Two-Way ANOVA Omnibus Test

Question 1

What is the aim of a two-way ANOVA?

Answer 1

1. Is there a main effect of Factor A?
2. Is there a main effect of Factor B?
3. Is there an A*B interaction?

Question 2

What does it mean to have a main effect in terms of variability?

Answer 2

Is there variability between the levels of A, averaging over the other factor?

Question 3

What does it mean to have a main effect in terms of marginal means?

Answer 3

Do the marginal means of a factor differ from each other/the grand mean?

Question 4

What does it mean to have an interaction in terms of simple effects?

Answer 4

Does the simple effect of one factor change across the levels of the other factor?

Question 5

What does it mean to have an interaction in terms of cells means?

Answer 5

Do the cell means differ more than would be expected given the effect of A and B?

Question 6

How is total variation partitioned in a two-way ANOVA?

Answer 6

1. Between-groups variance
   a. Variance due to Factor A
   b. Variance due to Factor B
   c. Variance due to A * B Interaction
2. Within-groups variance

Question 7

What is df total in a two-way ANOVA?

Answer 7

N - 1
Number of total observations - 1

Question 8

What is dffactor in a two-way ANOVA?

Answer 8

a - 1
Number of levels in the factor - 1

Question 9

What is dfinteraction in a two-way ANOVA?

Answer 9

(a - 1)(b - 1)
Product of df for factors in the interaction

Question 10

What is df error in a two-way ANOVA?

Answer 10

N - ab
Number of observations - number of treatments/cells

Question 11

What is the null hypothesis for the main effect(s)?

Answer 11

H0: μ1 = μ2 = μ3

Question 12

What is the alternate hypothesis for the main effect(s)?

Answer 12

H1: μ1 ≠ μ2 ≠ μ3
OR
Null is false

Question 13

What is the null hypothesis for the interaction?

Answer 13

H0: μ1k - μ.. = μ2k - μ..
Differences between the means of one factor and the grand mean are the same for the levels for the other factor

Question 14

What are the steps in a two-way ANOVA?

Answer 14

1. Estimate between-groups variability
2. Estimate within-groups variability
3. Weight each estimate by the number of observations used to generate the estimate (df)
4. Compare ratios (three omnibus tests/ F - ratios)

Question 15

What is included in between-groups variability in a two-way ANOVA?

Answer 15

1. Variability due to the main effect of the first factor
2. Variability due to the main effect of the second factor
3. Variability due to the interaction of both factors

Question 16

What are the three omnibus tests/ F ratios that are conducted in a two-way ANOVA?

Answer 16

1. Comparison of between-groups variability among the levels of the first factor to error (main effect)
2. Comparison of between-groups variability among the levels of the second factor to error (main effect)
3. Comparison of AB cells variability (adjusted for main effects) to error (interaction)

Question 17

What is included in the structural model of a two-way ANOVA

Answer 17

An individual DV score is comprised of:
- The grand mean
- Main effect of Factor A
- Main effect of Factor B
- The interaction
- Error

Question 18

What are the assumptions of a between-groups ANOVA?

Answer 18

1. Assumption of normality
2. Assumption of homogeneity
3. Observations are independent
4. Random sampling
5. Each sample has at least 2 observations and equal n
6. Data for DV scores is continuous

Question 19

What is the assumption of normality?

Answer 19

That the populations from which samples are picked are normally distributed

Question 20

What is the assumption of normality?

Answer 20

What the populations from which samples are picked have equal variance