Lektion 6. Measurement system! Measurement systems analysis _3 Chapter 7. Statistical process control requires measurement of good quality!
|
|
|
- Roxanne Wilson
- 5 years ago
- Views:
Transcription
1 Lektion _3 Chapter 7 Measurement systems analysis Measurement system! Statistical process control requires measurement of good quality! Wrong conclusion about the process due to measurement error! - Very expensive! Measurement systems analysis Make well-founded decisions Model quality Data Measurement error compared to product variation? Measurement error compared to tolerance limits? Measurement systems analysis can be complex. Measurement system covariates with the product. 1
2 Different types of measurement errors. Bias (Missvisning) Spread Big errors Wrong product Write wrong Model y = x + ε y is the observed value. x is the true value. ε is the measurement error. Variation model = + Total A simple model of the measurement system Bias: E[ ε ] 0 Spread: V Total [ ε ] > 0 Requirement: k ˆ = 0.10, rocess capability T USL LSL ˆ ρm = ( ) Some requirements on a measurement system. 1. The system must have adequate discrimination and sensitivity. The increments should be small relative the process variatoin or specification limits. Thumb rule of 10: states that instrument discrimination shoudl divide the tolerance (or process) into ten parts or more.. The measurement system ought to be in statistical control. That means that under repeatable conditions, the variation in the measurement system is due to common causes only. 3. For product control, variability of the measurement system must be small compared to the specification limits. 4. For process control, the variability of the measurement system ought to demonstrate effective resolution and be small compared to manufacturing process variation.
3 Requirements on measurement system Example of requirement: k ˆ = T USL LSL ˆ ρm = Total ( rocess capability ) ( rocess variation ) roblem: If the process variation decreases then the measurement system may be rejected. Calibration of measurement system F mg x m 10 x x 0 10 Regression x Control charts on the measurement system instead of calibration? Calibration control on individual measurements. SC to detect changes. Exemple: Measure a reference weight each day and plot it in a control chart. Shewhart, Cusum or EWMA? 3
4 MSA Some important characteristics Stability Control chart Bias Measure a reference many times. Linjaritet Repeatability and reproducability R&R ANOVA Repeteatability and reproducability (M. Arnér: Mätosäkerhet) Repeteatability: Repeatability or lack of repeatability is the variation that comes when the same operator uses the same measurement equipment and measures the same unit many times Reproducability: Reproducability or lack of reproducability is used for the variation that comes when e.g. different operators with the same measurement equipment measures hte same unit or one operator is measuring the same unint with different measurement equipment. = = + Measurement error Repeatability Reproducibility R&R ijk = µ + i + j + ( ) + ε ij ijk i j ( ) ε ij ijk ( i ) = ( j ) = O V ( yijk ) = + O + + (( ) ij ) = O ( εijk ) = y O, O,, are independent and normally distributed with average 0 V V O V V,,, are called variance components. ANOVA is used in the analysis. 4
5 Exemple (table 7.7) Inspector 1 Inspector Inspector 3 Detalj nr: Test 1 Test Test 3 Test 1 Test Test 3 Test 1 Test Test The sums of squares (see chap. 1-4.) SSTotal = SSarts + SSOperators + SS + SSError R&R Divide the sums of squares with the degrees of freedom: SS MS = = = p 1 9 SSO 39.7 MSO = = = o 1 SS MS = = = ( p )( o ) SSE MSE = = = po n ( ) ANOVA in Matlab Command: anova 5
6 Estimate the variance components ˆ = MS E = 0.51 MS MS n MS MS pn E ˆ = = 0.73 O ˆO = = 0.56 MS MS on ˆ = = 48.9 ˆ If < 0 then choose a model without interactions: y = µ + + O + ε ijk i j ijk Repeteatability and reproducability Repeatability = = 0.51 = + = 1.9 Reproducibility O = + = 1.80 Reproducibility Repeatability ( LSL = 18, USL = 58) ˆ T = = = 0.7 Är större än 0.10! USL LSL Conclusion: We should improve the measurement system to be able to measure the product variation. 6
Measurement Systems Analysis
Measurement Systems Analysis Since measurement systems represent a subprocess within a process They are subject to Variation. What could be the source of this variation? Why do Measurements Vary? Possible
Process Capability Analysis Using Experiments
Process Capability Analysis Using Experiments A designed experiment can aid in separating sources of variability in a quality characteristic. Example: bottling soft drinks Suppose the measured syrup content
Statistical Techniques II EXST7015 Simple Linear Regression
Statistical Techniques II EXST7015 Simple Linear Regression 03a_SLR 1 Y - the dependent variable 35 30 25 The objective Given points plotted on two coordinates, Y and X, find the best line to fit the data.
