Design and analysis of experiments

This is a work in progress. It will be completed by the end of the day on 04 January 2016.

Learning outcomes

• Learn the basic terminology of experiments: responses, factors, outcomes, real-world units vs coded units, confounding
• Analyze and interpret data from an experiment with 2, 3 or more factors by hand
• Use R to do the analysis, and interpret the various plots, such as the Pareto plot
• Analyze and interpret data from an experiment with 3 or more factors
• Recognize when to use a fractional factorial, to go mostly the same results as from a full factorial
• Understand when to use screening experiments
• Use the concepts of response surface methods to systematically reach an optimum
• What you can do when you make a mistake, or hit against constraints.

Extended readings/practice

• Don't accept what is often believed to be true: always experiment.
• In case you've been wondering how the trade-off table was constructed.
• You must cover steps 16, 21 and 22 of the detailed software tutorial to master this section of the course.
• Some extra videos about experimentation, as applied in this course:
  1. Interview 01: Experiments in a non-engineering context, a Hamilton baker: Made for you by Madeleine (05:23)
  2. Interview 02: Dr. Soo Chan Carusone talks about experiments in a medical context (07:16)
  3. Interview 03: David Latulippe and his student Jeff, talk about water treatment experiments (05:46)
  4. Interview 04: An interview with Dr. Joe Kim at McMaster University (10:54)

Resources

• Class notes 2015 This is a large file, at 219 Mb. You might prefer the smaller set of notes from 2014, but they are less comprehensive.
• Class notes 2014
• Textbook, chapter 5
• What experiments are you going to do for your course project? What are the factors, what are the levels? How did you chose your levels? What is your response? How will you measure your response?
• Quizzes (with solutions): attempt these after you have watched the videos

Tasks to do first	Quiz	Solution
Watch videos 1A, 1B, 1C and 1D	Quiz	Solution
Watch videos 2A, 2B, 2C, 3A and 3B (note!)	Quiz	Solution
Watch videos 2D, 3C and 3D and 4A (note!)	Quiz	Solution
Watch videos 4B, 4C, 4D, and 4E	Quiz	Solution
Watch videos 4F, 4G, 4H, 5A and 5B	Quiz	Solution
Watch videos 5C, 5D, 5E and 5F	Quiz	Solution

Class videos from prior years

Videos from 2015

• 00 - Introduction video for the Coursera online course [01:56]
• 1A - Why experiments are so important [07:48]
• 1B - Some basic terminology [06:37]
• 1C - Analysis of your first experiment [09:00]
• 1D - How NOT to run an experiment [03:07]
• 2A - Analysis of experiments in two factors by hand [13:37]
• 2B - Numeric predictions from two-factor experiments [07:25]
• 2C - Two-factor experiments with interactions [15:15]
• 2D - In-depth case study: analyzing a system with 3 factors by hand [17:28]
• 3A - Setting up the least squares model for a 2 factor experiment [05:46]
• 3B - Solving the mathematical model for a 2 factor experiment using software [08:46]
• 3C - Using computer software for a 3 factor experiment [08:37]
• 3D - Case study: a 4-factor system using computer software [09:03]
• 4A - The trade-offs when doing half-fraction factorials [13:20]
• 4B - The technical details behind half-fractions [09:38]
• 4C - A case study with aliasing in a fractional factorial [06:38]
• 4D - All about disturbances, why we randomize, and what covariates are [11:00]
• 4E - All about blocking [09:21]
• 4F - Fractional factorials: introducing aliasing notation [12:00]
• 4G - Fractional factorials: using aliasing notation to plan experiments [10:45]
• 4H - An example of an analyzing an experiment with aliasing [09:50]
• 5A - Response surface methods - an introduction [06:13]
• 5B - Response surface methods (RSM) in one variable [18:40]
• 5C - Why changing one factor at a time (OFAT) will mislead you [05:33]
• 5D - The concept of contour plots and which objectives should we maximize [03:40]
• 5E - RSM in 2 factors: introducing the case study [19:20]
• 5F - RSM case study continues: constraints and mistakes [13:45]
• 5G - RSM case study continues: approaching the optimum [17:05]
• 06 - Wrap-up: the course in review, multiple objectives, and references for the future [08:10]

Videos from 2014

See the webpage from 2014

Videos from 2013

See the webpage from 2013

Software codes for this section

Code to build a model for a 2-factor system

Try this code in a web-browser

T <- c(-1, +1, -1, +1)       # centered and scaled temperature
S <- c(-1, -1, +1, +1)       # centered and scaled substrate concentration
y <- c(69, 60, 64, 53)       # conversion is the response, y
mod <- lm(y ~ T + S + T * S) # this works, but is more typing
mod <- lm(y ~ T*S)           # preferred method
summary(mod)