What's Two-way ANOVA?

• The purpose is similar to One-way ANOVA, but now we have two factors.
• Example: Is the amount of weekly physical activity of college students different in three states for male and female?
• Two factors: state, gender.

What we want to test?

• Main effect
  • Will the state influence the amount?
  • Will gender influence the amount?
• Interaction
  • Is the influence of state the same for male and female?

How do you know whether there is interaction?

• If any lines cross each other, then you have an interaction.
• If the lines are all fairly parallel to each other, then you do not have an interaction.
• If the lines aren't parallel but don't cross each other either, then you might have an interaction.

Means plot

Check the assumption

• Need independent SRSs
• Population should be Normal with the same standard deviation
  • Largest std. < 2 * smallest std.

Interpret the result