Question 1

The F statistic for factor B in a two-factor between-subjects analysis of variance is formed by dividing MSB by.

Accepted Answer

The F statistic for factor B is formed by dividing the mean square between-subjects (MSB) for factor B by the mean square error (MSE).

Question 2

The term  $\bar { X } _ { A B } - \bar { X } _ { A } - \bar { X } _ { B } + \bar { X } _ { G }$ is involved in the computation of SS in a two-factor between-subjects analysis of variance.

Accepted Answer

The term involves the interaction between factors A and B, which is represented by the A×B component of the SS in a two-factor between-subjects ANOVA.

Question 3

The difference -is involved in the computation of SS in a two-factor $X - \bar { X } _ { A B }$ between-subjects analysis of variance.

Accepted Answer

In a between-subjects ANOVA, the error term is computed using the difference between individual scores and the cell means ($X - \bar{X}_{AB}$), which represents the variability not explained by the main effects or interaction.

Question 4

If $S S _ { \text {Total } } = 150.00 , S S _ { A } = 8.00 , S S _ { B } = 10.00 , S S _ { A } \times B = 12.00 , S S _ { \text {Error } } = 120.00 , d f _ { \text {Total } } = 65$, $d f _ { A } = 2 , d f _ { B } = 1 , d f _ {{ A } \times B} = 2$, and $d f _ { \text {Error } } = 60$ in a two-factor between-subjects analysis of variance, then $M S _ { B } =$ and $M S _ { A \times B } =$

Accepted Answer

Mean Square (MS) is calculated by dividing the sum of squares (SS) by the degrees of freedom (df). Therefore, $MS_B = \frac{SS_B}{df_B} = \frac{10.00}{1} = 10.00$ and $MS_{A \times B} = \frac{SS_{A \times B}}{df_{A \times B}} = \frac{12.00}{2} = 6.00$.

Question 5

The degrees of freedom for factor B in a two-factor between-subjects analysis of variance are given by.

Accepted Answer

The degrees of freedom for factor B in a two-factor between-subjects ANOVA are equal to the number of levels of factor B minus 1. Therefore, the correct choice is D, which is b-1.

Question 6

Suppose a 2 × 2 between-subjects design had 11 participants randomly assigned to each cell. The df for SSTotal are equal to and the df for SSError are equal to for the analysis of variance of this design.

Accepted Answer

43; 40In a 2 × 2 between-subjects design with 11 participants in each cell, there are a total of 4 cells (2 conditions in one factor × 2 conditions in the other factor). With 11 participants per cell, the total number of participants is 4 × 11 = 44. Degrees of freedom for SSTotal (dfTotal) are calculated as the total number of observations minus 1, which is 44 - 1 = 43. Degrees of freedom for SSError (dfError) are calculated as the total number of observations minus the number of groups, which is 44 - 4 = 40.

Question 7

Suppose a 3 × 2 between-subjects design had 10 participants randomly assigned to each cell. The df for SSA × B are for the analysis of variance of this design.

Accepted Answer

The answer of Suppose a 3 × 2 between-subjects design...

Question 8

The degrees of freedom for factor A in a two-factor between-subjects analysis of variance are given by.

Accepted Answer

The degrees of freedom for factor A in a two-factor between-subjects ANOVA is equal to the number of levels of factor A minus 1 (a-1). This is because the number of levels of factor A determines the number of independent groups being compared, and the degrees of freedom correspond to the number of independent pieces of information available for estimating the population parameter of interest (the mean difference between levels of factor A).

Question 9

The degrees of freedom for the interaction of factors A and B in a two-factor between-subjects analysis of variance are given by.

Accepted Answer

The degrees of freedom for the interaction of factors A and B in a two-factor between-subjects ANOVA are calculated using the formula (a-1)(b-1), where a is the number of levels of factor A and b is the number of levels of factor B. This formula takes into account the number of independent groups within each level of both factors. Therefore, the correct answer is (a-1)(b-1).

Question 10

The mean square for the interaction of factors A and B in a two-factor between subjects analysis of variance is defined as SSA × B divided by.

Accepted Answer

The mean square for the interaction of factors A and B (MSAxB) in a two-factor between subjects analysis of variance is calculated by dividing the sum of squares for the interaction (SSAxB) by its associated degrees of freedom, which is (a - 1)(b - 1), where a is the number of levels of factor A, and b is the number of levels of factor B.

