Stat 3520: Design of Experiments-1
Randomized Block Designs
Oct 21, 23 & 25 2013
Outline
Introduction
The model
Partitioning the Total Variance
ANOVA table
Need for Blocking
In CRD, we assume that there are no other inuential factors
on the response, othe
Stat 3520: Design of Experiments
Analysis of Variance
30 Sept 2013
1
What If There Are More Than
Two Factor Levels?
The t-test does not directly apply
There are lots of practical situations where there are
either more than two levels of interest, or the
Statistics 3520: Experimental Design I, Fall 2016
Assignment #2: Solutions
Q1. 15 pts. We want to show that SST = SSTrt + SSE. Notice that
a X
n
a X
n
X
X
2
(yij y. ) =
[(yij yi. ) + (
yi. y. )]2
i=1 j=1
=
i=1 j=1
a X
n
X
a X
n
a X
n
X
X
2
(
yi. y. ) +
(y
Statistics 3520: Experimental Design I, Fall 2016
Assignment #1: Due on October 5, 2016 (In class by 2:50pm)
Q1. 10 pts. (a) What is an experiment? What is an observational study? (b) What is the main
difference between an experiment and an observational
Supplementary Reading Material #2
Section 3.4. Simultaneous Confidence Intervals on Treatment Means
In section 3.3.3 we discuss finding confidence intervals on a treatment mean and on
differences between a pair of means. We also show how to find simultane
Statistics 3520: Experimental Design I, Fall 2016
Assignment #1: Solutions
Q1.10 pts. (a) An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. On the other hand, an experiment
deli
Statistics 3520: Experimental Design I, Fall 2016
Assignment #2: Due on October 17, 2016 (In class by 2:50pm)
15 pts. Let SST = ai=1 nj=1 (yij y. )2 , SSTrt =
Pa Pn
i. )2 . Show that SST = SSTrt + SSE.
j=1 (yij y
i=1
Q1.
P
P
Pa
i=1
Pn
yi.
j=1 (
y. )2 and
Statistics 3520: Experimental Design I, Fall 2016
R Code - Chapter 3
#
#R Code for the Analysis of Plasma Etching Data
etch.rate <- read.table("etchrate.txt", header = TRUE)
etch.rate
#for each treatment group find the averages:
grp.means <- with(etch.rat
Sept 28, 2016
Introduction to R
Introduction to R
STAT 3520: Fall 2016
Installing R on a Windows/Mac/Linux PC
R is a software environment for statistical analysis which is similar to S plus but free.
If you want to download R and install it on a (Availabl
Experimental Design 1
Lecture Notes 1: Introduction
Instructor: Candemir Cigsar
Memorial University
Department of Math & Stat
[email protected]
September 79, 2016
Keywords: Statistical Science, Data Collection, Observational Studies vs. Experiments, Basic Pr
Stat 3520: Design of Experiments-1
Analysis of Covariance
Nov 18, 2013
Local Control with a Measured Covariate
Randomization is a design technique used to control the
nuisance factors which are unknown and uncontrollable.
Blocking is a design technique us
Stat 3520: Design of Experiments-1
Analysis of Fixed Eect Model
Oct 9, 2013
Outline
Checking the Model Assumptions
Non-paremetric Tests
Treatment Comparisons
Parameter Estimates & Condence Intervals
Overall mean, = y.
i = yi . y ., i = 1, 2, . . . , a
A 1
Memorial University of Newfoundland
Stat 3520: Design of Experiments -1
(Fall 2013)
Fundamental Principles
Instructor
Asokan M Variyath
6 Sept 2013
Outline
Introduction
Examples
Some Terminology
Objectives of Experiments
Three Basic Principles
Replication
Stat 3520: Design of Experiments-1
Comparative Experiments
Sept 11, 2013
Outline
Hypothesis testing frame work
One sample tests
Two sample tests
Checking assumptions, validity
Hypothesis Testing Framework
Statistical hypothesis testing is a useful framewo
Stat 3520: Design of Experiments-1
Linear Regression
27 Sept, 2013
Outline
Introduction
Simple linear regression
Multiple linear regression
Introduction
In many problems, two or more variables are involved and
related, and one variable can be measured qui
Stat 3520: Design of Experiments-1
Analysis of Fixed Eect Model
Oct 7, 2011
Outline
ANOVA - An Example
R Code
Example
A product developer is investigating the tensile strength of a
new synthetic ber that will be used to make cloth for mens
shirts. Strengt
Stat 3520: Design of Experiments - 1
Experiments with Random Factors
Nov 20, 2013
Outline
Review of Previous Experiments
Experiments with Random Eects
Examples
One Factor Random Eect Models
Two Factor Random Eect Models
Examples & R Code
Review
CRD, RBD a
Stat 3520: Fall 2013
Latin Square Designs
Nov 4
1
Project
Group of two members
Identify a problem of interest
Define the problem and quantify if possible
Understand the process
Construct a Cause and Effect diagram, if
appropriate
Choose proper design
2
P
Statistics 3520: Experimental Design I: Fall 2013
Assignment #3
Due 20 Nov 2013
1. The ANOVA from a randomized block design experiment output is show below:
Source
D.F.
SS
MS
F
P-value
Treatment
4
1010.56
?
29.84
?
Block
?
?
66.765
?
?
Error
20
169.33
?
T
Stat 3520: Design of Experiments-1
LSD, Graco LSD and Missing Data
Oct 21, 2011
Nov 6, 2013
Outline
Latin Square Design
Replicated LSD
Graeco LSD
Example - Problem 4.21
An industrial engineer is investigating the eect of four assembly
methods (A, B, C,D)
Stat 3520: Design of Experiments-1
Balanced Incomplete Block Designs
Nov 13, 2013
Incomplete Block Designs
Blocking is a design technique used to control the nuisance
factors which are known and controllable and thereby decrease
the experimental error.
By
Statistics 3520
October 23, 2015
STAT 3520: Experimental Design I, Fall 2015
Midterm Exam - Solution Key
1. (10 points) (a) (2 points) An observational study observes individuals and measures
variables of interest but does not attempt to influence the res