Deck 13: Factorial Anova: Fixed-Effects Model

Question 1

For a three-factor fixed-effects ANOVA, how many F tests will there be?

A) 3
B) 4
C) 6
D) 7

Answer 1

D

Question 2

For a design with four factors, how many three-way interactions will there be?

A) 3
B) 4
C) 8
D) 16

Answer 2

A

Question 3

In a two-factor ANOVA, factor A has three levels and factor B has two levels. If each cell has five observations, the F_A ratio has degrees of freedom equal to?

A) 2,24
B) 3,24
C) 2,29
D) 3,29

Answer 3

B

Question 4

In a two-factor ANOVA, df_A = 2, df_B = 3, and each cell has five observations. what is df_AB?

A) 2
B) 3
C) 6
D) 10

Question 5

In a two-factor ANOVA, df_A = 2, df_B = 3, and each cell has five observations. what is df_with?

A) 24
B) 36
C) 48
D) 60

Question 6

In a two-factor fixed-effects ANOVA, F_A = 3, F_B = 3.5, df_A = 3, df_B = 3. If the null hypothesis for factor A is rejected at .05 level of significance, the null hypothesis for factor B will be

A) rejected at .10 level of significance.
B) rejected at .05 level of significance.
C) both a and b
D) neither a nor b

Question 7

In a three-factor fixed-effects ANOVA, the three-way interaction effect is found to be significant. Which of the following statements is always true?

A) All of the two-way interaction effects and main effects are significant.
B) None of the two-way interaction effects or main effects are significant.
C) At least one of the two-way interaction effects or main effects is significant.
D) None of the above.

Question 8

A researcher used ANOVA to examine the effects of different types of diet on the weight gains of sheep. Specifically, he wants to see if the effect of diet type is different for sheep of different ages. Ten sheep were assigned to each of the four diet groups. Within each diet group, half of the sheep were younger than one year old, and the other half were older than one year old. How many factors are in this experiment and how many levels do these factors have?

A) 1 factor; 4 levels
B) 1 factor; 8 levels
C) 2 factors; one with 4 levels, one with 2 levels.
D) 2 factors; one with 10 levels, one with 5 levels.

Question 9

A three-factor fixed-effects design always has which one of the following?

A) Three independent variables
B) Three levels in each factor
C) Three dependent variables
D) A significant three-way interaction

Question 10

In a two-factor fixed-effects ANOVA, the interaction effect is definitely not present when

A) The effect of one factor is different across levels of the other factor.
B) Column effects are not consistent across rows.
C) Main effects and residual error do not account for all of the variation in
The dependent variable.
D) Main effects and residual error have accounted for all of the variation in
The dependent variable.

Question 11

In a 2*2 factorial design, the cell means are given as follows: cell 11=10, cell 12 = 20, cell 21 = 10, cell 22 = 0. Assume that the within-cell variation is small. Which one of the following conclusions seems most probable?

A) All effects are significant.
B) Only the two main effects is significant.
C) Only the interaction is significant.
D) The interaction and one of the main effects are significant.

Question 12

Which of the following situations would result in the greatest generalizability of the main effect for factor B across the levels of factor A?

A) for factor A, p = .06; for factor B, p = .05; and interaction AB, p = .01.
B) for factor A, p = .06; for factor B, p = .10; and interaction AB, p = .05.
C) for factor A, p = .20; for factor B, p = .05; and interaction AB, p = .10.
D) for factor A, p = .20; for factor B, p = .10; and interaction AB, p = .05.

Question 13

based on the following plots of cell means. Assume that the within-cell variation is very small.
1) 2) 3) 4)
-Which plot indicates that both main effects are significant but the interaction effect is nonsignificant?

A) plot (1)
B) plot (2)
C) plot (3)
D) plot (4)

Question 14

based on the following plots of cell means. Assume that the within-cell variation is very small.
1) 2) 3) 4)
-Which plot indicates that neither of the main effects are significant but the interaction effect is significant?

A) plot (1)
B) plot (2)
C) plot (3)
D) plot (4)

Question 15

based on the following plots of cell means. Assume that the within-cell variation is very small.
1) 2) 3) 4)
-Which plot(s) indicate(s) significant interaction effects?

A) plot (1) and (2)
B) plot (2) and (3)
C) plot (1), (2), and (3)
D) plot (1) and (4)

Question 16

Using the same data set (J = 3, K = 2, n = 10), Jane conducted two one-factor ANOVA, whereas Joe conducted a two-factor ANOVA. Which of the following statements is not true?

A) Jane and Joe would get the same df_A.
B) Jane and Joe would get the same df_B.
C) Jane and Joe would get the same df_with.
D) Jane and Joe would get the same df_total.

Question 17

The results of a two-factor ANOVA (J = 3, K = 2) show that both main effects are significant, but the interaction is not significant. We need to

A) conduct MCPs to examine the two main effects and the interaction
effect.
B) conduct MCPs to examine the interaction effect only.
C) conduct MCPs to examine the two main effects.
D) conduct MCPs to examine one main effect only.

