
STA2004F: Design of experiments
Announcements
January 17:
Solutions to the final homework, although I haven't had a chance to do the bonus question yet.
December 6:
Final homework is here.
It is due on December 21.
Data for Question 1.
Data for Question 5.
Homework 3
Sketch of solutions
Lectures
 December 5, 2006
 Solutions to HW 2
 Details on analysis of variance for split plots
 Handout on
mixed and random effects models for factorial experiments
 Two handouts from the literature that both used split plot designs: please drop by to get copies if you missed class
 Topics not covered: response surface designs, cost of
experimentation (choice of sample size), optimal designs,
Taguchi methods, designs for microarray analysis
 November 28, 2006
 split plot experiments: one whole plot factor and one subplot factor
 analysis of variance and comparison of means
 fractional factorial experiments in split plot designs
 November 21, 2006
 Algebra of 2 level factorials; contrast group and treatment group
 Fractional factorials and alias sets: half and quarter fractions
 Example: Section 5.7 of book
 Confounding effects with blocks, partial confounding
 Confounding main effects > split plot experiments
 November 14, 2006
 Further thoughts on HW 2
 Factorial treatment structure with 2 levels for each factor
 Estimation of main effects and interactions
 Table of signs
 Example of a 2^4 factorial design and its analysis
 Use of higher order interactions to estimate error
 A replicated 2^3 experiment embedded in the 2^4 experiment
 November 7, 2006
 suggestions re HW 2
 factorial treatment structure
 interpretation of interaction
 Example K from CS, see also Ch 5 of CR
 October 24, 2006
 Latin squares and GraecoLatin squares: reminder of definitions
 analysis of Latin squares using Set 9 from Cox and Snell
 the error sum of squares composed of various interactions
 an alternative analysis correcting for days and time of day within each of the two replicates
 (sets of) Latin squares in which each treatment follows each other treatment the same number of times can be used for crossover designs
 crossover designs use the same experimental units over time
 gives strong control of block (subject) effects, but needs care
 washout periods can sometimes ensure that order of treatments does not affect response
 if not successful then carry over effects need to be estimated from the data; some details outlined in 4.3.2. and 4.3.3
 balanced incomplete block designs: more treatments than units per block
 treatment means need to be adjusted for block means
 October 17, 2006
 Randomization in design
 Randomization in inference: justifies usual linear model; randomization distribution of summary statistics (handout from Hinkelmann and Kempthorne, Vol 1).
 Analysis of covariance: adjustment for baseline variables or other covariates; least squares estimates and their mean and variance;
handout
 Efficiency of randomized block design relative to CR design;
handout
 Latin squares: definition and existence; pairs of orthogonal Latin squares
 Article on Latin squares by Ivars Peterson
 Article on Sudoku and Latin squares by Ivars Peterson
 Demonstration of completion of Latin squares (reference from Peterson's first article)
 Picture of a 10 by 10 GraecoLatin square
 October 10, 2006
 Modified matched pairs analysis: inclusion of pairs in which both units receive T or both units receive C (\S 3.3.2)
 Completely randomized design: linear model and analysis (p.23)
 Randomization: a means of reducing bias, the unittreatment additivity assumption, causal effects
 Randomization analysis (\S 2.2): justifies the usual linear model
 Handout: Current list of errata for textbook.
 October 3, 2006
 Analysis of randomized block designs: analysis of variance table, comparison of treatment means, orthogonal contrasts for ordered factors, partitioning treatment sum of squares
 Multiple comparisons of a set of treatment means using: Bonferroni, Tukey's studentized range test (references coming)
 The noncentral $\chi^2$ distribution
 The error sum of squares in RB design is an interaction SS between treatments and blocks
 Handout on the construction of orthogonal polynomials (from Montgomery)
 September 26, 2006
 Homework 1 is due on October 10.
 A randomized block design with just two treatments is a matched pair
design; we developed the usual ttest based on difference by transforming the responses in each pair to sums and differences
 The randomization analysis of the matched pair design will follow after we cover Chapter 2
 Model based analysis of the randomized block design, using the conventional linear model: estimation of parameters under constraints, estimation of residual variance via the analysis of variance table, linear contrasts and their estimates and estimated variances
 September 19, 2006
 Some definitions: experiments, observational studies, units, treatments, response
 Series of experiments (Section 1.8): phase 1, 2 and 3 clinical trials (a good reference is the Cancer Research UK website; evolutionary operation/response surface methodology/Taguchi methods/robust parameter design; variety trials

A 3 stage design for a casecontrol study of genetic causes of disease described in Prentice and Qi, Biostatistics 7, 339354.
 Understanding the mechanisms: causation, intention to treat, baseline and intermediate variables
 Statistical Analysis: randomization as a basis for analysis (called designbased in sample surveys) and model based analysis (called population models in sample surveys)
 Features of a good experiment: Ch. 1 of Planning of Experiments by D.R. Cox
 Introduction to randomized block designs (Section 3.4 of CR)
 Next week: please read Chapter 3 of CR; we will discuss Ch 3 and then go to Ch 2.
 September 12, 2006
here is a link to the MS of chapter 1.
