21: One-Factor Experiments
"To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of." - Ronald Fisher."The world’s best statistical analysis cannot rescue a poorly planned experimental program." - Gerry Hahn."It (ANOVA) is probably the most useful technique in the field of statistical inference." – Doug Montgomery (author of ‘Design and Analysis of Experiments’).
Lecture outline: how to conduct experiments in which one-factor is changed at a time?
1. Comparing multiple treatments
Comparing two samples (t tests)
ANOVA: used for comparing more than two treatments
2. ANOVA example
One-factor three-level comparison example
F-distribution and F-statistic
Follow up t tests.
Statistical vs. Practical significance.
3. ANOVA model
ANOVA means model
ANOVA effects model
Visual tests to validate ANOVA assumptions
Primary reference for this lecture:
“The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling” by Raj Jain; Chapter 20: “One-Factor Experiments”.