Two-way layout design: experiment about
survival times of animals
Background:
An experiment was conducted to investigate the eects of two factors
on the survival times of animals.
In the experiment, a group of four animals were randomly allocated to
each
Summary of Ch4: Fractional factorial experiments at two levels
In this chapter, we mainly consider fractional factorial experiments at two levels.
How to generate a 2kp design?
Let q = k p.
Step 1: choose q factors to generate 2kp = 2q runs. These q fact
Assignment #1 (Due June 7 in the class)
1. Consider the following model for one-way layout:
yij = i + ij , ij N (0, 2 ), i = 1, . . . , k, j = 1, . . . , n.
We rewrite the above model as
yij = + i + ij , ij N (0, 2 ), i = 1, . . . , k, j = 1, . . . , n.
I
Stat 430/830: Analysis of Variance 430/830: Analysis
Motivation Motivation
Methods for comparing two populations, or two formulations or two levels of a factor are studied in introductory courses of statistics (e.g., comparison of two means). However, in
Chapter 8(a) Solutions
8.3. Consider the plasma etch experiment described in Example 6.1. Suppose that only a one-half fraction of the design could be run. Set up the design and analyze the data. Because Example 6.1 is a replicated 23 factorial experiment
Chapter 8(b) Solutions
8.5. Continuation of Problem 8.4. Suppose you have made the eight runs in the 25-2 design in Problem 8.4. What additional runs would be required to identify the factor effects that are of interest? What are the alias relationships i
Stat 430/830: Analysis of Variance
Lecture September 26, 2012
Factorial Designs
Factorial Experiments
General principles of factorial
experiments
The two-factor factorial with fixed
effects
The ANOVA for factorials
Extensions to more than two factors
Chapter 13 Solutions
13.1. A textile mill has a large number of looms. Each loom is supposed to provide the same output of cloth per minute. To investigate this assumption, five looms are chosen at random and their output is noted at different times. The
Chapter 6 Solutions
6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are
Stat 430/830
Lecture October 18, 2016
Outline
Blocking in factorial designs
Confounding
Partial confounding
Fractional Factorials
Definition
How to construct them
Aliasing
Blocking in the 2k Factorial Design
If it is possible to include all the fac
Tutorial September 27, 2016
4.2. Consider the single-factor completely randomized experiment shown in Problem 3.4.
Suppose that this experiment had been conducted in a randomized complete block design, and
that the sum of squares for blocks was 80.00. Mod
Solution Chp. 7 October 24, 2016
7.1 Consider the experiment described in Problem 6.1. Analyze this experiment assuming that each replicate
represents a block of a single production shift.
Source of
Sum of
Degrees of
Mean
Variation
Squares
Freedom
Square
Solution Chap. 5 - September 29, 2016
5.2. The following output was obtained from a computer program that performed a two-factor ANOVA on a
factorial experiment.
Two-way ANOVA: y versus A, B
Source
DF
SS
MS
F
P
A
1
?
0.0002
?
?
B
?
180.378
?
?
?
Interacti
Stat 430/830
Unrestricted Mixed Models
Nested Designs
Lecture November 10, 2016
Outline
Unrestricted Mixed Model
Review rules for E(MS)
Nested Designs
Two Random Factors
Suppose we have a two factor design with factor A fixed and
factor B random. The r
Solution Chap 6 October 17, 2016
6.12. An article in the AT&T Technical Journal (March/April 1986, Vol. 65, pp. 39-50) describes the application of
two-level factorial designs to integrated circuit manufacturing. A basic processing step is to grow an epit
Solutions Chp 8 - October 27, 2016
4
8.6 In the Example 6.6, a 2 factorial design was used to improve the response rate to a credit card marketing offer.
Suppose that the researchers had used the 2 fraction factorial design with I=ABCD instead. Set up the
Tutorial September 13, 2016
3.4.
A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value.
One-way ANOVA
Source
DF
SS
MS
F
P
Factor
?
?
246.93
?
?
Error
25
186.53
?
Total
29
1174.24
Completed table is:
By difference D
Stat 430/830
Randomized Block Designs
Factorial Designs
Lecture September 22, 2016
Randomized Complete Block Designs
RCBD: when each block contains all treatment and treatments are
randomized within block
Statistical Model
Model (Assuming blocks is a Rand
Stat 430/830: Analysis of Variance
Lecture September 8, 2016
Introduction
Methods for comparing two populations, or
two formulations or two levels of a factor are
studied in introductory courses of statistics
(e.g., comparison of two means).
However, in
STATS 430 / 830 EXPERIMENTAL DESIGN COURSE OUTLINE
Instructor: Fernando Camacho Office M3 4102
Office hours: 8:30 am 10:00 am Tuesdays and Thursdays
Textbook: Design and Analysis of Experiments, 8th edition, by D.C. Montgomery,
John Wiley & Sons, New York
Stat 430/830
Randomized Block Designs
Factorial Designs
Lecture September 29, 2015
Outline
Estimable equations
Factorial design with one replication
Goodness of fit test
Blocking in factorial designs
Three factors factorial design
Estimable Equations
Note
Stat 430/830
Lecture October 13, 2016
Outline
Prediction SS
A single replicated or unreplicated 2k
design
Optimal Design
Addition of center point & augmented
designs
Prediction Sum of Squares
In matrix notation the model can be expressed as
Ynx1 X nxp
STATS 430/830 - Pop Quiz N. 2
November 20, 2016
NAME :_
NUMBER :_
COURSE: _
An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in
hours) of a machine tool. Two levels of each factor are chosen,
Stat 430/830: Analysis of Variance
Lecture October 6, 2016
Outline
Sample size for multifactorial
designs
2k Factorial Designs
Estimation using contrast
Regression and response surface
A single replicated design
Determining Sample Size
An engineer ne
Solution Problems Chapter 3
3.3.
A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value.
One-way ANOVA
Source
DF
SS
MS
F
P
Factor
3
36.15
?
?
?
Error
?
?
?
Total
19
196.04
Completed table is:
One-way ANOVA
Source
DF
Stat 430/830
Lecture September 20, 2016
Outline
Randomized block designs
Nuisance factor
Controllable and uncontrollable factors
Blocking
Randomization restriction
Interactio
Latin square designs
Example
Consider an experiment to
compare four hormo
Stat 430/830
Random Effects
Lecture November 1, 2016
Outline
Review one-factor random effect model
Review estimation of variance components
Two factor factorial with random factors
The two-factor mixed model
Multi-factorial designs with random factors
Exp
Stat 430/830
Lecture October 20, 2016
Outline
Continuation of Fractional Factorials
Aliasing review
How to construct them
Resolution of a Designs (III, IV, V)
Blocking in Fractional Factorials
One-Half Fraction of 2k
One
If the + are selected, then I
Stat 430/830
Lecture September 15, 2016
Outline
Non-parametric analysis of one-factor
designs
Variance stabilization transformations
Random effects model
Sample size
Nonparametric Methods For
Comparing K Treatments
Kruskal Wallis Test
Used to test the
Stat 430/830: Analysis of Variance
Lecture September 13, 2016
Outline
Model and estimation
ANOVA as Regression
Model Checking
Treatment comparison
1
Analysis of Variance
The main idea of ANOVA is to compare the
between and the within variability
If betw