Statistical Quality Control, IE 3255 March Homework #6 Due: Fri, April points
Statistical Quality Control, IE 355 March 30 007 Homework #6 Due: Fri, April 6 007 00 points Use Ecel, Minitab and a word processor to present quality answers to the following statistical process control
Factorial designs. Experiments
Chapter 5: Factorial designs Petter Mostad mostad@chalmers.se Experiments Actively making changes and observing the result, to find causal relationships. Many types of experimental plans Measuring response
Analysis of Variance
Statistical Techniques II EXST7015 Analysis of Variance 15a_ANOVA_Introduction 1 Design The simplest model for Analysis of Variance (ANOVA) is the CRD, the Completely Randomized Design This model is also
Inference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
Analysis of Variance and Design of Experiments-I
Analysis of Variance and Design of Experiments-I MODULE VIII LECTURE - 35 ANALYSIS OF VARIANCE IN RANDOM-EFFECTS MODEL AND MIXED-EFFECTS MODEL Dr. Shalabh Department of Mathematics and Statistics Indian
STAT Final Practice Problems
STAT 48 -- Final Practice Problems.Out of 5 women who had uterine cancer, 0 claimed to have used estrogens. Out of 30 women without uterine cancer 5 claimed to have used estrogens. Exposure Outcome (Cancer)
Measuring System Analysis in Six Sigma methodology application Case Study
Measuring System Analysis in Six Sigma methodology application Case Study M.Sc Sibalija Tatjana 1, Prof.Dr Majstorovic Vidosav 1 1 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije
Ch 2: Simple Linear Regression
Ch 2: Simple Linear Regression 1. Simple Linear Regression Model A simple regression model with a single regressor x is y = β 0 + β 1 x + ɛ, where we assume that the error ɛ is independent random component
The Multiple Regression Model
Multiple Regression The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & or more independent variables (X i ) Multiple Regression Model with k Independent Variables:
Chapter 8 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.
1 Learning Objectives Chapter 8 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. 2 Process Capability Natural tolerance limits are defined as follows: Chapter 8 Statistical Quality Control,
Lecture #26. Gage R&R Study. Oct. 29, 2003
Lecture #26 Gage R&R Study Oct. 29, 2003 Background - Measurement: Integral part of manufacturing Estimate the contribution attributable to the measurement system itself SPC requires accurate and precise
Chapter 14 Simple Linear Regression (A)
Chapter 14 Simple Linear Regression (A) 1. Characteristics Managerial decisions often are based on the relationship between two or more variables. can be used to develop an equation showing how the variables
2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Inferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
STAT Chapter 10: Analysis of Variance
STAT 515 -- Chapter 10: Analysis of Variance Designed Experiment A study in which the researcher controls the levels of one or more variables to determine their effect on the variable of interest (called
CHAPTER 4 Analysis of Variance. One-way ANOVA Two-way ANOVA i) Two way ANOVA without replication ii) Two way ANOVA with replication
CHAPTER 4 Analysis of Variance One-way ANOVA Two-way ANOVA i) Two way ANOVA without replication ii) Two way ANOVA with replication 1 Introduction In this chapter, expand the idea of hypothesis tests. We
Week 12 Hypothesis Testing, Part II Comparing Two Populations
Week 12 Hypothesis Testing, Part II Week 12 Hypothesis Testing, Part II Week 12 Objectives 1 The principle of Analysis of Variance is introduced and used to derive the F-test for testing the model utility
