Deck 13: Analysis of Variance: Factorial Design

Question 1

A 3 x 5 factorial ANOVA has two independent variables.

Answer 1

True

Question 2

A factorial ANOVA produces three F values.

Answer 2

True

Question 3

The factorial ANOVA described in Chapter 13 is appropriate when the cells have an unequal number of scores.

Answer 3

False

Question 4

The sum of squares for cells is equal to the sum of the sums of squares of A, B, and AB.

Question 5

An interaction occurs when one main effect in a factorial ANOVA is significant but the second one is not.

Question 6

A significant interaction is characterized by parallel lines.

Question 7

A histogram graphing an interaction that is not significant shows stairs with steps that are about equal.

Question 8

If the interaction is significant, the main effects can be interpreted as if they came from a one-way ANOVA.

Question 9

If the interaction is significant, a Tukey HSD is not appropriate.

Question 10

The effect size index, d, can be used on factorial ANOVA problems.

Question 11

A factorial ANOVA can analyze two independent variables.

Question 12

A factorial ANOVA produces two F values.

Question 13

The factorial ANOVA described in Chapter 13 is appropriate when the cells have an equal number of scores.

Question 14

The sum of squares for cells is equal to the sum of the sums of squares of A, B, and error.

Question 15

An interaction occurs when both main effects in a factorial ANOVA show a significant difference.

Question 16

A interaction that is not significant is characterized by parallel lines.

Question 17

A histogram with stairs steps that ascend for one treatment and descent for the other treatment indicates a significant interaction.

Question 18

If the interaction is not significant, the main effects can be interpreted as if they came from a one-way ANOVA.

Question 19

If the interaction is significant, a Tukey HSD is appropriate.

Question 20

The effect size index. f, can be used on factorial ANOVA problems.

Question 21

An F test on an independent variable in a factorial ANOVA is called a main effect.

Question 22

A factorial ANOVA produces four F values.

Question 23

The factorial ANOVA described in Chapter 13 is not appropriate when the cells have an unequal number of scores.

Question 24

The sum of squares for cells is equal to the total sum of squares minus the sums of squares of A and B.

Question 25

A significant interaction is characterized by lines that are not parallel.

Question 26

A histogram of a significant interaction shows stairs with steps that are about equal.

Question 27

As long as the interaction is significant, interpretation of the main effects is straightforward.

Question 28

If the interaction is not significant, a Tukey HSD is appropriate.

Question 29

The two effect size indexes described for factorial ANOVA were d and f.

Question 30

Data Set 13-1: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 6 and 18.

-Refer to Data Set 13-1. With $\alpha$ = .05 the null hypothesis for this interaction mean square should be

A) retained
B) rejected
C) cannot tell from the information given.

Question 31

Data Set 13-1: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 6 and 18.

-Refer to Data Set 13-1. The number of levels of one of the independent variables was

A) 9
B) 6
C) 4
D) 1.

Question 32

Data Set 13-1: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 6 and 18.

-Refer to Data Set 13-1. The number of factors in this design must have been

A) 1
B) 2
C) either 1 or 2
D) 6.

Question 33

Data Set 13-1: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 6 and 18.

-Refer to Data Set 13-1. This could be an example of

A) a simple ANOVA
B) a 2 x 2 factorial ANOVA
C) a 2 x 3 factorial ANOVA
D) a 3 x 4 factorial ANOVA.

Question 34

Data Set 13-2
Numbers in the cell are means based on 8 scores for each cell.
$\begin{array}{llll} &&&\text { A }\\&& \mathrm{A}_{1} & \mathrm{~A}_{2} & \mathrm{~A}_{3} \\&\mathrm{~B}_{1} & 10 & 20 & 30 \\\text { B }&\mathrm{~B}_{2} & 40 & 50 & 60 \\&\mathrm{~B}_{3} & 50 & 30 & 10\end{array}$


-In Data Set 13-2 the main effect of A appears to be

A) significant
B) not significant
C) based on 2, 60 df
D) both not significant and based on 2, 60 df.

