Two-way ANOVA

Question 1

What are the possible hypotheses for a two-way ANOVA?

Answer 1

1. total effect hypothesis.
2. main effect A hypothesis.
3. main effect B hypothesis.
4. interaction effect hypothesis.

Question 2

How do you calculate an interaction effect?

Answer 2

interaction effect = u jk - u j - u k + u..

Question 3

Explain mean squares.

Answer 3

1. H0 mean squares reflect random differences in the population.
2. h1 is true and mean squares reflect random differences + significant differences in the population.

Question 4

What is the syntax for a two-way ANOVA analysis?

Answer 4

UNIANOVA y BY A B 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/PLOT = PROFILE (A*B) 
/PRINT = ETASQ DESCRIPTIVE HOMOGENEITY 
/CRITERIA = ALPHA (0.05) 
/DESIGN = A B A*B

Question 5

What is the linear additive model for a two-way ANOVA?

Answer 5

Y ik = u.. + Aj + Bk + AB jk + e

Question 6

What is the syntax for a simple effects analysis in SPSS?

Answer 6

SORT CASES by A
SPLIT FILE SEPARATE BY A

UNIANOVA Y BY B 
/METHOD = SSTYPE (3) 
/INTERCEPT = INCLUDE 
/PRINT = ETASQ DESCRIPTIVE HOMOGENEITY 
/CRITERIA = ALPHA (0.05) 
/DESIGN = (B) 

SPLIT FILE OFF

Question 7

Explain balanced and unbalanced design.

Answer 7

1. balanced design: the sample sizes are equal or proportional.
2. unbalanced design: all other scenarios.

SSB = SSA + SSB+ SSAB
SSB > SSA + SSB + SSAB

Question 8

What are the benefits of a two-way ANOVA vs one-way ANOVA?

Answer 8

1. efficiency.
2. control.
3. interaction.
4. power.

Question 9

What are the differences between fixed factor models and random factor models?

Answer 9

1. fixed factor: selected levels of a factor.

2. random factors: also interested in not selected levels of a factor.