Question 11

Suppose a 3 × 2 between-subjects design had 10 participants randomly assigned to each cell. The df for SSTotal are equal to and the df for SSA are equal to for the analysis of variance of this design.

Accepted Answer

The total degrees of freedom (df for SSTotal) is calculated as the total number of participants minus 1, which is (3*2*10) - 1 = 59. The degrees of freedom for SSA (factor A) is the number of levels of factor A minus 1, which is 3 - 1 = 2.

Question 12

Suppose a 3 × 2 between-subjects design had 10 participants randomly assigned to each cell. The df for SSB are equal to and the df for SSError are equal to for the analysis of variance of this design.

Accepted Answer

The answer of Suppose a 3 × 2 between-subjects design...

Question 13

If SSTotal = 500.00, SSA = 150.00, SSB = 50.00, and SSError = 100.00 in a two-factor between-subjects analysis of variance, then SSA × B =.

Accepted Answer

SSA × B is calculated by subtracting SSA, SSB, and SSError from SSTotal: SSA × B = SSTotal - (SSA + SSB + SSError) = 500.00 - (150.00 + 50.00 + 100.00) = 200.00.

Question 14

The degrees of freedom for the error in a two-factor between-subjects analysis of variance are given by.

Accepted Answer

The degrees of freedom for the error term in a two-factor between-subjects ANOVA are calculated as follows: DFE = N - k, where N = total number of observations and k = total number of parameters estimated. In a two-factor design, k includes the main effects of each factor, the interaction effect, and the error term. For the error term, we estimate a separate variance for each cell of the design, and so the number of parameters estimated is the product of the number of levels of each factor minus one (i.e., a-1 and b-1), multiplied by the total number of participants minus one (i.e., nAB-1). Therefore, the correct formula for DFE is (a-1)(b-1)(nAB-1).

Question 15

If $S S _ { \text {Total } } = 150.00 , S S _ { A } = 8.00 , S S _ { B } = 10.00 , S S _ { A } \times B = 12.00 , S S _ { \text {Error } } = 120.00 , d f$ Total $= 65$, $d f _ { A } = 2 , d f _ { B } = 1 , d f _ {{ A } \times B} = 2$, and $d f _ { \text {Error } } = 60$ in a two-factor between-subjects analysis of variance, then $M S _ { A } = \ldots$ and $M S _ { \text {Error } } =$

Accepted Answer

Mean Square (MS) is calculated by dividing the sum of squares (SS) by the degrees of freedom (df). For factor A, $MS_A = \frac{SS_A}{df_A} = \frac{8.00}{2} = 4.00$. For error, $MS_{Error} = \frac{SS_{Error}}{df_{Error}} = \frac{120.00}{60} = 2.00$.

Question 16

The mean square for factor B in a two-factor between-subjects analysis of variance is defined as SSB divided by.

Accepted Answer

The mean square for factor B (MSB) in a two-factor between-subjects analysis of variance is calculated by dividing the sum of squares for factor B (SSB) by its degrees of freedom, which is the number of levels of factor B minus 1 (b - 1).

Question 17

The total degrees of freedom in a two-factor between-subjects analysis of variance is defined as the number of minus one.

Accepted Answer

The total degrees of freedom in a two-factor between-subjects analysis of variance is defined as the number of scores minus one. This encompasses all the variability in the data, not just that associated with the main effects or interactions.

Question 18

The F statistic for factor A in a two-factor between-subjects analysis of variance is formed by dividing MSA by.

Accepted Answer

The F statistic for a factor in an analysis of variance (ANOVA) is calculated by dividing the mean square of the factor (MSA for factor A) by the mean square error (MSError). This ratio helps determine if there are significant differences between the groups' means being compared.

Question 19

The mean square for factor A in a two-factor between-subjects analysis of variance is defined as SSA divided by.

Accepted Answer

The mean square for factor A (MSA) is calculated by dividing the sum of squares for factor A (SSA) by its degrees of freedom, which is the number of levels of factor A minus 1 (a - 1).

Question 20

The mean square for the error term in a two-factor between-subjects analysis of variance is defined as the SSError divided by.

Accepted Answer

The mean square for the error term in a two-factor between-subjects analysis of variance is calculated by dividing the sum of squares error (SSError) by the degrees of freedom for error, which is given by ab(n - 1) where a and b are the number of levels for the two factors, and n is the number of observations per cell. This formula accounts for the total number of observations contributing to the error term, adjusting for the structure of a two-factor design.

Quiz 11: Two-Factor Between-Subjects Analysis of Variance