Question 35

Data Set 13-2
Numbers in the cell are means based on 8 scores for each cell.
$\begin{array}{llll} &&&\text { A }\\&& \mathrm{A}_{1} & \mathrm{~A}_{2} & \mathrm{~A}_{3} \\&\mathrm{~B}_{1} & 10 & 20 & 30 \\\text { B }&\mathrm{~B}_{2} & 40 & 50 & 60 \\&\mathrm{~B}_{3} & 50 & 30 & 10\end{array}$


-In Data Set 13-2 the interaction appears to be

A) significant
B) not significant
C) based on 2, 60 df
D) both not significant and based on 2, 60 df.

Question 36

Data Set 13-2
Numbers in the cell are means based on 8 scores for each cell.
$\begin{array}{llll} &&&\text { A }\\&& \mathrm{A}_{1} & \mathrm{~A}_{2} & \mathrm{~A}_{3} \\&\mathrm{~B}_{1} & 10 & 20 & 30 \\\text { B }&\mathrm{~B}_{2} & 40 & 50 & 60 \\&\mathrm{~B}_{3} & 50 & 30 & 10\end{array}$


-In Data Set 13-2 a test of the main effect of variable B would be based on df.

A) 2, 8
B) 2, 60
C) 2, 63
D) df are not determinable from the information given.

Question 37

Data Set 13-2
Numbers in the cell are means based on 8 scores for each cell.
$\begin{array}{llll} &&&\text { A }\\&& \mathrm{A}_{1} & \mathrm{~A}_{2} & \mathrm{~A}_{3} \\&\mathrm{~B}_{1} & 10 & 20 & 30 \\\text { B }&\mathrm{~B}_{2} & 40 & 50 & 60 \\&\mathrm{~B}_{3} & 50 & 30 & 10\end{array}$


-Data Set 13-2 is an example of

A) a simple ANOVA
B) a 2 x 2 factorial
C) a 3 x 3 factorial
D) an experiment with df_tot equal to 4.

Question 38

Data Set 13-2
Numbers in the cell are means based on 8 scores for each cell.
$\begin{array}{llll} &&&\text { A }\\&& \mathrm{A}_{1} & \mathrm{~A}_{2} & \mathrm{~A}_{3} \\&\mathrm{~B}_{1} & 10 & 20 & 30 \\\text { B }&\mathrm{~B}_{2} & 40 & 50 & 60 \\&\mathrm{~B}_{3} & 50 & 30 & 10\end{array}$


-Data Set 13-2 has independent variables.

A) 1
B) 2
C) 3
D) none of the other alternatives are correct it has _____.

Question 39

Data Set 13-3:

-Refer to Data Set 13-3. The figure that shows an interaction is

A) W
B) X
C) Y
D) Z
E) none of the other alternatives are correct.

Question 40

Data Set 13-3:

-Refer to Data Set 13-3. The figure for which the main effect of variable B is not significant is

A) W
B) X
C) Y
D) Z
E) all of the other alternatives are correct.

Question 41

Data Set 13-3:

-For any graph in Data Set 13-3 there are independent variables.

A) 3 and 2
B) 2
C) 3
D) none of the other alternatives are correct it has _____.

Question 42

Data Set 13-3:

-The degrees of freedom for MS_error in Data Set 13-3 would be

A) 1
B) 2
C) 3
D) not determinable from the information given.

Question 43

Data Set 13-4: The number in each cell is the mean of 5 participants on the Loose Label Political Opinion Poll (high scores = liberal, low scores = conservative).
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Socioeconomic Status }$
$\begin{array}{clccc} & & \text { Low } & \text { Medium } & \text { High } \\\text { Major in } & \text { Humanities } & 50 & 20 & 50 \\\text { College } & \text { Nat. Science } & 30 & 60 & 30\end{array}$


-In Data Set 13-4, the interaction appears to be

A) significant
B) not significant
C) based on 2, 18 df
D) both not significant and based on 2, 18 df.

