Class 10: comparing group means across two
X-variables.
What you need to have learnt from Class 9: Comparing group means.
- Know the objectives of ANOVA and multiple comparisons.
- Understand why we can't compare each pair (i.e. do lots of
two-sample t-tests).
- Be able to interpret the tables that come with Hsu's and Tukey's
comparison procedures.
- Know and check the assumptions for ANOVA.
New material for today: ANOVA with two X-variables.
- Objective: compare means (of a Y-variable) across different
groups and combinations of groups.
- Example: how do gas station average profits depend on
incentive scheme and geographic location?
- A single continuous Y-variable and TWO categorical X-variables
- Recognize: the X-variables are both categorical.
- Two basic models:
- No interaction: the impact of X1 on Y does not depend on the
level of X2.
- Interaction: the impact of X1 on Y depends on the level of X2.
- Practical consequences:
- If NO interaction, then you can investigate the impact of
each X by itself.
- If there is interaction (consider practical importance as
well as statistical significance) then you must consider both X1
and X2 together.
- Key graphic - the profile plot. A graphical diagnostic for
interaction - look for parallel versus non-parallel lines.
- After doing a TWOWAY ANOVA, we often compare different
combinations of the variables by concatenating the two X's into a
single column and
doing multiple comparisons. See p.283 and p.293 of the BulkPack.
- We have the usual assumptions on the errors: independent,
constant variance and approximately normal.
- In JMP we do the TWOWAY ANOVA from the ``fit model''
platform. Residuals can be saved from here. Profile plots are also
obtained via this output.
Richard Waterman
Mon Oct 7 21:48:00 EDT 1996