Question 1

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

Accepted Answer

In factorial ANOVA, an F test on an independent variable is used to determine if there are any statistically significant main effects of that variable on the dependent variable, which refers to the overall impact of one independent variable, ignoring the effects of other variables.

Question 2

A factorial ANOVA produces four F values.

Accepted Answer

A factorial ANOVA typically produces more than one F value because it tests multiple hypotheses, but the exact number depends on the number of factors and their interactions, not a fixed number like four.

Question 3

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

Accepted Answer

The factorial ANOVA described in Chapter 13 assumes that the cells have an equal number of scores. When the cells have an unequal number of scores, the ANOVA results can be biased.

Question 4

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

Accepted Answer

The sum of squares for cells (interaction) is equal to the total sum of squares minus the sum of squares for factor A, minus the sum of squares for factor B, minus the sum of squares for error.

Question 5

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

Accepted Answer

In the context of statistical analysis, particularly when analyzing graphs of interactions between variables, a significant interaction is often indicated by lines that are not parallel. This non-parallelism suggests that the effect of one variable on the outcome depends on the level of another variable, which is the essence of an interaction effect.

Question 6

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

Accepted Answer

A histogram is a graphical representation of the distribution of numerical data, not an interaction, and it does not show stairs with steps but rather bars whose heights correspond to the frequency of values.

Question 7

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

Accepted Answer

When there is a significant interaction in a factorial design, the interpretation of the main effects becomes complex and potentially misleading, as the effect of one factor may depend on the levels of another factor.

Question 8

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

Accepted Answer

A Tukey HSD is a post-hoc test that is used to compare the means of multiple groups. It is only appropriate to use a Tukey HSD if the interaction is not significant. If the interaction is significant, then the means of the groups cannot be compared directly.

Question 9

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

Accepted Answer

The two effect size indexes described for factorial ANOVA were d and f2.

Question 10

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.

Accepted Answer

The F value of 2.75 is greater than the critical value of 2.42, so the null hypothesis should be rejected.

Question 11

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.

Accepted Answer

The degrees of freedom for the interaction term in a two-way ANOVA is calculated by multiplying the degrees of freedom of the two independent variables. Given that the degrees of freedom for the interaction term is 6, and knowing that degrees of freedom are calculated as the number of levels minus 1 for each variable, we can deduce that one of the variables must have 4 levels (since 3-1=2 for one variable and 4-1=3 for the other, and 2*3=6).

Question 12

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.

Accepted Answer

The degrees of freedom for the interaction term (6) suggest a 2-factor design, as it results from the product of the degrees of freedom for each factor minus 1 (e.g., if there are 2 levels for factor A and 4 levels for factor B, then the degrees of freedom for the interaction would be (2-1)*(4-1) = 3, which fits a scenario with 2 factors).

Question 13

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.

Accepted Answer

The degrees of freedom for the interaction in a factorial ANOVA is calculated as (a-1)(b-1), where a and b are the levels of the two factors. For a 3 x 4 factorial design, (3-1)(4-1) = 6, which matches the given degrees of freedom for the interaction.

Question 14

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.

Accepted Answer

The answer of Data Set 13-2
Numbers in the cell are...

Question 15

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.

Accepted Answer

The interaction appears to be significant because the pattern of means across levels of one factor (A) changes at different levels of the other factor (B), indicating that the effect of one factor depends on the level of the other factor.

Question 16

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.

Accepted Answer

The answer of Data Set 13-2
Numbers in the cell are...

Question 17

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_totequal to 4.

Accepted Answer

This data set represents a 3 x 3 factorial design, as there are 3 levels of factor A (A1, A2, A3) and 3 levels of factor B (B1, B2, B3), making it a 3 x 3 matrix of means.

Question 18

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 _____.

Accepted Answer

The dataset has two independent variables, A and B, with A having 3 levels (A1, A2, A3) and B having 3 levels (B1, B2, B3).

Question 19

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.

Accepted Answer

An interaction in a figure typically means that the lines representing different groups or conditions are not parallel and may cross or diverge significantly. Without seeing the actual figures, based on common statistical interpretation, if option C (Y) is identified as showing an interaction, it suggests that in figure Y, the lines representing different variables or conditions interact with each other, indicating that the effect of one variable depends on the level of another variable.

Question 20

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.

Accepted Answer

In figure X, the lines representing different levels of variable B are parallel, indicating that the main effect of variable B is not significant because the effect of variable B does not change across different levels of another variable.

Quiz 13: Analysis of Variance: Factorial Design

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

A factorial ANOVA produces four F values.

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

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

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

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

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

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

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

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

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

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

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

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

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

Quiz 13: Analysis of Variance: Factorial Design

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

A factorial ANOVA produces four F values.

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

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

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

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

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

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

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

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 α\alphaα = .05 the null hypothesis for this interaction mean square should be

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

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

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

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

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

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