Methods for Identifying Out-of-Trend Data in Analysis of Stability Measurements Part II: By-Time-Point and Multivariate Control Chart
Peer-Reviewed Methods for Identifying Out-of-Trend Data in Analysis of Stability Measurements Part II: By-Time-Point and Multivariate Control Chart Máté Mihalovits and Sándor Kemény T his article is a
DESAIN EKSPERIMEN BLOCKING FACTORS. Semester Genap 2017/2018 Jurusan Teknik Industri Universitas Brawijaya
DESAIN EKSPERIMEN BLOCKING FACTORS Semester Genap Jurusan Teknik Industri Universitas Brawijaya Outline The Randomized Complete Block Design The Latin Square Design The Graeco-Latin Square Design Balanced
AMS 315/576 Lecture Notes. Chapter 11. Simple Linear Regression
AMS 315/576 Lecture Notes Chapter 11. Simple Linear Regression 11.1 Motivation A restaurant opening on a reservations-only basis would like to use the number of advance reservations x to predict the number
Simple Linear Regression
9-1 l Chapter 9 l Simple Linear Regression 9.1 Simple Linear Regression 9.2 Scatter Diagram 9.3 Graphical Method for Determining Regression 9.4 Least Square Method 9.5 Correlation Coefficient and Coefficient
In a one-way ANOVA, the total sums of squares among observations is partitioned into two components: Sums of squares represent:
Activity #10: AxS ANOVA (Repeated subjects design) Resources: optimism.sav So far in MATH 300 and 301, we have studied the following hypothesis testing procedures: 1) Binomial test, sign-test, Fisher s
One-Way Analysis of Variance. With regression, we related two quantitative, typically continuous variables.
One-Way Analysis of Variance With regression, we related two quantitative, typically continuous variables. Often we wish to relate a quantitative response variable with a qualitative (or simply discrete)
MAT3378 ANOVA Summary
MAT3378 ANOVA Summary April 18, 2016 Before you do the analysis: How many factors? (one-factor/one-way ANOVA, two-factor ANOVA etc.) Fixed or Random or Mixed effects? Crossed-factors; nested factors or
Fractional Factorial Designs
k-p Fractional Factorial Designs Fractional Factorial Designs If we have 7 factors, a 7 factorial design will require 8 experiments How much information can we obtain from fewer experiments, e.g. 7-4 =
Simple Linear Regression
Simple Linear Regression September 24, 2008 Reading HH 8, GIll 4 Simple Linear Regression p.1/20 Problem Data: Observe pairs (Y i,x i ),i = 1,...n Response or dependent variable Y Predictor or independent
Categorical Predictor Variables
Categorical Predictor Variables We often wish to use categorical (or qualitative) variables as covariates in a regression model. For binary variables (taking on only 2 values, e.g. sex), it is relatively
Econ 3790: Business and Economic Statistics. Instructor: Yogesh Uppal
Econ 3790: Business and Economic Statistics Instructor: Yogesh Uppal Email: yuppal@ysu.edu Chapter 13, Part A: Analysis of Variance and Experimental Design Introduction to Analysis of Variance Analysis
Chapter 4: Randomized Blocks and Latin Squares
Chapter 4: Randomized Blocks and Latin Squares 1 Design of Engineering Experiments The Blocking Principle Blocking and nuisance factors The randomized complete block design or the RCBD Extension of the
Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
What is Multiple Linear Regression Several independent variables may influence the change in response variable we are trying to study. When several independent variables are included in the equation, the
If we have many sets of populations, we may compare the means of populations in each set with one experiment.
