Question 1

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.How many participants are in each of the treatment conditions?​
A)​4
B)​5
C)​6
D)​10

Accepted Answer

The answer of The results of a two-factor analysis of...

Question 2

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.What are the df values for the A x B interaction?​
A)1, 36​
B)​2, 36
C)​3, 36
D)​4, 36

Accepted Answer

The degrees of freedom for the A x B interaction is calculated by multiplying the degrees of freedom of factor A by the degrees of freedom of factor B. Since both factors have df = 2, the interaction df = 2 * 2 = 4 for the numerator. The denominator remains the same, so the correct answer is 4, 36.

Question 3

A two-factor research study has two levels of factor A and three levels of factor B with n = 8 participants in each treatment condition.For this study,what is the value for df_{between treatments}? A)3 B)4 C)5 D)6

Accepted Answer

The degrees of freedom between treatments (df_between) is calculated as the product of the degrees of freedom for each factor. For factor A with 2 levels, df_A = 2 - 1 = 1. For factor B with 3 levels, df_B = 3 - 1 = 2. The interaction df is df_A * df_B = 1 * 2 = 2. Therefore, df_between = df_A + df_B + df_interaction = 1 + 2 + 2 = 5.

Question 4

For the following data,what is the value of SS_{within treatment}?? $$\begin{array} { c | c | c } & \mathrm { n } = 5 & \mathrm { n } = 5 \ \text { A1 } & \mathrm { M } = 1 & \mathrm { M } = 2 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \ & \mathrm { n } = 5 & \mathrm { n } = 5 \ \mathrm {~A} 2 & \mathrm { M } = 1 & \mathrm { M } = 4 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \end{array}$$ A) 10 B) 20 C) 40 D) 60

Accepted Answer

The value of $SS_{1U1B1}$ within treatment $S1U1B0$ is calculated by adding the SS values within each treatment condition. Given the data, we have SS values of 10, 20, 10, and 20 for the four conditions. Adding these together gives $10 + 20 + 10 + 20 = 60$.

Question 5

Which of the following is best to present a structure of a two-factor experiment?​
A)pie chart​
B)​matrix
C)​Venn diagram
D)​line graph

Accepted Answer

A matrix is the best option for presenting the structure of a two-factor experiment as it allows for a clear and organized display of the levels of each factor and their combinations. A pie chart would not be appropriate as it is not designed to display multiple variables. A Venn diagram would not be suitable either as it is typically used to show overlapping sets or attributes. A line graph would not be appropriate as it is used to show trends over time rather than the structure of an experiment.

Question 6

Which of the following is used to calculate the degrees of freedom for the A x B interaction? A)df_{between. treatments} - df_A - df_B B)df_A - df_B C)df_within - (df_A + df_B) D)df_{between. treatments} - df_{within treatments}

Accepted Answer

The degrees of freedom for the A x B interaction is calculated by subtracting the degrees of freedom for the A main effect, the degrees of freedom for the B main effect, and the degrees of freedom for the within-treatments from the degrees of freedom for the between-treatments.

Question 7

For a two-factor study with two levels of factor A,two levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the value of SS_{between treatments}? A)10 B)40 C)50 D)300

Accepted Answer

The SS_between treatments is calculated by finding the sum of squares of the differences between each treatment mean and the grand mean, multiplied by the number of participants in each treatment. The grand mean is (4+1+3+2)/4 = 2.5. The SS_between treatments = 10[(4-2.5)² + (1-2.5)² + (3-2.5)² + (2-2.5)²] = 50.

Question 8

A two-factor ANOVA produces an F-ratio for factor A with df = 1,36 and an F-ratio for factor B with df = 2,36.Which of the following describes the experiment producing these F-ratios?​
A)​1 level of factor A and 2 levels of factor B
B)​2 levels of factor A and 3 levels of factor B
C)​2 levels for both factors
D)​3 levels for both factors

Accepted Answer

The degrees of freedom (df) for an F-ratio in ANOVA are determined by the number of levels of the factor minus one (for the numerator) and the total number of observations minus the number of levels of the factor (for the denominator). Given df = 1,36 for factor A, this indicates 2 levels of factor A (since 2-1=1) and given df = 2,36 for factor B, this indicates 3 levels of factor B (since 3-1=2). Therefore, the experiment must have 2 levels of factor A and 3 levels of factor B.

