Statistics 101A
Homework one
Professor Esfandiari
All of the relevant data sets for this homework are posted on week one of CCLE
Problems one to six are review.
Problem one: Download
Chapter 8
Two-Level Fractional Factorial Designs
Part 3
k-p
The General 2
Fractional Factorial Design
A 2k fractional factorial design containing 2k-p
runs is called a 1/2p fraction of the 2k design,
or 2k-p fractional factorial design.
These designs requ
Review
Chapters 13 and 14
Different Models
Fixed effects model: the levels of the factors
used by the experimenter were the specific
levels of interest
Random effects model: the factors levels are
chosen at random from a larger population of
possible leve
Q&A for Exam 2
Chapter 7 Slides Example starting on slide 3
What is the formula for SSBlocks?
This is the same formula from the anova table from blocking in a factorial design in
Chapter 5 Part 4 lecture slides (slide 20). See below. a is the levels
Chapter 4
Experiments with More than One Factor
Part 2
Randomized Complete Block Designs
- Review
We have a randomized complete block
design when we can sort units into blocks,
then randomly assign treatments within each
block.
Each unit gets one treatmen
Group Project
Group Project Tips
How to collect data?
Group Project Tips
How to collect data?
Group Project Tips
How to collect data?
Group Project Tips
How to collect data?
Group Project Tips
Sometimes
Group Project Tips
In your contacts, you will find e
Chapter 6
The 2k Factorial Design
Part 1
Introduction
In Chapter 5 we were introduced to the general
methods for the analysis of factorial designs.
An important special case of the general
factorial design is that of k factors, each at only
two levels.
Th
Announcements
HW 2 due today at 5pm on CCLE!
HW 3 will be posted later today.
Next week you will have your first miniassignment for the group project (submit on
CCLE).
The Islands
The Islands
Chapter 4
Experiments with More than One Factor
Part 3
Latin Sq
Announcements
HW 3 is posted on CCLE. Due Friday at 5pm.
Group project mini-assignment is posted on
CCLE. Due Friday at 5pm.
For midterm: One handwritten cheat sheet
with formulas is allowed. NO graphing
calculators allowed.
Group Project Mini Assignment
Chapter 7
Blocking and Confounding
in the 2k Factorial Design
Introduction
In Chapter 5, we were introduced to blocking
in factorial designs.
In Chapter 7, we will focus on some special
techniques for blocking in the 2k factorial
design.
Example
Consider
Chapter 14
Nested and Split-Plot Designs
The Two-Stage Nested Design
In some experiments, the levels of one factor
are similar but not identical for different levels
of another factor.
Hence we have a nested design with the
levels of one factor nested und
Announcements
HW 3 and mini-assignment 1 due today at
5pm.
No homework due next Friday.
Exam I next Friday in class.
Chapter 5
Introduction to Factorial Designs
Part 3
Example
Lets consider the battery example from earlier:
Factor A: Material
Factor B: Te
Chapter 5
Introduction to Factorial Designs
Part 4
Example
A soft drink bottler is interested in obtaining more
uniform fill heights in the bottles produced by his
manufacturing process. The filling machine
theoretically fills each bottle to the correct t
Chapter 8
Two-Level Fractional Factorial Designs
Introduction
k
As the number of factors in a 2 factorial design increases, the
number of runs required for a complete replicate of the design
rapidly outgrows the resources of most experimenters.
For exampl
Group Projects
Projects
State your hypothesis.
Not just we want to study the effects of
sports drink on running speed but
we believed that drinking the sports drink
would improve time on a 20 m sprint. We
hoped that times would improve by at least
.5 s
Statistics 101B
Professor Esfandiari
Assignment one
Winter 2016
Assignment One Part One (Group one)
Part 1. (Group members one and two are responsible for this part)
Professor Hanson teaches an organic
Statistics 101B
Statistical Reasoning for Social Sciences
University of California Los Angeles (UCLA)
DEPARTMENT OF STATISTICS
COURSE SYLLABUS (TENTATIVE)
Course:
STAT 101B: INTRODUCTION TO DESIGN AND ANALYSIS OF EXPERIMENTS
Lecture Meeting:
Lecture 1: TR
Chapter 11
Design & Analysis of Experiments
8E 2012 Montgomery
1
Chapter 11. Response Surface
Methods and Designs
Primary focus of previous chapters is factor
screening
Two-level factorials, fractional factorials are widely
used
Objective of RSM is opt
Solutions for HW8
11.22
(a)
[ ] ( ) X y
= (X X ) X E [y ]
= (X X ) X (X + X )
= (X X ) X X + (X X ) X X
= E X' X
E
1
1 1
'
1
1
'
1
1
'
1
1
'
1
1
'
1
1
1
1
'
1
1 1
'
1
2 2
1
'
1
1 1
1
'
1
2 2
= 1 + A 2
(
where A = X1' X1
1
)
X1' X 2
(b) In this situati
Solutions for HW5
5.1
(a)
(b) 3 levels.
(c) 3 replicates.
(d) Only factor B is significant; factor A and the two-factor interaction are not significant.
5.4
(a) The depth (A) and feed rate (B) are significant, as is the interaction (AB).
(b) The residual
Solutions for HW2
2.10
(a) t0=-11.5/SE=-1.88 so SE=-11.5/(-1.88)=6.12.
(b) Two-sided test for a t0 = -1.88 is a P-value of 0.0723.
(c) Accept the null hypothesis, there is no difference in the means.
(d) -11.5 +/- (2.064)*(6.12)=(-24.13, 1.13)
Solutions for HW6
6.17 (a)
(b) = Intercept+38.475! -33.76! -25.66!"
6.24 (a) The normal or half-norm probability plot of effects is difficult to interpret. Since we have replicates, we can look at
the ANOVA table, which identifies all three two factor int
Solutions for HW3
3.4
3.5 This is not a designed experiment, and it does not establish a cause-and-effect link between chocolate
consumption and depression. An experiment could be run by giving a group of people a defined amount of
chocolate s
Stat 101B HW8 Solution
2. (a) This is a randomized block design experiment. The two researchers form two blocks.
(b) The defining relation is I=ABCDE and the resolution is V.
(c) The alias structure is
I = ABCDE, A = BCDE, B = ACDE, C = ABDE, D = ABCE, E
Solutions for HW7
7.21
8.11
(a)
(b) Complete defining relation: I=BDE=ACE=ABCD.
The aliases are
(c)
(d) The analysis of variance table is shown below. Part (b) shows that AB and AD are aliased with other factors. If all
two-factor and three factor interac