Statistical Methods in Business Lecture 3. Factorial Design: If we have many sets of populations we may compare the means of populations in each set with one experiment. Assume we have two factors with
Chapter 14 Student Lecture Notes Department of Quantitative Methods & Information Systems. Business Statistics. Chapter 14 Multiple Regression
Chapter 14 Student Lecture Notes 14-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 14 Multiple Regression QMIS 0 Dr. Mohammad Zainal Chapter Goals After completing
Outline Topic 21 - Two Factor ANOVA
Outline Topic 21 - Two Factor ANOVA Data Model Parameter Estimates - Fall 2013 Equal Sample Size One replicate per cell Unequal Sample size Topic 21 2 Overview Now have two factors (A and B) Suppose each
IndyASQ Workshop September 12, Measure for Six Sigma and Beyond
IndyASQ Workshop September 12, 2007 Measure for Six Sigma and Beyond 1 Introductions Tom Pearson 317-507 507-53585358 tpcindy@insightbb.com MS OR Old #7 Golf Guy Innovator Dog Lover Tomorrowist Entrepreneur
IE 316 Exam 1 Fall 2011
IE 316 Exam 1 Fall 2011 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed 1 1. Suppose the actual diameters x in a batch of steel cylinders are normally
2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analysis of Variance and Design of Experiment-I MODULE IX LECTURE - 38 EXERCISES Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Example (Completely randomized
Analysis of Variance. ภาว น ศ ร ประภาน ก ล คณะเศรษฐศาสตร มหาว ทยาล ยธรรมศาสตร
Analysis of Variance ภาว น ศ ร ประภาน ก ล คณะเศรษฐศาสตร มหาว ทยาล ยธรรมศาสตร pawin@econ.tu.ac.th Outline Introduction One Factor Analysis of Variance Two Factor Analysis of Variance ANCOVA MANOVA Introduction
Design of Engineering Experiments Chapter 5 Introduction to Factorials
Design of Engineering Experiments Chapter 5 Introduction to Factorials Text reference, Chapter 5 page 170 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA
Sociology 6Z03 Review II
Sociology 6Z03 Review II John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review II Fall 2016 1 / 35 Outline: Review II Probability Part I Sampling Distributions Probability
CS 147: Computer Systems Performance Analysis
CS 147: Computer Systems Performance Analysis CS 147: Computer Systems Performance Analysis 1 / 34 Overview Overview Overview Adding Replications Adding Replications 2 / 34 Two-Factor Design Without Replications
Quantitative. Accurate. Precise. Measurement Error
Measurement Error Before we do any experiments, collect any data, or set up any process: We need to ensure we have a way to measure the results that is: Quantitative Accurate Precise So how do we test
Multiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company
Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple
Estimating σ 2. We can do simple prediction of Y and estimation of the mean of Y at any value of X.
Estimating σ 2 We can do simple prediction of Y and estimation of the mean of Y at any value of X. To perform inferences about our regression line, we must estimate σ 2, the variance of the error term.
Chap The McGraw-Hill Companies, Inc. All rights reserved.
11 pter11 Chap Analysis of Variance Overview of ANOVA Multiple Comparisons Tests for Homogeneity of Variances Two-Factor ANOVA Without Replication General Linear Model Experimental Design: An Overview
Summary of Chapter 7 (Sections ) and Chapter 8 (Section 8.1)
Summary of Chapter 7 (Sections 7.2-7.5) and Chapter 8 (Section 8.1) Chapter 7. Tests of Statistical Hypotheses 7.2. Tests about One Mean (1) Test about One Mean Case 1: σ is known. Assume that X N(µ, σ
Correlation Analysis
Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the
STAT22200 Spring 2014 Chapter 8A
STAT22200 Spring 2014 Chapter 8A Yibi Huang May 13, 2014 81-86 Two-Way Factorial Designs Chapter 8A - 1 Problem 81 Sprouting Barley (p166 in Oehlert) Brewer s malt is produced from germinating barley,
3. Design Experiments and Variance Analysis
3. Design Experiments and Variance Analysis Isabel M. Rodrigues 1 / 46 3.1. Completely randomized experiment. Experimentation allows an investigator to find out what happens to the output variables when
Two-Way Factorial Designs
81-86 Two-Way Factorial Designs Yibi Huang 81-86 Two-Way Factorial Designs Chapter 8A - 1 Problem 81 Sprouting Barley (p166 in Oehlert) Brewer s malt is produced from germinating barley, so brewers like
