Two way ANOVA

Question 1

What is a two way ANOVA often called?

Answer 1

Factorial ANOVA

Question 2

Why is it called a factorial anova?

Answer 2

Two IV’s (or factors, or grouping variables, or treatments)

e.g. Ability and teaching method.

Question 3

What are the advantages of using a Two-way ANOVA?

Answer 3

1. Can examine the joint (interactive) effect of the IV’s on the DV.
2. Increase power by decreasing variance with in cells of the matrix.
3. The economy of subjects: need only half as many subjects to do 2-way ANOVA than you would need for two 1-way ANOVA to get the same information.

Question 4

Referring to the first advantage of the 2-way ANOVA, what are the two types of joint interactions?

Answer 4

a) Ordinal interaction

b) disordinal interaction.

Question 5

What is an ordinal interaction?

Answer 5

Magnitude of the differences changes but one sub-group is always higher than another.

Question 6

What is a disordinal interaction?

Answer 6

One treatment is best with one group, but another treatment is better for a different group.

Question 7

What are the sources of variability in a 2-way ANOVA?

Answer 7

1. Variability due to factor A => main effect A
2. Variability due to factor B => main effect B
3. Variability due to the interaction => AxB interaction
4. Unsystematic variability (ID’s, random error) => error

Question 8

State the null hypotheses for main effect A, Main effect B, and AxB interaction

Answer 8

Main effect A: H0: Mu1. = Mu2. = Mu3. = … = Mua.
Population row means are equal

Main effect B: H0: Mu.1 = Mu.2 = Mu.3 = … = Mu.b
Population column means are equal

AxB interaction:
H0: All phiab = 0
All the interactions equal zero, or all interactions are zero.

Question 9

What is an individual raw score made up of?

Answer 9

The general effect + main effect A + main effect B + our interaction + error.

Question 10

What is an individual raw score made up of?

Answer 10

The general effect + main effect A + main effect B + our interaction + error.
This is our linear model.

Question 11

What is Phicarrotab?

Answer 11

That part of the cell mean that CAN NOT be accounted for by the grand mean (over all effect) And the main effect for A & B.

Question 12

What is Phicarrotab?

Answer 12

That part of the cell mean that CAN NOT be accounted for by the grand mean (over all effect) And the main effect for A & B. i.e. the interaction effect.
The interaction effect is NOT the same as the error effect.

Question 13

What does the interaction effect of for every row and column equal when added together?

Answer 13

Zero.

Question 14

Give the flow chart

Answer 14

1. Look at your interaction FIRST
   - If the interaction is significant you can not interpret the main effects of A & B (PERIOD)
   - You have to further analyze and interpret the interaction.
2. If the interaction is non-significant then look at your main effects
   - Is the main effect for A significant?
   - Is the main effect for B significant?
   (Talk about A&B seperately, talk like you did a one way ANOVA on A, and a one way ANOVA on B.

Question 15

What is your design has equal n in all cells?

Answer 15

a balanced design.

Question 16

What is your design called if you have unequal n in your cells?

Answer 16

an unbalanced design

Question 17

In the equation for main effects (either a or b), why do we multiply the levels of a or b by n?

Answer 17

Because it is the number of observations on which each row Ybar is based.