Question 9

For the following data,what is the value of SS_{between.treatments}?? $$\begin{array} { c c c } & \mathrm { B } 1 & \mathrm {~B} 2 \ \text { A1 } & \mathrm { n } = 5 & \mathrm { n } = 5 \ & \mathrm { M } = 1 & \mathrm { M } = 2 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \ \mathrm {~A} 2 & \mathrm { n } = 5 & \mathrm { n } = 5 \ & \mathrm { M } = 1 & \mathrm { M } = 4 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \end{array}$$ A)?10 B)?20 C)?30 D)?40

Accepted Answer

SS_{between.treatments} = SS_B1 + SS_B2 = 10 + 20 = 30

Question 10

For an experiment involving three levels of factor A and three levels of factor B,with a sample of n = 8 in each treatment condition,what are the df values for the F-ratio for the AxB interaction?​
A)2, 63​
B)​4, 63
C)​6, 63
D)​8, 63

Accepted Answer

The degrees of freedom for the AxB interaction is calculated as (levels of A - 1) * (levels of B - 1), which is (3-1)*(3-1) = 4. The denominator df is calculated as total number of observations minus the number of groups, which is (3*3*8) - (3*3) = 63.

Question 11

For a two-factor experiment with two levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor A?​
A)10​
B)​20
C)​30
D)​60

Accepted Answer

There are 3 levels of factor B, each with 10 subjects, for each level of factor A. Therefore, each level of factor A has 3 * 10 = 30 participants.

Question 12

For the following data,what is the value of SS_B?? $$\begin{array} { c c c } & \mathrm { B } 1 & \mathrm {~B} 2 \ \text { A1 } & \mathrm { n } = 5 & \mathrm { n } = 5 \ & \mathrm { M } = 1 & \mathrm { M } = 2 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \ \mathrm {~A} 2 & \mathrm { n } = 5 & \mathrm { n } = 5 \ & \mathrm { M } = 1 & \mathrm { M } = 4 \ & \mathrm { SS } = 10 & \mathrm { SS } = 20 \end{array}$$ A) 0 B) 10 C) 20 D) 40

Accepted Answer

SS_B can be broken down into: - SSS: Sum of squares (within group variance) - 1U1: Degrees of freedom (within group) - B1: Number of groups (level 1) - BS1: Number of subjects per group (level 1) - U1: Number of predictors (level 1) - B0: Number of intercepts (level 0) Using the given data, we can find the values for each of these components: - SSS = 10 + 10 = 20 - 1U1 = (5-1) + (5-1) = 8 - B1 = 2 - BS1 = 5 - U1 = 1 - B0 = 1 Putting these values together, we get: SS_B = 20 8 2 5 1 1 Therefore, the value of SS_B is 20.

Question 13

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,what is df_{within treatments}? A)9 B)18 C)36 D)39

Accepted Answer

The degrees of freedom within treatments (df within) is calculated as the total number of observations minus the number of treatment conditions. There are 2 levels of factor A and 2 levels of factor B, resulting in 2x2=4 treatment conditions. With n=10 participants per condition, there are 4x10=40 total observations. Therefore, df within = 40 - 4 = 36.

Question 14

A two-factor,independent-measures research study is evaluated using an analysis of variance.The F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40.Based on this information,what are the df values for the A x B interaction?​
A)​df = 2, 40
B)​df = 3, 40
C)​df = 4, 40
D)​df = 7, 40

Accepted Answer

The answer of A two-factor,independent-measures research study is evaluated using...

Question 15

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the SS value for factor A (SS_A)? A)0 B)50 C)125 D)250

Accepted Answer

The SS value for factor A is calculated based on the differences between the group means and the overall mean. In this case, the means for A1 are 4 and 1, and for A2 are 3 and 2. The overall mean is (4+1+3+2)/4 = 2.5. Since the means for each level of factor A (2.5 for A1 and 2.5 for A2) are the same as the overall mean, the SS for factor A is 0, indicating no variability due to factor A alone.

Question 16

For a two-factor experiment with two levels of factor A and three levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor B?​
A)10​
B)​20
C)​30
D)​60

Accepted Answer

Since there are two levels of factor A and three levels of factor B, with 10 subjects in each treatment condition, each level of factor B is combined with both levels of factor A. Therefore, for each level of factor B, there are 2 * 10 = 20 participants.

Question 17

The following table shows the results of a two-factor analysis of variance with two levels of factor A,three levels of factor B,and a separate sample of n = 5 participants in each of the treatment conditions.Note that several values are missing in the table.What is the missing value for the F-ratio for the A x B interaction? $$\begin{array} { c c c c c } 
\text { Source } & \text { SS } & d f & M S & \
\text { Between } & 80 & \mathrm { xx } & & \
\text { A } & 8 & \mathrm { xx } & \mathrm { xx } & F = x x \
\text { B } & \mathrm { xx } & \mathrm { xx } & 20 & F = x x \
\text { Ax B } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \
\text { Within } & \mathrm { xx } & \mathrm { x } & \mathrm { xx } & \
\text { Total } & 76 & \mathrm { xx } & & \
\hline
\end{array}$$
A)?2
B)?4
C)?8
D)?16

Accepted Answer

The answer of The following table shows the results of...

Question 18

How many separate F-ratios are used in a two-factor ANOVA?​
A)​one overall F-ratio
B)​two overall F-ratios
C)​three overall F-ratios
D)​four overall F-ratios

Accepted Answer

A two-factor ANOVA involves examining the main effects of two different factors as well as their interaction. Therefore, there are three separate sources of variance to consider, each of which produces a separate F-ratio: one for Factor 1, one for Factor 2, and one for the interaction of the two factors.

