Stat 641 (Spring 2012) Peter F. Craigmile
Fruity reproduction and longevity, revisited
The one-way analysis of variance (ANOVA)
The fruity expt is an example of a completely randomized
Reading: Dean and Voss [1999], Sections 3.5
design (CRD).
Fruity rep
Stat 641 (Spring 2012) Peter F. Craigmile
Multiway analysis of variance:
Balanced experiments, and single replicates
Equations for the balanced case
Reading: Dean and Voss [1999], Sections 7.3, 7.5
Equations for balanced multiway ANOVA.
Calculating the
Stat 641 (Spring 2012) Peter F. Craigmile
What is a contrast?
Contrasts
Reading: Dean and Voss [1999], Sections 4.14.3
We previously dened a contrast to be a linear combination
of the treatment eects
v
What is a contrast?
c i i ,
=
i=1
Examples of cont
Stat 641 (Spring 2012) Peter F. Craigmile
Checking assumptions
Flowering of cyclamen
In an experiment on induction of owering of cyclamen, plants of
Reading: Dean and Voss [1999], Chapter 5.
4 varieties of cyclamen were subject to a combination of 6 tem-
# =
# An example CRD randomization
# Stat 641
# Peter Craigmile, [email protected], Mar 2012.
# =
# How many observations per treatment level do we require?
r.i <- c(5, 2, 3)
# 'n' is the total number of expt units
n <- sum(r.i)
# 'v' is number of treatm
Stat 641 (Spring 2012) Peter F. Craigmile
Incomplete block designs
Dening incomplete block designs
Reading: Dean and Voss [1999], Sections 11.1-11.4, 11.10
Incomplete block designs
In the complete randomized block design, each block
contains all possibl
Stat 641 (Spring 2012) Peter F. Craigmile
Introduction
More random eects, and mixed eects models
Reading: Dean and Voss [1999], Sections 17.617.10
Two examples: Penicillin data and TV tubes
Two way random eects models
So far we have t the one way rando
Stat 641 (Spring 2012) Peter F. Craigmile
Row-column designs and Latin squares
Reading: Dean and Voss [1999], Sections 12.112.5
Row-column designs and Latin squares
Example: Fertilizing potatoes
Dening a standard Latin square
Dening a Latin square up
Stat 641 (Spring 2012) Peter F. Craigmile
A motivating example: ANOVA
Multiple comparisons
Reading: Dean and Voss [1999], Sections 4.4 and 4.5.
A motivating example: ANOVA
Two dierent error rates (individual vs. experimentwise)
Controlling the individu
Stat 641 (Spring 2012) Peter F. Craigmile
The completely randomized design (CRD)
Reading: Dean and Voss [1999], Sections 3.13.4
The completely randomized design (CRD)
How to actually randomize treatments to subjects
A model for the completely randomize
1
Principles and Techniques
1.1
1.2
1.1
Design: Basic Principles and Techniques
Analysis: Basic Principles and Techniques
Design: Basic Principles and Techniques
1.1.1
The Art of Experimentation
One of the rst questions facing an experimenter is, How many
9
Analysis of Covariance
9.1 Introduction
9.2 Models
9.3 Least Squares Estimates
9.4 Analysis of Covariance
9.5 Treatment Contrasts and Condence Intervals
9.6 Using SAS Software
Exercises
9.1
Introduction
In Chapters 37, we used completely randomized desi
Stat 641 (Spring 2012) Peter F. Craigmile
Examinable material: before the midterm
Final summary
A sample experiment, and two sample procedures
The nal exam will be held in our regular classroom from
9.30am - 11.30am on Tue 5 June.
The exam will cover a