8 Multifactor designs: 2-way between-subjects ANOVA

Question 1

For a 2x2x2 ANOVA, how many effects (including interactions) would there be in the equation?

Answer 1

3 main effects
3 two-way interactions
1 three-way interaction

Question 2

In the ANOVA equation, what is μ (mu)?

Answer 2

The grand mean

Question 3

How many groups will there be in a 2x2x2 design?

Answer 3

8

Question 4

How can you make a three-way design into a one-way design?

Answer 4

By averaging over two of the IVs.

Question 5

What are the 6 assumptions of ANOVA?

Answer 5

1. Quantitative DV (interval or ratio scaling)
2. Random sampling
3. Random allocation to conditions (independence of observations)
4. Homoscedasticity*
   - For each level of A, the variance is equal.
5. Balanced design*
6. Normal distribution*
   within conditions
   * the last three can be violated

Question 6

Homoscedasticity –is it about gay skiers?

Answer 6

Yes.

Question 7

Partial η (eta) squared is the same as R-squared when there is…

Answer 7

Only one predictor (or IV) in the model.

Question 8

Marginal means will differ from descriptives if…

Answer 8

Marginal means will differ from descriptives if you include a covariate.

Question 9

In a 2x2 design, what do significant main effects, but no significant interaction, mean?

Answer 9

There are differences between the levels of each IV, and that these differences are consistent across the levels of the other IV.

Question 10

How is partial eta squared calculated?

Answer 10

The SS for that condition over the SS for that condition plus error.

Question 11

Why is partial eta squared partial?

Answer 11

Because the denominator is not the total SS – it doesn’t account for the SS of other conditions in the model or of interactions.

Question 12

In a three-way design, where the two-way interactions are not significant, but the three-way IS significant, what does this mean?

Answer 12

That each of the two-way interactions differ depending on the level of the third variable.

AxB @ C1 is different from AxB @C2
AxC @B1 is different from AxC @B2
BxC @A1 is different from BxC @A2

Question 13

How do you get an F value from a contrast estimate?

Answer 13

Divide contrast estimate by std. error to get t, then square to get F.

Question 14

How do you describe a significant three-way interaction in a 2x2x2 model for variables A, B and C?

Answer 14

The difference between A1 and A2 is different between B1 and B2 depending on whether C1 or C2.

Question 15

_____-order interactions qualify _____-order interactions and ____ effects.

Answer 15

Higher-order interactions qualify lower-order interactions and main effects.