STATISTICS 512, QUIZ #1, 9/27/12
READ BEFORE YOU BEGIN
This is a closed book, closed notes test; you should have only a pencil (no calculator, cell phone, et cetera). Please
do all work on this paper
STAT 512
2-Level Factorial Experiments: Basics
TWO-LEVEL FACTORIAL EXPERIMENTS (Basics)
Treatments dened by f binary bits
2f treatments
For example, fertilizer treatments dened by including:
N at
STAT 512
Complete Block Designs
1
RANDOMIZED COMPLETE BLOCK DESIGN (CBD)
As with CRD, t unstructured treatments
b blocks, each of size t, one unit/treatment/block
Pairs of units from the same block
STAT 512
Completely Randomized Designs
COMPLETELY RANDOMIZED DESIGNS (CRD)
For now, t unstructured treatments (e.g. no factorial structure)
Completely randomized means no restrictions on the
randomi
STAT 512
Factorial Treatments, Split-Plot Designs
FACTORIAL TREATMENT STRUCTURE
A treatment is dened by a combination of factors, each set to a
specic level.
Example:
Response: torque required to t
STAT 512
Latin Square Designs
LATIN SQUARE DESIGNS (LSD)
Like CBD, but arranged with 2 KINDS of blocks, crossed with
each other
Example:
machined parts are made t dierent ways (treatments)
b1 mach
STAT 512
Analysis
1
ANALYSIS: CRDs & ORTHOGONALLY BLOCKED DESIGNS
DIAGNOSTICS
Results depend on the assumption y M V N (XA A , 2 I)
Checks are based on r = y y = (I HA )y
Under HypA , E [r] = 0 V a
STAT 512
Introduction to Response Surface Methodology
RESPONSE SURFACE METHODOLOGY (RSM): A BRIEF INTRO
Statistical modeling strategies for dealing with processes:
y = (1 , 2 , ., k ) +
y = response
STAT 512
2-Level Factorial Experiments: Irregular Fractions
IRREGULAR TWO-LEVEL FRACTIONAL FACTORIALS
A major practical weakness of regular fractional factorial designs
is that N must be a power of 2
STAT 512
General Factorial Systems
GENERAL FACTORIAL SYSTEMS
f factors, each at p levels, with p a prime number
will talk about why prime comes into it later
Denote a particular treatment by its le
STAT 512
2-Level Factorial Experiments: Blocking
TWO-LEVEL FACTORIAL EXPERIMENTS (Blocking)
Some traditional notation:
Upper-case letters are associated with factors, or regressors of
factorial eects
STAT 512
2-Level Factorial Experiments: Regular Fractions
TWO-LEVEL FACTORIAL EXPERIMENTS (Fractional Factorials)
Bottom Line: A regular fractional factorial design consists of the
treatments in one
STATISTICS 512, QUIZ #2, 11/2/12
READ BEFORE YOU BEGIN
This is a closed book, closed notes test; you should have only a pencil (no calculator, cell phone, et cetera). Please
do all work on this paper
Homework 6, solution notes.
After getting the file into R as a matrix named "data",
the following makes a data vector y and +/- model matrix X:
y <- data[,6]
X0 <- matrix(1,nrow=32,ncol=1)
X1 <- 2*(da
STAT 512
Balanced Incomplete Block Designs
1
BALANCED INCOMPLETE BLOCK DESIGNS (BIBD) & RELATED
As with CBD b blocks, now each of size k < t units
N = bk
NOW all treatments cannot t in any one bloc