Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level  simple interpretation,

Slides:



Advertisements
Similar presentations
Quantitative Methods Interactions - getting more complex.
Advertisements

Scatterplots and Correlation
Factorial Designs. Time in Instruction 1 hour per week 4 hours per week SettingIn-classPull-out A Simple Example RX 11 O RX 12 O RX 21 O RX 22 O Factor.
FACTORIAL ANOVA Overview of Factorial ANOVA Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random.
Chapter 6 The 2k Factorial Design
The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I:
Statistics for the Behavioral Sciences Two-Way Between-Groups ANOVA
Approaches to Data Acquisition The LCA depends upon data acquisition Qualitative vs. Quantitative –While some quantitative analysis is appropriate, inappropriate.
Interactions - factorial designs. A typical application Synthesis catalysttemperature Yield of product Yield=f (catalyst, temperature) Is there an optimal.
FACTORIAL DESIGNS F Terms for Factorials F Types of Factorial Designs F Notation for Factorials F Types of Effects F Looking at Tables of Means F Looking.
1 Chapter 6 The 2 k Factorial Design Introduction The special cases of the general factorial design (Chapter 5) k factors and each factor has only.
Experimental design and statistical analyses of data
Lecture 8 Last day: 3.1 Today: Next day: , Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as qualitative factors),
FACTORIAL DESIGNS What is a Factorial Design?Why are Factorials Useful?What is a Main Effect?What is an Interaction?Examples of Factorial Designs.
Chapter 7 Blocking and Confounding in the 2k Factorial Design
Complex Experimental Designs. INCREASING THE NUMBER OF LEVELS OF AN INDEPENDENT VARIABLE Provides more information about the relationship than a two level.
1 Chapter 7 Blocking and Confounding in the 2 k Factorial Design.
Lecture 10 Comparison and Evaluation of Alternative System Designs.
Review of the fundamental concepts of probability Exploratory data analysis: quantitative and graphical data description Estimation techniques, hypothesis.
Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 1 Factorial Experiments Text reference, Chapter 5 General principles of factorial experiments.
IE 405 QUALITY MANAGEMENT -2k factorial experiments -Reliability
Unit 2 Present Progressive and Simple Present. Unit 2 Present Progressive and Simple Present 2 Present Progressive.
A P STATISTICS LESSON 3 – 2 CORRELATION.
COMPLEX EXPERIMENTAL DESIGNS © 2012 The McGraw-Hill Companies, Inc.
Design of Engineering Experiments Part 4 – Introduction to Factorials
1 The General Factorial Design Two-factor factorial design General case: Factor A – a levels Factor B – b levels … n replicate (n  2) Total observations:
Design of Engineering Experiments Part 5 – The 2k Factorial Design
1 Chapter 3: Screening Designs 3.1 Fractional Factorial Designs 3.2 Blocking with Screening Designs.
Two-Way Between Groups ANOVA Chapter 14. Two-Way ANOVAs >Are used to evaluate effects of more than one IV on a DV >Can determine individual and combined.
DOX 6E Montgomery1 Design of Engineering Experiments Part 4 – Introduction to Factorials Text reference, Chapter 5 General principles of factorial experiments.
Formula? Unit?.  Formula ?  Unit?  Formula?  Unit?
Lecture 3.11 © 2014 Michael Stuart Design and Analysis of Experiments Lecture Review of Lecture 2.2 –2-level factors –Homework A 2 3 experiment.
Design Of Experiments With Several Factors
Chapter 11 Correlation and Simple Linear Regression Statistics for Business (Econ) 1.
1 The 2 k-p Fractional Factorial Design Text reference, Chapter 8 Motivation for fractional factorials is obvious; as the number of factors becomes large.
SWBAT: Measure and interpret the linear association between two variables using correlation. Do Now: You have data for many years on the average price.
The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I:
You can calculate: Central tendency Variability You could graph the data.
1 Forecasting/ Causal Model MGS Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert.
1 Simulation Scenarios. 2 Computer Based Experiments Systematically planning and conducting scientific studies that change experimental variables together.
PowerPoint presentation to accompany Research Design Explained 6th edition ; ©2007 Mark Mitchell & Janina Jolley Chapter 12 Factorial Designs.
PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Chapter 11 Factorial Designs.
1 Design of Engineering Experiments – The 2 k Factorial Design Text reference, Chapter 6 Special case of the general factorial design; k factors, all at.
12b - 1 © 2000 Prentice-Hall, Inc. Statistics Multiple Regression and Model Building Chapter 12 part II.
Engineering Statistics Design of Engineering Experiments.
Diploma in Statistics Design and Analysis of Experiments Lecture 2.21 © 2010 Michael Stuart Design and Analysis of Experiments Lecture Review of.
Variability Mechanics. The Average Deviation Another approach to estimating variance is to directly measure the degree to which individual data points.
BUS 308 Week 4 Quiz Check this A+ tutorial guideline at 1. With reference to problem 1, what.
Design of Experiments (DOE)
CHAPTER 3 Describing Relationships
Chapter 7 Blocking and Confounding in the 2k Factorial Design
Quantitative Methods Simple Regression.
مبررات إدخال الحاسوب في رياض الأطفال
Confounding the 2k Factorial Design in Four Blocks
Design & Analysis of Experiments 8E 2012 Montgomery
بسم الله الرحمن الرحیم.
مديريت موثر جلسات Running a Meeting that Works
Complex Experimental Designs
21twelveinteractive.com/ twitter.com/21twelveI/ facebook.com/21twelveinteractive/ linkedin.com/company/21twelve-interactive/ pinterest.com/21twelveinteractive/
Additional notes on random variables
Factorial Design.
Additional notes on random variables
Unit 2 Quantitative Interpretation of Correlation
The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch.
DESIGN OF EXPERIMENTS by R. C. Baker
Correlation Coefficient
14 Design of Experiments with Several Factors CHAPTER OUTLINE
DOE Terminologies IE-432.
Presentation transcript:

Factorial designs at two levels Ch. 5

Factorial Design Two levels All possible combinations. Two factors and variables. Two level  simple interpretation, few runs per factor Quantitative or qualitative factors Factors can interact (nonzero correlations!)

Example Three factors on clarity of film (wax formula): A: emulsifier, B: emulsifier, C: catalyst concentration. Each factor at two levels: 2 3 factorial design.

Example 1

Example 2

Example 3

Interactions: TK=(33-13)/2 =10 TK=( )/2 =10 TCK=[(35-31)/2- (14-12)/2]/2 =0.5 CKT=[(-3+4)/2- (-7+6)/2]/2 =0.5

Example 3 TCK=( )/4=0.5

Example 3

if each factor was replicated a different number of times: Each estimated effect is a difference between two averages: v(effect)=(1/8+1/8)s 2 =8/4=2 Standard error=sqrt(2)=1.4

Ejemplo 3

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.