Introductions, Designing Experiments
Descriptive Statistics
Elements of probability
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Monday, Tuesday, July 16-17, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic P
Homework 5 - solution, ST711
1. Design a 4 4 latin-square balanced for carryover:
Subject
1
2
3
4
1
1
4
3
2
Period
23
23
32
14
41
4
Subject
4
1
1
2
2
3
3
4
1
c
a
b
d
Period
23
db
bd
ca
ac
4
a
c
d
b
The above indicates that the treatment labels were assign
BU.510.601
Statistical Analysis
Chapter 4
Probability
Fall 2014
BU.510.601
Probability
1
Experiment, outcomes, sample space
Instatistics,wecollectdata(makeobservations).Thisprocesscan
beconsideredasanexperiment.
Potentialresultsofanexperimentarecalledoutc
Principles of experimental design
Representativeness, randomization, replication, blocking,
Representativeness - the extent to which experimental
material (units) is representative of the universe/population
about which inferences are to be made. Examples
Linear Models
Consider a simple experiment to study the way weld-strength, y
is related to velocity x of a rotating component of the weld.
120
120
140
BHH Table 10.5, welding strength
140
BHH Table 10.5, welding strength
y
q
100
q
q
q
qqq
q
q
80
q
60
80
q
ST711, Fall Semester, 2013, Quiz 1
Directions: There are 5 problems. Please show work. Name:
1. (21pts) The model Yij = + i + Eij is t to data from a completely randomized design
(CRD) using three dierent parameterizations (with constraints 1 = 0, i = 0 a
ST711, Fall Semester, 2012, Quiz 1
Directions: Show work. Partial credit is possible. Name:
1. (21 points) A completely randomized design experiment was run with three treatments. The
usual model will be considered
Yij = + i + eij
where i = 1, 2, 3 is an
Plackett-Burman Designs
1946, Biometrika
Developed for experiments to investigate effects of many
factors on anti-aircraft proximity fuse prototypes.
Fractional factorials for studying k = N 1 two-level
factors in N runs.
If N a power of 2, these are frac
Statistics 6401, Winter 2012
1
Modes of Convergence
Let Z1 , Z2 , ., Zn be a sequence of jointly distributed random variables dened on the same sample space .
Let Z be another random variable dened on this sample space . We now consider what is meant by Z
Latin Squares (G&G Ch.6)
RCBDs enable experimentalists to control for a suspected
source of variability among exp. units (like rows in a eld).
Latin Squares enable control of two sources of variability
(like rows and columns) among experimental units.
Exa
Do you prefer peanuts to be roasted or unroasted? Recall the example from page 14
of the 4th packet of notes (dated Friday, July 20, 2012). We used the central limit
theorem to approximate P (X 5) when X is a binomial random variable with n = 100
and p =
Testing the equality of two (normal) population means using JMP or SAS
(i) Independent samples, (ii), Matched samples
1. Independent samples example: green lynx spider lengths.
(a) Click on the SAS program to begin a session.
(b) Create a SAS dataset of s
HW7 solutions, ST711
1. In the four-factor unreplicated experiment below (taken from Montgomerys textbook),
(a) What is the run label for the last observation, y2222 = 96?
The label is abcd
(b) Fit the full-factorial model to estimate all fteen eects.
The
ST711, Fall Semester, 2013, Quiz 2
Directions: There are 5 problems. Please show work. Name:
1. An expt. measures y time-to-relief from asthma, in minutes. It randomizes t = 4 treatment
combinations of drug (A/B) and dose (L/H) to four patients, measured
ST711, Fall Semester, 2013, Quiz 1 - Solutions
1. The model Yij = + i + Eij is t to data from a completely randomized design (CRD) using
three dierent parameterizations (with constraints 1 = 0, i = 0 and = 0):
Standard
Parameter
Estimate
Error
t Value
Pr
Ch. 4 Probability: practice problems.
1.
2.
3.
4.
Three cards are drawn from a deck of 52 without replacement. What is the probability of
a. All 3 queens?
b. No queens?
c. Exactly 1 queen?
You draw 6 balls out of a jar without replacement. Balls are
ANOVA
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Thursday, July 26, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
ANOVA
Comparing several means (1 , 2 , . . . , mut ) using ANOVA
Data come from s
Split-plot Designs (G&G Ch. 7)
CRSPD
RCBSPD
Split-split plot (brief)
Strip plot
1 / 18
Split-plot designs - called for when it is harder to randomize
levels of one factor to units than another.
Split-plot" suggests agricultural expts. Consider a crossed,
Hypothesis Testing
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Tuesday, July 24, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
Hypothesis Testing
t -tests
t -tests
An example
Example: A study seek
Review
Regression
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Friday, July 27, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
Review
Regression
Topics weve covered
Designed experiments vs observati
Sampling Distributions
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Friday, July 20, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
Sampling Distributions
Some terminology for sampling theory
Popula
Probability (continued)
Random variables and probability distributions
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Tuesday, July 27, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
Probability (cont
Some special continuous distributions
Introduction to Statistics
Xiamen Academic Program
Dr. Jason A. Osborne
Friday, July 20, 2012
Dr. Jason A. Osborne
Introduction to Statistics Xiamen Academic Program
Some special continuous distributions
Continuously
Response Surface Designs
G&G Ch. 15
Central Composite Design
Factorial, Axial, Central design points
Quadratic model
Lack of t
Software
PROC RSREG
Documentation!
JMP
Central composite design with N factors.
factorial points:
each factor at level 1:
e.g. (
Response Surface Designs
G&G Ch. 15
Central Composite Design
Factorial, Axial, Central design points
Quadratic model
Lack of t
Software
PROC RSREG
Documentation!
JMP
Central composite design with N factors.
factorial points:
each factor at level 1:
e.g. (
Repeated Treatment Designs (G&G Ch. 9)
Period
1st
2nd
3rd
4th
(5th )
1
A 88
B 76
C 88
D 92
D
Carburetor
2
3
B 78 C 87.5
D 94 A 95.5
A 90 D 95.5
C 90 B 87.5
C
B
4
D 90.5
C 78.5
B 82.5
A 94.5
A
(Table 9.6) An expt with de-icers on carburators.
Four de-icer