STA2004F: Design of experiments


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


  • 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 micro-array 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 Graeco-Latin 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 cross-over designs
    • cross-over 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 Graeco-Latin 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 unit-treatment 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 non-central $\chi^2$ 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 t-test 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 case-control study of genetic causes of disease described in Prentice and Qi, Biostatistics 7, 339--354.
    • Understanding the mechanisms: causation, intention to treat, baseline and intermediate variables
    • Statistical Analysis: randomization as a basis for analysis (called design-based 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.