of Experimental Design

wi2144st

wi2144st

Aim
• Introduction probability and statistics
• Familiarise engineering students with the jargon of the statisticians
• Model-based analysis of experimental data
• Design of experiments

wi2144st

Contents

Probability

Example 1:

Probability of success in test

Distributions

Descriptive Statistics

Estimation theory

Example 2:

Probability of success in test 2

given that test 1<5.5?

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Probability

Distributions

Descriptive Statistics

Estimation theory

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Probability

Distributions

Descriptive Statistics

Estimation theory

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Descriptive Statistics

Probability

Distributions

Example:

What is mu and sigma?

Estimation theory

Estimation theory

• Bias
• Robustness
• Confidence Interval
• Bootstrap methods

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

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Contents

Descriptive Statistics

Probability

Example 1:

When you have less than 4. 5

on test 1, you will not pass

Distributions

Estimation theory

Hypothesis testing

Example 2:

Average Test1=Average Test 2

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Descriptive Statistics

Probability

Distributions

Estimation theory

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Descriptive Statistics

Probability

Distributions

Estimation theory

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Descriptive Statistics

Probability

Distributions

Estimation theory

… To improve estimate

... To improve prediction of model

Hypothesis testing

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

wi2144st

Contents

Descriptive Statistics

Probability

Given Data:

Choose between models

Distributions

Estimation theory

Hypothesis testing

Given Different Models:

Choose between experiments

Linear Model

Non-linear regression

Design of experiment

Model selection/discrimination

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The Lectures
• Introduction, probability
• Probability distributions
• Simulation, expectation and variance
• Joint distributions
• Central limit theorem, data exploration
• Estimation
• Hypothesis testing
• Stochastic vectors: linear model and estimation
• Linear model, confidence interval and hypothesis testing
• Linear model, Non-linear regression
• Non-linear regression
• Experimental design
• Model selection
• Review

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Overview

Entities

Data = Model + Experimental Error

Actions

Characterisation

Experimentation

Estimation

Hypothesis testing

… to be continued

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Course Material and Information
• Part I: A Modern Introduction to Probability and
• Statistics by Dekking et al, ISBN 1-85233-896-2;
• (Autumn 2004 and later versions of Kanstat lecture notes still usable.)
• Part II: Lecture Notes, plus exercises
• Exercises and Examination Set Edition 7 available as PDF
• Data for exercises and past examinations
• Software:
• SSORstat
• PastiFit
• PastiMos
• Excel
• …. any other, eg Splus, SAS, SPSS, Matlab

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Where, what
• VSSD
• A Modern Introduction to Probability and Statistics by
• Dekking et al, ISBN 1-85233-896-2
• Computer rooms
• Data for exercises and past examinations
• Software: SSORstat, PastiFit, PastiMos and Excel
• Web page: http://dutiosc.twi.tudelft.nl/~a90 (also via BB page)
• Data for exercises and past examinations (zip-file)
• Exercises and Examination Set (1994-2006) as pdf
• Lecture notes Statistiek van Proefopzetten as pdf
• And of course e-mail to the lecturers:
• L.E.Meester@tudelft.nl, P.J.T.Verheijen@tudelft.nl

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Course Material and Information

Changes with respect to 2005/2006

Lecture notes: Statistiek van proefopzetten ONLY available as

pdf on website.

Exercises and Examination Set: minor updates and inclusion of

exams 2004/2005; ONLY available as pdf on website.

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Timetable
• Course schedule 3rd period Room B
• Thursday: hour 1+2 Lectures (/Exercises)
• Friday: hour 5+6+7 Lectures/(Computer) Exercises
• Course schedule 4th period Room B
• Wednesday: hour 2+3+4 Lectures/(Computer) Exercises
• Thursday: hour 3+4 Lectures/Exercises
• Examination schedule
• Full course examination: Thu., June 14, 14-17
• Full course examination: Tue., August 28, 14-17

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Examination

Material present:

• Computer with
• SSORstat
• PastiFit
• PastiMos
• Excel
• Formulas (from appendices Lecture Notes)

Allowed: normal calculator

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Examination

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…. or ‘’Chance favors the prepared mind!’’

…. or “Het toeval begunstigt de voorbereide geest’’

… and what else

Dans le domaine de la science, le hasard ne favorise que les esprits qui ont été préparés.

Louis Pasteur, 1822-1895

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