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 and hand it in at the end of the class period. You may
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 level i (1 or 2) (nitrogen)
P at level j (1 or 2) (pho
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 are thought to be more alike
or more homogeneous, than
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
randomization of units to treatments (except for sample sizes
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 tighten nut
Treatments: mechanical conditions, determin
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 machinists may also have an eect (type 1 blocks)
b2 lathes
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 ar[r] = 2 (I HA )
1
e.g. for CRD, HA = diag( n1 Jn1 n1
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
s = factors, independent variables, now explicitly con
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:
8
16
32
64
128
(large gaps)
A broader class of 2-lev
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 levels as:
x = (x1 , x2 , x3 , ., xf ) , with each xi = 0
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, e.g.
ABC x1 x2 x3
The treatment combination associa
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 block of a blocked full 2f experiment
Example: f = 5,
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 and hand it in at the end of the class period. You may
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*(data[,1:5]-1)-1
X2 <- matrix(0,nrow=32,ncol=10)
i <- 0
fo
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 block
Examples: b = 4, k = 3, t = 4
Usually a bad idea
Usu