Chapter 13 Experiments with Random Factors Solutions
Solutions from Montgomery, D. C. (01) Design and Analysis of Experiments, Wiley, NY Chapter 13 Experiments with Random Factors Solutions 13.. An article by Hoof and Berman ( Statistical Analysis of Power
Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analysis of Variance and Design of Experiments-I MODULE IV LECTURE - 3 EXPERIMENTAL DESIGNS AND THEIR ANALYSIS Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Lecture #14. Prof. John W. Sutherland. Sept. 28, 2005
Lecture #14 Prof. John W. Sutherland Sept. 28, 2005 Process as a Statistical Distn. Process 11 AM 0.044 10 AM 0.043 9 AM 0.046 Statistical Model 0.043 0.045 0.047 0.043 0.045 0.047 0.048?? Process Behavior
Inference for the Regression Coefficient
Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression line. We can shows that b 0 and b 1 are the unbiased estimates
STAT 115:Experimental Designs
STAT 115:Experimental Designs Josefina V. Almeda 2013 Multisample inference: Analysis of Variance 1 Learning Objectives 1. Describe Analysis of Variance (ANOVA) 2. Explain the Rationale of ANOVA 3. Compare
Practical Statistics for the Analytical Scientist Table of Contents
Practical Statistics for the Analytical Scientist Table of Contents Chapter 1 Introduction - Choosing the Correct Statistics 1.1 Introduction 1.2 Choosing the Right Statistical Procedures 1.2.1 Planning
Multiple Linear Regression
Multiple Linear Regression Simple linear regression tries to fit a simple line between two variables Y and X. If X is linearly related to Y this explains some of the variability in Y. In most cases, there
Statistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 13 Simple Linear Regression 13-1 Learning Objectives In this chapter, you learn: How to use regression analysis to predict the value of
DESAIN EKSPERIMEN Analysis of Variances (ANOVA) Semester Genap 2017/2018 Jurusan Teknik Industri Universitas Brawijaya
DESAIN EKSPERIMEN Analysis of Variances (ANOVA) Semester Jurusan Teknik Industri Universitas Brawijaya Outline Introduction The Analysis of Variance Models for the Data Post-ANOVA Comparison of Means Sample
Econ 3790: Business and Economics Statistics. Instructor: Yogesh Uppal
Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal yuppal@ysu.edu Sampling Distribution of b 1 Expected value of b 1 : Variance of b 1 : E(b 1 ) = 1 Var(b 1 ) = σ 2 /SS x Estimate of
2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/term
CHAPTER-5 MEASUREMENT SYSTEM ANALYSIS. Two case studies (case study-3 and 4) conducted in bearing
6 CHAPTER-5 MEASUREMENT SYSTEM ANALYSIS 5.0 INTRODUCTION: Two case studies (case study- and 4) conducted in bearing manufacturing facility. In this industry the core process is bearing rings machining
Master s Written Examination
Master s Written Examination Option: Statistics and Probability Spring 016 Full points may be obtained for correct answers to eight questions. Each numbered question which may have several parts is worth
Chapter 11 - Lecture 1 Single Factor ANOVA
April 5, 2013 Chapter 9 : hypothesis testing for one population mean. Chapter 10: hypothesis testing for two population means. What comes next? Chapter 9 : hypothesis testing for one population mean. Chapter
Tentative solutions TMA4255 Applied Statistics 16 May, 2015
Norwegian University of Science and Technology Department of Mathematical Sciences Page of 9 Tentative solutions TMA455 Applied Statistics 6 May, 05 Problem Manufacturer of fertilizers a) Are these independent
Business Statistics. Chapter 14 Introduction to Linear Regression and Correlation Analysis QMIS 220. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 14 Introduction to Linear Regression and Correlation Analysis QMIS 220 Dr. Mohammad Zainal Chapter Goals After completing
Simple Linear Regression Analysis
LINEAR REGRESSION ANALYSIS MODULE II Lecture - 6 Simple Linear Regression Analysis Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Prediction of values of study
n i n T Note: You can use the fact that t(.975; 10) = 2.228, t(.95; 10) = 1.813, t(.975; 12) = 2.179, t(.95; 12) =
MAT 3378 3X Midterm Examination (Solutions) 1. An experiment with a completely randomized design was run to determine whether four specific firing temperatures affect the density of a certain type of brick.