Question 19

What is the relationship among the separate F-ratios in a two-factor ANOVA?​
A)​They may have different df values but they all have the same denominator.
B)​They all have the same df values and they all have the same denominator.
C)​They may have different df values and may have different denominators.
D)​They all have the same df values but they may have different denominators.

Accepted Answer

The separate F-ratios in a two-factor ANOVA may have different degrees of freedom values but they all have the same denominator, which is the mean square error (MSE). Each F-ratio represents the variance between groups divided by the variance within groups for a specific factor. Since the denominator (MSE) is the same for each F-ratio, the F-ratios can be compared to determine if there is a significant main effect or interaction effect for each factor.

Question 20

The results of a two-factor analysis of variance produce df = 1,30 for the F-ratio for factor A,and df = 2,30 for the F-ratio for the A x B interaction.Based on this information,how many levels of factor B were compared in the study?​
A)​one
B)​two
C)​three
D)​four

Accepted Answer

The degrees of freedom for the A x B interaction (df = 2,30) indicate that there are 3 levels of factor B. The degrees of freedom for an interaction are calculated by multiplying the degrees of freedom of each factor minus one. Since the interaction's degrees of freedom are 2, it means (levels of B - 1) = 2, thus levels of B = 3.

Quiz 14: Two-Factor Analysis of Variance Independent Measures

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.How many participants are in each of the treatment conditions?

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.What are the df values for the A x B interaction?

A two-factor research study has two levels of factor A and three levels of factor B with n = 8 participants in each treatment condition.For this study,what is the value for df_{between treatments}?

Which of the following is best to present a structure of a two-factor experiment?

Which of the following is used to calculate the degrees of freedom for the A x B interaction?

For a two-factor study with two levels of factor A,two levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the value of SS_{between treatments}?

A two-factor ANOVA produces an F-ratio for factor A with df = 1,36 and an F-ratio for factor B with df = 2,36.Which of the following describes the experiment producing these F-ratios?

For an experiment involving three levels of factor A and three levels of factor B,with a sample of n = 8 in each treatment condition,what are the df values for the F-ratio for the AxB interaction?

For a two-factor experiment with two levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor A?

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,what is df_{within treatments}?

A two-factor,independent-measures research study is evaluated using an analysis of variance.The F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40.Based on this information,what are the df values for the A x B interaction?

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the SS value for factor A (SS_A) ?

For a two-factor experiment with two levels of factor A and three levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor B?

How many separate F-ratios are used in a two-factor ANOVA?

What is the relationship among the separate F-ratios in a two-factor ANOVA?

The results of a two-factor analysis of variance produce df = 1,30 for the F-ratio for factor A,and df = 2,30 for the F-ratio for the A x B interaction.Based on this information,how many levels of factor B were compared in the study?

Quiz 14: Two-Factor Analysis of Variance Independent Measures

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.How many participants are in each of the treatment conditions?​

The results of a two-factor analysis of variance produce df = 2,36 for the F-ratio for factor A and df = 2,36 for the F-ratio for factor B.What are the df values for the A x B interaction?​

A two-factor research study has two levels of factor A and three levels of factor B with n = 8 participants in each treatment condition.For this study,what is the value for dfbetween treatments?​

Which of the following is best to present a structure of a two-factor experiment?​

Which of the following is used to calculate the degrees of freedom for the A x B interaction?​

​For a two-factor study with two levels of factor A,two levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the value of SSbetween treatments?

A two-factor ANOVA produces an F-ratio for factor A with df = 1,36 and an F-ratio for factor B with df = 2,36.Which of the following describes the experiment producing these F-ratios?​

For an experiment involving three levels of factor A and three levels of factor B,with a sample of n = 8 in each treatment condition,what are the df values for the F-ratio for the AxB interaction?​

For a two-factor experiment with two levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor A?​

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,what is dfwithin treatments?​

A two-factor,independent-measures research study is evaluated using an analysis of variance.The F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40.Based on this information,what are the df values for the A x B interaction?​

For a two-factor study with two levels of factor A,2 levels of factor B,and a separate sample of n = 10 participants in each treatment condition,the two means for level A1 are 4 and 1,and the two means for level A2 are 3 and 2.For these data,what is the SS value for factor A (SSA) ?​

For a two-factor experiment with two levels of factor A and three levels of factor B and n = 10 subjects in each treatment condition,how many participants are in each level of factor B?​

How many separate F-ratios are used in a two-factor ANOVA?​

What is the relationship among the separate F-ratios in a two-factor ANOVA?​

The results of a two-factor analysis of variance produce df = 1,30 for the F-ratio for factor A,and df = 2,30 for the F-ratio for the A x B interaction.Based on this information,how many levels of factor B were compared in the study?​