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.