Theorem A: Expectations of Sums of Squares Under the two-way ANOVA model, E(X i X) 2 = (µ i µ) 2 + n 1 n σ2
identity Y ijk Ȳ = (Y ijk Ȳij ) + (Ȳi Ȳ ) + (Ȳ j Ȳ ) + (Ȳij Ȳi Ȳ j + Ȳ ) Theorem A: Expectations of Sums of Squares Under the two-way ANOVA model, (1) E(MSE) = E(SSE/[IJ(K 1)]) = (2) E(MSA) = E(SSA/(I
16.3 One-Way ANOVA: The Procedure
16.3 One-Way ANOVA: The Procedure Tom Lewis Fall Term 2009 Tom Lewis () 16.3 One-Way ANOVA: The Procedure Fall Term 2009 1 / 10 Outline 1 The background 2 Computing formulas 3 The ANOVA Identity 4 Tom
AN IMPROVEMENT TO THE ALIGNED RANK STATISTIC
Journal of Applied Statistical Science ISSN 1067-5817 Volume 14, Number 3/4, pp. 225-235 2005 Nova Science Publishers, Inc. AN IMPROVEMENT TO THE ALIGNED RANK STATISTIC FOR TWO-FACTOR ANALYSIS OF VARIANCE
Statistics for Managers Using Microsoft Excel Chapter 10 ANOVA and Other C-Sample Tests With Numerical Data
Statistics for Managers Using Microsoft Excel Chapter 10 ANOVA and Other C-Sample Tests With Numerical Data 1999 Prentice-Hall, Inc. Chap. 10-1 Chapter Topics The Completely Randomized Model: One-Factor
Chemometrics. Matti Hotokka Physical chemistry Åbo Akademi University
Chemometrics Matti Hotokka Physical chemistry Åbo Akademi University Hypothesis testing Inference method Confidence levels Descriptive statistics Hypotesis testing Predictive statistics Hypothesis testing
Two-Factor Full Factorial Design with Replications
Two-Factor Full Factorial Design with Replications Dr. John Mellor-Crummey Department of Computer Science Rice University johnmc@cs.rice.edu COMP 58 Lecture 17 March 005 Goals for Today Understand Two-factor
One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups
One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups In analysis of variance, the main research question is whether the sample means are from different populations. The
Y it = µ + τ i + ε it ; ε it ~ N(0, σ 2 ) (1)
DOE (Linear Model) Strategy for checking experimental model assumptions Part 1 When we discuss experiments whose data are described or analyzed by the one-way analysis of variance ANOVA model, we note
STATISTICAL DATA ANALYSIS IN EXCEL
Microarra Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 5 Linear Regression dr. Petr Nazarov 14-1-213 petr.nazarov@crp-sante.lu Statistical data analsis in Ecel. 5. Linear regression OUTLINE Lecture
Analysis of variance
Analysis of variance 1 Method If the null hypothesis is true, then the populations are the same: they are normal, and they have the same mean and the same variance. We will estimate the numerical value
ANOVA: Analysis of Variation
ANOVA: Analysis of Variation The basic ANOVA situation Two variables: 1 Categorical, 1 Quantitative Main Question: Do the (means of) the quantitative variables depend on which group (given by categorical
Multiple Regression Methods
Chapter 1: Multiple Regression Methods Hildebrand, Ott and Gray Basic Statistical Ideas for Managers Second Edition 1 Learning Objectives for Ch. 1 The Multiple Linear Regression Model How to interpret
Table 1: Fish Biomass data set on 26 streams
Math 221: Multiple Regression S. K. Hyde Chapter 27 (Moore, 5th Ed.) The following data set contains observations on the fish biomass of 26 streams. The potential regressors from which we wish to explain
Stat 511 HW#10 Spring 2003 (corrected)
Stat 511 HW#10 Spring 003 (corrected) 1. Below is a small set of fake unbalanced -way factorial (in factors A and B) data from (unbalanced) blocks. Level of A Level of B Block Response 1 1 1 9.5 1 1 11.3
Chapter 15: Analysis of Variance
Chapter 5: Analysis of Variance 5. Introduction In this chapter, we introduced the analysis of variance technique, which deals with problems whose objective is to compare two or more populations of quantitative
Week 14 Comparing k(> 2) Populations
Week 14 Comparing k(> 2) Populations Week 14 Objectives Methods associated with testing for the equality of k(> 2) means or proportions are presented. Post-testing concepts and analysis are introduced.
