Question 1

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

Accepted Answer

The answer of Data Set 13-3: 
-For any graph in...

Question 2

Data Set 13-3: -The degrees of freedom for MS_errorin Data Set 13-3 would be

Accepted Answer

The degrees of freedom for the specified error term cannot be determined without additional information about the structure of Data Set 13-3, such as the number of groups, sample sizes, or the design of the study.

Question 3

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

Accepted Answer

The interaction is significant because the difference between the means of the two groups is greater than the standard error of the difference.

Question 4

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

Accepted Answer

A main effect refers to the impact of one independent variable on a dependent variable, ignoring other variables. In this case, socioeconomic status is an independent variable that could affect political attitudes (scores), making it an example of a main effect.

Question 5

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

Accepted Answer

The means for the low, medium, and high socioeconomic status levels are the same across the two majors (Humanities and Natural Science), suggesting no main effect of socioeconomic status on political attitudes.

Question 6

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?

Accepted Answer

The dependent variable is the outcome variable that researchers are interested in explaining or predicting, which in this case is the political attitudes as indicated by the scores on the Loose Label Political Opinion Poll.

Question 7

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

Accepted Answer

The data set represents a 2 x 3 factorial design, not a 2 x 2, and does not provide enough information to determine the total degrees of freedom.

Question 8

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

Accepted Answer

The F value of 2.75 with degrees of freedom 4 and 24 does not exceed the critical F value at the .05 significance level (approximately 2.78), so the null hypothesis for the interaction should be retained.

Question 9

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

Accepted Answer

The degrees of freedom for the interaction term (4) suggest a 2x2 factorial design, implying there are 2 independent variables. Each variable has 2 levels, and the interaction term's degrees of freedom are calculated as (levels of IV1 - 1) * (levels of IV2 - 1) = (2-1)*(2-1) = 1*1 = 1 for each combination, but given the degrees of freedom is 4, it suggests there are multiple combinations, consistent with 2 independent variables.

Question 10

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

Accepted Answer

The answer of Data Set 13-5: An F value of...

Question 11

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

Accepted Answer

In Experiment Y, the means for B1 and B2 are the same across levels of A, indicating no main effect of B. In Experiment Z, the means for B1 and B2 change from A1 to A2, suggesting a potential interaction rather than a clear main effect of B. Only in Experiment X is there a clear difference in the means for B1 and B2 across both levels of A, indicating a potential main effect of B.

Question 12

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

Accepted Answer

In Experiment X, the effect of changing levels of B depends on the level of A (from 5 to 10 and from 10 to 5), indicating an interaction. In Experiment Z, the effect of changing levels of B also depends on the level of A (from 5 to 5 and from 5 to 10), indicating an interaction. Experiment Y shows consistent effects across levels of A, indicating no interaction.

Question 13

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

Accepted Answer

The answer of Data Set 13-6: The numbers in the...

Question 14

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 _________ .

Accepted Answer

The degrees of freedom for the interaction in a two-way ANOVA are calculated based on the number of levels of each factor minus one, multiplied together for the numerator, and the total number of observations minus the number of conditions for the denominator. In Experiment X, there are 2 levels of A and 2 levels of B, so the degrees of freedom for the interaction (AxB) are (2-1)*(2-1) = 1 for the numerator. There are 4 groups with 5 observations each, totaling 20 observations. The denominator's degrees of freedom are 20 - 4 = 16.

Question 15

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

Accepted Answer

The degrees of freedom for the interaction in a factorial ANOVA are calculated by multiplying the degrees of freedom of the factors involved in the interaction. Here, we have two factors: type of occupation (4 groups) and age (2 groups). The degrees of freedom for occupation are 4 - 1 = 3, and for age, they are 2 - 1 = 1. Thus, the degrees of freedom for the interaction are 3 * 1 = 3.

Question 16

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.

Accepted Answer

The answer of Data Set 13-7: A political scientist reported...

Question 17

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?

Accepted Answer

The significant interaction in the factorial ANOVA suggests that the effect of occupation on attitudes toward military buildup varies depending on the age of the participants, which is what option C describes.

Question 18

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

Accepted Answer

The two factors are occupation (US Army officers, corporate managers, public school teachers, and assembly-line workers) and age (under 35, over 35).

Question 19

Data Set 13-8: N = 10 for each cell.
 
-In Data Set 13-8, the main effect of B could be significant in

Accepted Answer

The answer of Data Set 13-8: N = 10 for...

Question 20

Data Set 13-8: N = 10 for each cell.
 
-In Data Set 13-8, there could be an interaction in

Accepted Answer

The answer of Data Set 13-8: N = 10 for...

Quiz 13: Analysis of Variance: Factorial Design

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

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

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

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

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

Data Set 13-8: N = 10 for each cell. -In Data Set 13-8, the main effect of B could be significant in

Data Set 13-8: N = 10 for each cell. -In Data Set 13-8, there could be an interaction in

Data Set 13-3: -The degrees of freedom for MS_errorin Data Set 13-3 would be