Question 44

Data Set 13-4: The number in each cell is the mean of 5 participants on the Loose Label Political Opinion Poll (high scores = liberal, low scores = conservative).
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Socioeconomic Status }$
$\begin{array}{clccc} & & \text { Low } & \text { Medium } & \text { High } \\\text { Major in } & \text { Humanities } & 50 & 20 & 50 \\\text { College } & \text { Nat. Science } & 30 & 60 & 30\end{array}$


-In Data Set 13-4, an example of a main effect is

A) political attitudes
B) socioeconomic status
C) whether scores for humanities majors depend on socio-economic status
D) none of the other alternatives are correct.

Question 45

Data Set 13-4: The number in each cell is the mean of 5 participants on the Loose Label Political Opinion Poll (high scores = liberal, low scores = conservative).
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Socioeconomic Status }$
$\begin{array}{clccc} & & \text { Low } & \text { Medium } & \text { High } \\\text { Major in } & \text { Humanities } & 50 & 20 & 50 \\\text { College } & \text { Nat. Science } & 30 & 60 & 30\end{array}$


-In the factorial ANOVA of Data Set 13-4, the main effect that compares the political attitudes of low, medium and high socio-economic levels would appear to be

A) significant
B) not significant
C) cannot tell from the information given.

Question 46

Data Set 13-4: The number in each cell is the mean of 5 participants on the Loose Label Political Opinion Poll (high scores = liberal, low scores = conservative).
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Socioeconomic Status }$
$\begin{array}{clccc} & & \text { Low } & \text { Medium } & \text { High } \\\text { Major in } & \text { Humanities } & 50 & 20 & 50 \\\text { College } & \text { Nat. Science } & 30 & 60 & 30\end{array}$


-Which of the following qualify as dependent variables in Data Set 13-4?

A) political attitudes
B) socioeconomic status
C) major in college
D) none of the other alternatives are correct.

Question 47

Data Set 13-4: The number in each cell is the mean of 5 participants on the Loose Label Political Opinion Poll (high scores = liberal, low scores = conservative).
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Socioeconomic Status }$
$\begin{array}{clccc} & & \text { Low } & \text { Medium } & \text { High } \\\text { Major in } & \text { Humanities } & 50 & 20 & 50 \\\text { College } & \text { Nat. Science } & 30 & 60 & 30\end{array}$


-Data Set 13-4 is an example of

A) a simple ANOVA
B) a 2 x 2 factorial ANOVA
C) an experiment with df_tot = 30
D) none of the other alternatives are correct.

Question 48

Data Set 13-5: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 4 and 24.

-Refer to Data Set 13-5. With ? = .05, the null hypothesis for the interaction should be

A) retained
B) rejected
C) cannot tell from the information given.

Question 49

Data Set 13-5: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 4 and 24.

-Refer to Data Set 13-5. The number of independent variables in this design must have been

A) 1
B) 2
C) 3
D) none of the other alternatives are correct.

Question 50

Data Set 13-5: An F value of 2.75 was obtained when an interaction mean square was divided by a error mean square. The degrees of freedom were 4 and 24.

-Refer to Data Set 13-5. This could be an example of a

A) simple ANOVA
B) 2 x 2 factorial ANOVA
C) 4 x 4 factorial ANOVA
D) none of the other alternatives are correct.

Question 51

Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
$\begin{array}{c}\begin{array}{ccc} &{\text { Experiment X }} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 10 & 5\end{array}\quad\begin{array}{ccc} & {\text { Experiment } \mathrm{Y}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 5 & 10\end{array}\\quad\begin{array}{rlr}{\text { Experiment } \mathrm{Z}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 5 \\\mathrm{~A}_{2} & 5 & 10\end{array}\end{array}$


-In Data Set 13-6, the main effect of B could be significant in

A) X and Y
B) X and Z
C) Y and Z

Question 52

Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
$\begin{array}{c}\begin{array}{ccc} &{\text { Experiment X }} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 10 & 5\end{array}\quad\begin{array}{ccc} & {\text { Experiment } \mathrm{Y}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 5 & 10\end{array}\\quad\begin{array}{rlr}{\text { Experiment } \mathrm{Z}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 5 \\\mathrm{~A}_{2} & 5 & 10\end{array}\end{array}$