Formal Statement of Simple Linear Regression Model
Formal Statement of Simple Linear Regression Model Y i = β 0 + β 1 X i + ɛ i Y i value of the response variable in the i th trial β 0 and β 1 are parameters X i is a known constant, the value of the predictor
Statistics For Economics & Business
Statistics For Economics & Business Analysis of Variance In this chapter, you learn: Learning Objectives The basic concepts of experimental design How to use one-way analysis of variance to test for differences
ECO220Y Simple Regression: Testing the Slope
ECO220Y Simple Regression: Testing the Slope Readings: Chapter 18 (Sections 18.3-18.5) Winter 2012 Lecture 19 (Winter 2012) Simple Regression Lecture 19 1 / 32 Simple Regression Model y i = β 0 + β 1 x
Econ 3790: Statistics Business and Economics. Instructor: Yogesh Uppal
Econ 3790: Statistics Business and Economics Instructor: Yogesh Uppal Email: yuppal@ysu.edu Chapter 14 Covariance and Simple Correlation Coefficient Simple Linear Regression Covariance Covariance between
ANOVA CIVL 7012/8012
ANOVA CIVL 7012/8012 ANOVA ANOVA = Analysis of Variance A statistical method used to compare means among various datasets (2 or more samples) Can provide summary of any regression analysis in a table called
Lecture 5: Linear Regression
EAS31136/B9036: Statistics in Earth & Atmospheric Sciences Lecture 5: Linear Regression Instructor: Prof. Johnny Luo www.sci.ccny.cuny.edu/~luo Dates Topic Reading (Based on the 2 nd Edition of Wilks book)
ANOVA Randomized Block Design
Biostatistics 301 ANOVA Randomized Block Design 1 ORIGIN 1 Data Structure: Let index i,j indicate the ith column (treatment class) and jth row (block). For each i,j combination, there are n replicates.
Chapter 12. ANalysis Of VAriance. Lecture 1 Sections:
Chapter 1 ANalysis Of VAriance Lecture 1 Sections: 1.1 1. ANOVA test is an extension of two sample independent t-test demonstrated how to compare differences of means between two groups. The t-test is
Stat 217 Final Exam. Name: May 1, 2002
Stat 217 Final Exam Name: May 1, 2002 Problem 1. Three brands of batteries are under study. It is suspected that the lives (in weeks) of the three brands are different. Five batteries of each brand are
Simple Linear Regression
Simple Linear Regression Reading: Hoff Chapter 9 November 4, 2009 Problem Data: Observe pairs (Y i,x i ),i = 1,... n Response or dependent variable Y Predictor or independent variable X GOALS: Exploring
Greg Larsen G. A. Larsen Consulting Ops A La Carte
Greg Larsen G. A. Larsen Consulting Ops A La Carte 2/23/2012 1 Discriminate among products Monitor performance of production process Manufacturing process improvement Specification setting 2/23/2012 2
One-way ANOVA. Experimental Design. One-way ANOVA
Method to compare more than two samples simultaneously without inflating Type I Error rate (α) Simplicity Few assumptions Adequate for highly complex hypothesis testing 09/30/12 1 Outline of this class
Dr. Maddah ENMG 617 EM Statistics 11/28/12. Multiple Regression (3) (Chapter 15, Hines)
Dr. Maddah ENMG 617 EM Statistics 11/28/12 Multiple Regression (3) (Chapter 15, Hines) Problems in multiple regression: Multicollinearity This arises when the independent variables x 1, x 2,, x k, are