Test 2: Factorial ANOVA

Question 1

Factorial ANOVA

Answer 1

Examining the simultaneous effects of several (two or more) factors on the dependent variable. (ANOVA simultaneously analyze two or more factors)

Question 2

Example of a Factorial ANOVA

Answer 2

Does the effect of Factor A on our dependent variable depend on the level of Factor B?

Question 3

Factorial ANOVA is the same thing as…

Answer 3

two-way ANOVA models

Question 4

How many factors are in a Two-Way ANOVA?

Answer 4

There are two factors/IVs (Factor A & Factor B); factors can be between-subjects factors, within-subjects factors, or a combination of the two

Question 5

Between-Between Design

Answer 5

Occur when both Factor A and Factor B are between-subjects factors; ex. effects of age (young or old) and obesity (healthy weight or obese) on knee extensor strength. (2x2 between-subjects factorial ANOVA)

Question 6

Between-Within (or mixed) Designs

Answer 6

Occur when Factor A is a between-subjects factor and Factor B is a within-subjects factor; ex. effects of age (2 groups, young or old) and leg dominance (measured 2x, dominant or non-dominant) on knee strength (2x2 mixed-model factorial ANOVA)

Question 7

Within-Within Designs

Answer 7

occur when both Factor A and Factor B are within-subjects factors; ex. effects of leg dominance (dominant & non-dominant) and protein supplementation (low dose & high dose) on knee-extensor strength (1 group measured 4 times)

Question 8

Between-Subjects Factor

Answer 8

Cannot be a member of more than one group

Question 9

Within-Subjects Factor

Answer 9

Same subjects are being tested on each variable across each group

Question 10

Main Effect

Answer 10

What is the effect of Factor A independent of Factor B? (vice versa)

Question 11

Interaction Effect

Answer 11

What is the simultaneous/joint effect of Factors A and B? (are the differences in population means on the dependent variable among levels of Factor A the same across levels of Factor B?); Factor A x Factor B

Question 12

Interaction Plot

Answer 12

Factor A on the x-axis; Means of the DV on the y-axis; Separate lines for each level of Factor B

Question 13

The interaction can be thought of as a measure of whether the lines describing the effects of two factors are…

Answer 13

Parallel; If the lines are parallel (regardless of the shape of that line) the interaction effect is NOT statistically significant• If the lines are not parallel, then the interaction is statistically significant (it doesn’t matter what it looks like)

Question 14

What do Interaction Plots infer about Main Effect for Factor A?

Answer 14

If the levels of Factor A are along the X-axis, the slope of the line indicates if a main effect of Factor A is present (no slope = no effect);

Question 15

What do Interaction Plots infer about Main Effect for Factor B?

Answer 15

If levels of Factor B are on separate lines, the offset (or separation) of the lines indicate if a main effect for Factor B is present (close together = no effect)

Question 16

If values change between the levels of Factor A?

Answer 16

Main effect of Factor A

Question 17

If Lines are parallel for Factor A or B?

Answer 17

No interaction effect

Question 18

If lines are close together for Factor A?

Answer 18

Little difference between the levels of Factor B = no main effect for Factor B

Question 19

If lines are separated for Factor B?

Answer 19

Indicates a main effect for Factor B

Question 20

If there is little to no slope in the lines?

Answer 20

Mean values do not change much between levels of Factor A, no main effect of Factor A

Question 21

If lines have slope?

Answer 21

Main effect of Factor A

Question 22

H0: μA1 = μA2 =

Answer 22

… μAa (a = # of levels of A)

Question 23

H0: μB1 = μB2 =

Answer 23

… μBb (b = # of levels of B)

Question 24

H0: μA1,B1 = μA1,B2 =

Answer 24

… μAa, μBb

Question 25

The alternative hypotheses for each of these is that…

Answer 25

at least 2 means differ (if only two levels, it means the IV has an effect)

Question 26

Variance due to the treatment effect of A

Answer 26

Deviation of marginal means of factor A from grand mean

Question 27

Variance due to the treatment effect of B

Answer 27

Deviation of marginal means of factor B from grand mean

Question 28

Variance due to the combined effects of A & B

Answer 28

Deviation of group mean from respective marginal mean of Factor A, marginal mean of Factor B, and the grand mean

Question 29

Unexplained variance (error)

Answer 29

Deviation of observation from group mean

Question 30

these 4 sources combine to make up the total variance

Answer 30

Deviation of observation from the grand mean

Question 31

ANOVA table: Factor A

Answer 31

Sum of Squares: SSA, df: a-1, Mean Square: MSA = SSA/dfA, F: MSA/MSE

Question 32

ANOVA table: Factor B

Answer 32

Sum of Squares: SSB, df: b-1, Mean Square: MSB = SSB/dfA, F: MSB/MSE

Question 33

ANOVA table: A*B Interaction

Answer 33

Sum of Squares: SSAxB, df: (a-1)(b-1), Mean Square: MSAxB = SSAxB/dfA, F: MSAxB/MSE

Question 34

ANOVA table: Error

Answer 34

Sum of Squares: SSE, df: (N-ab), Mean Square: MSE = SSE/dfE

Question 35

ANOVA table: Total

Answer 35

Sum of Squares: SST, df: N-1

Question 36

What do the variables a, b, and N mean in an ANOVA table?

Answer 36

a = # of levels of A, b = # of levels of B, N = total # of participants