Chapter 20 Analysis of Variance (ANOVA)

ANOVA is using the same underlying mechanism as linear regression. However, the angle that ANOVA chooses to look at is slightly different from the traditional linear regression. It can be more useful in the case with qualitative variables and designed experiments.

Experimental Design

  • Factor: explanatory or predictor variable to be studied in an investigation
  • Treatment (or Factor Level): “value” of a factor applied to the experimental unit
  • Experimental Unit: person, animal, piece of material, etc. that is subjected to treatment(s) and provides a response
  • Single Factor Experiment: one explanatory variable considered
  • Multifactor Experiment: more than one explanatory variable
  • Classification Factor: A factor that is not under the control of the experimenter (observational data)
  • Experimental Factor: assigned by the experimenter

Basics of experimental design:

  • Choices that a statistician has to make:

    • set of treatments
    • set of experimental units
    • treatment assignment (selection bias)
    • measurement (measurement bias, blind experiments)
  • Advancements in experimental design:

    1. Factorial Experiments:
      consider multiple factors at the same time (interaction)

    2. Replication: repetition of experiment

      • assess mean squared error
      • control over precision of experiment (power)
    3. Randomization

      • Before R.A. Fisher (1900s), treatments were assigned systematically or subjectively
      • randomization: assign treatments to experimental units at random, which averages out systematic effects that cannot be control by the investigator
    4. Local control: Blocking or Stratification

      • Reduce experimental errors and increase power by placing restrictions on the randomization of treatments to experimental units.

Randomization may also eliminate correlations due to time and space.