Two way ANOVA

• Administrivia:
  • Data analysis is due a week from Thursday

Motivating example

• Suppose you collect data twice on the individual
• A "pre-test" and a "post-test", left-vs-right
• Example: sensitivity training, education, nutrition,
• detailed example: Suntan lotion
  • Compare a new formulation of suntan lotion with an existing one
  • Plot histogram of "new suntan lotion" (Why can't you learn anything from this?)
  • Plot histogram of "old suntan lotion" (Now why can't you learn anything?)
  • The two histograms overlap significantly--not much difference
    • Aside: which comparison do we do?
    • each-pair, all-pairs, compare-with-best?
    • doesn't matter! all will be the same

  • Some people burn more than others
  • So look at difference for each person
  • Draw histogram

How do we analyse such data?

• Easy case, only two posibilities. Just subtract go generate constrast.
• More general case, many possibilities. Lots of pairs to compare
• Think regression
• We have two effects--subject and treatment
• Treat each as a categorical X-planatory variable
• What does the subject effect explain? (skin color, hair color, eye color, general burning ability)
• What does the treatment explain? (Effect of suntan lotion)
• Suppose we got an R-sq of 90%, do we know the treatment made a difference? NO! It could all be subject effect.
• But, the treatment might very significant now that we have controled for the subject effect

JMP IN example (Boys wearing shoes data)

• Which material is better for the sole of a shoe?
• In this case--only two types are tested.
• If we were using ponies instead of boys, we could use 4 types of material!
• Boys are very different in their use of shoes
• What if we just look at the one-way ANOVA?
• Nothing significant
• So do a regression

Last modified: Tue Apr 11 11:10:03 2000