Question 18

In a three-factor fixed-effects ANOVA, F_A = 3, df_A = 2, df_B = 3, df_C = 2, and df_with = 60. The null hypothesis for factor A can be rejected

A) at the .01 level.
B) at the .05 level, but not at the .01 level.
C) at the .10 level, but not at the .05 level.
D) None of the above.

Question 19

Adding a second factor to a one-factor design may

A) increase df_total
B) increase df_with
C) decrease SS_total
D) decrease MS_with

Question 20

based on the following ANOVA summary table (fixed effects):

-For which source of variation is the null hypothesis rejected at the .10 level of significance?

A) A
B) B
C) AB
D) All of the above.

Question 21

based on the following ANOVA summary table (fixed effects):

-How many cells are there in the design?

A) 6
B) 8
C) 9
D) None of the above

Question 22

based on the following ANOVA summary table (fixed effects):

-The total sample size for the design is which one of the following?

A) 131
B) 132
C) 134
D) None of the above

Question 23

based on the following ANOVA summary table (fixed effects):

-For which source of variation is the null hypothesis rejected at the .05 level of significance?

A) A
B) B
C) AB
D) All of the above.

Question 24

based on the following ANOVA summary table (fixed effects):

-How many cells are there in the design?

A) 6
B) 10
C) 12
D) None of the above

Question 25

based on the following ANOVA summary table (fixed effects):

-The total sample size for the design is which one of the following?

A) 72
B) 74
C) 77
D) None of the above

Question 26

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are three levels of factor A (teaching method) and two levels of factor B (time of class). Each cell includes six students and $\alpha$ = .05.
$\begin{array}{ccccccc}\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \\\hline \text { A } & & & 6.5 & & & \\\text { B } & & & & & \\\mathrm{AB} & & & 5.2 & & \\\text { Within } & 39 & & & & \\\text { Total } & 65 & & & & \\\hline\end{array}$

Question 27

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are four levels of factor A (grade level) and three levels of factor B (textbook). Each cell includes 11 students and $\alpha$ = .05.
$\begin{array}{ccccccc}\hline \text { Source } & \text { SS } & \text { df } & M S & F & \text { Critical Value } & \text { Decision } \\\hline \mathrm{A} & & & 5 & & & \\\mathrm{~B} & 42 & & & & \\\mathrm{AB} & & & 25 & & \\\text { Within } & 240 & & & & \\\text { Total } & & & & &\end{array}$

Question 28

Complete the following ANOVA summary table for a two-factor fixed-effects ANOVA, where there are two levels of factor A (type of counseling) and four levels of factor B (frequency of counseling). Each cell includes six people and $\alpha$ = .01.
$\begin{array}{clccccc}\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \\\hline \mathrm{A} & 60 & & & 6 & \\\mathrm{~B} & & & & \\\mathrm{AB} & 60 & & & & \\\text { Within } & & & & \\\text { Total } & 640 & & & & \\\hline\end{array}$

Question 29

A researcher wanted to examine the effects of types of diet (factor A) and the age (factor B) on the weight gains of sheep. Diet type has four levels (i.e., four types of diet) and age has two levels (younger than one year old and older than one year old). Five sheep were assigned to each of the eight cells. The following are the scores (weight gains) from the individual cells:
A₁B₁: 11.8, 11.7, 11.1, 10.7, 10.4
A₁B₂: 11.1, 9.8, 9.5, 9.2, 8.8
A₂B₁: 10.2, 10.0, 8.7, 8.1, 7.3
A₂B₂: 8.6, 8.2, 7.7, 7.4, 5.6
A₃B₁: 12.0, 10.8, 10.5, 10.2, 10.2
A₃B₂: 10.7, 9.8, 9.7, 9.5, 8.9
A₄B₁: 9.8, 9.6, 9.4, 9.1, 7.9
A₄B₂: 8.0, 7.4, 7.4, 6.7, 5.8
Use SPSS to conduct a two-factor fixed-effects ANOVA to determine if there are any effects due to diet type, diet amount, or the interaction ( $\alpha$ = 0.05). Conduct Tukey HSD post hoc comparisons, if necessary. (Presume all assumptions of ANOVA are satisfied.)

Question 30

A small-scale taste test is conducted to find out how the levels of moisture (factor A) and sweetness (factor B) of the cakes are related to people's preference to the cake. Participants' gender (factor C) is also considered. Each factor consists of two levels. Thirty-two participants are assigned to eight cells (i.e., four per cell), one for each of the factor combinations. The following are the scores (rating of the cakes by the participants) from the individual cells:
A₁B₁C₁: 64, 61, 65, 70
A₁B₁C₂: 63, 60, 64, 68
A₁B₂C₁: 73, 76, 72, 71
A₁B₂C₂: 72, 75, 79, 77
A₂B₁C₁: 72, 78, 81, 75
A₂B₁C₂: 74, 73, 75, 69
A₂B₂C₁: 98, 97, 93, 89
A₂B₂C₂: 86, 93, 88, 94
Use SPSS to conduct a three-factor fixed-effects ANOVA ( $\alpha$ = 0.01). If there is (are) any significant interaction(s), graph and interpret the interaction(s).