-In Data Set 13-6, there could be an interaction in

A) X and Y
B) X and Z
C) Y and Z

Question 53

Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
$\begin{array}{c}\begin{array}{ccc} &{\text { Experiment X }} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 10 & 5\end{array}\quad\begin{array}{ccc} & {\text { Experiment } \mathrm{Y}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 5 & 10\end{array}\\quad\begin{array}{rlr}{\text { Experiment } \mathrm{Z}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 5 \\\mathrm{~A}_{2} & 5 & 10\end{array}\end{array}$


-In Data Set 13-6, the main effect of A is not significant in

A) X and Y
B) X and Z
C) Y and Z

Question 54

Data Set 13-6: The numbers in the cells are means based on samples of 5 in each cell.
$\begin{array}{c}\begin{array}{ccc} &{\text { Experiment X }} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 10 & 5\end{array}\quad\begin{array}{ccc} & {\text { Experiment } \mathrm{Y}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 10 \\\mathrm{~A}_{2} & 5 & 10\end{array}\\quad\begin{array}{rlr}{\text { Experiment } \mathrm{Z}} \\& \mathrm{B}_{1} & \mathrm{~B}_{2} \\\mathrm{~A}_{1} & 5 & 5 \\\mathrm{~A}_{2} & 5 & 10\end{array}\end{array}$


-The F value for the interaction in Experiment X of Data Set 13-6 would be based on degrees for freedom of _________ and _________ .

A) 1, 19
B) 2, 16
C) 3, 19
D) 1 , 16

Question 55

Data Set 13-7: A political scientist reported a study on attitudes toward increasing military expenditures. The attitudes of four groups were reported: US Army officers, corporate managers, public school teachers, and assembly-line workers. Within each of the categories, those under age 35 were tabulated separately from those over 35. A factorial ANOVA on the data produced a significant interaction; the main effect for age was not significant.

-The degrees of freedom for the interaction mean square in Data Set 13-7 is

A) 1
B) 3
C) 6

Question 56

Data Set 13-7: A political scientist reported a study on attitudes toward increasing military expenditures. The attitudes of four groups were reported: US Army officers, corporate managers, public school teachers, and assembly-line workers. Within each of the categories, those under age 35 were tabulated separately from those over 35. A factorial ANOVA on the data produced a significant interaction; the main effect for age was not significant.

-Data Set 13-7 is an example of a ANOVA.

A) simple
B) 2 x 2 factorial
C) 4 x 4 factorial
D) none of the other alternatives are correct.

Question 57

Data Set 13-7: A political scientist reported a study on attitudes toward increasing military expenditures. The attitudes of four groups were reported: US Army officers, corporate managers, public school teachers, and assembly-line workers. Within each of the categories, those under age 35 were tabulated separately from those over 35. A factorial ANOVA on the data produced a significant interaction; the main effect for age was not significant.

-Which of the following is a possible conclusion from Data Set 13-7?

A) the four occupations differ in attitudes toward military buildup
B) older participants favored increases while younger participants did not
C) the attitude toward buildup among the different occupations depends on the age of the person making the judgment
D) none of the other alternatives are correct.

Question 58

Data Set 13-7: A political scientist reported a study on attitudes toward increasing military expenditures. The attitudes of four groups were reported: US Army officers, corporate managers, public school teachers, and assembly-line workers. Within each of the categories, those under age 35 were tabulated separately from those over 35. A factorial ANOVA on the data produced a significant interaction; the main effect for age was not significant.

-The number of factors in Data Set 13-7 is

A) 2
B) 4
C) 8

Question 59

Data Set 13-8: N = 10 for each cell.


-In Data Set 13-8, the main effect of B could be significant in

A) X and Y
B) X and Z
C) Y and Z
D) X

Question 60

Data Set 13-8: N = 10 for each cell.


-In Data Set 13-8, there could be an interaction in

A) X and Y
B) X and Z
C) Y and Z
D) Y

Question 61

Data Set 13-8: N = 10 for each cell.


-The F value for the interaction in Experiment X of Data Set 13-8 is based on degrees of freedom of and .

A) 1, 36
B) 3, 36
C) 1, 39
D) 4, 39.

Question 62

Data Set 13-9: Each point represents a mean based on 5 scores.


-In Data Set 13-9, the main effect of B could be significant in

A) X and Y
B) X and Z
C) Y and Z

Question 63

Data Set 13-9: Each point represents a mean based on 5 scores.


-In Data Set 13-9, there could be an interaction in

A) X and Y
B) X and Z
C) Y and Z

Question 64

Data Set 13-9: Each point represents a mean based on 5 scores.


-In Data Set 13-9, the main effect of A is not significant in

A) X and Y
B) X and Z
C) Y and Z

Question 65

Data Set 13-9: Each point represents a mean based on 5 scores.


-The data in Data Set 13-9 are all examples of afactorial ANOVA.

A) 2x2
B) 2x3
C) 3x3

Question 66

Data Set 13-10: The bar graphs show the results of Experiment X and Experiment Y. Each bar is based on a sample of 8.


-In Data Set 13-10, there appears to be an interaction in Experiment

A) X
B) Y
C) both X and Y
D) neither X nor Y.

Question 67

Data Set 13-10: The bar graphs show the results of Experiment X and Experiment Y. Each bar is based on a sample of 8.


-In Data Set 13-10, the main effect for B appears to be significant in Experiment

A) X
B) Y
C) both X and Y
D) neither X nor Y.

Question 68

Data Set 13-10: The bar graphs show the results of Experiment X and Experiment Y. Each bar is based on a sample of 8.


-In Data Set 13-10, the main effect for A appears to be significant in Experiment

A) X
B) Y
C) both X and Y
D) neither X nor Y.

Question 69

Data Set 13-10: The bar graphs show the results of Experiment X and Experiment Y. Each bar is based on a sample of 8.


-The degrees of freedom for the interaction in Experiment Y in Data Set 13-10 are

A) 4, 40
B) 2, 37
C) 1, 36
D) 1 , 28

Question 70

Among behavioral scientists, factorial ANOVA designs were used in __________ of a sample of articles.

A) about 18 %
B) about 25%
C) about one-third
D) more than half.

Question 71

With respect to the number of independent variables, which of these designs is not like the others?

A) repeated-measures ANOVA
B) one-way ANOVA
C) factorial ANOVA.

Question 72

With respect to the number of independent variables, which of these designs is not like the others?

A) independent t test
B) repeated-measures ANOVA
C) factorial ANOVA.

Question 73

With respect to the number of independent variables, which of these designs is not like the others?

A) factorial ANOVA
B) repeated-measures ANOVA
C) paired-samples t test.

Question 74

If you add the number of independent variables and dependent variables in a 2 x 2 factorial ANOVA, the sum is

A) one
B) two
C) three
D) four

Question 75

A cell in a factorial ANOVA refers to

A) one level of the independent variable
B) one level of the dependent variable
C) one level of one independent variable and one level of a second independent variable
D) all the participants in the experiment.

Question 76

In a factorial ANOVA, a comparison among the means of a factor is referred to as

A) a main effect
B) an interaction
C) both a main effect and as an interaction
D) neither a main effect nor an interaction.

Question 77

The term main effect refers to a comparison of

A) means
B) interactions
C) both means and interactions
D) neither means nor interactions.

Question 78

Which of the following designs have two factors?

A) t tests
B) one way ANOVA's
C) factorial ANOVA's
D) all of the other alternatives are correct.

Question 79

A factorial ANOVA producesF tests.

A) one
B) two
C) three

Question 80

Which of the following is true for factorial ANOVA but not true for one-way ANOVA?

A) the populations from which the samples were drawn are expected to have equal variances
B) the subjects are randomly assigned
C) the populations are normally distributed
D) the number of observations in each treatment must be equal.