Question 1

In a two-factor analysis of variance,a main effect is defined as _____.

Accepted Answer

A main effect is the mean differences among the levels of one factor, regardless of the levels of the other factor. It represents the overall effect of one factor on the dependent variable.

Question 2

In a two-factor experiment with 2 levels of factor A and 2 levels of factor B,three of the treatment means are essentially identical and one is substantially different from the others.What result(s)would be produced by this pattern of treatment means?

Accepted Answer

The answer of In a two-factor experiment with 2 levels...

Question 3

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?

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). For factor A, df = 1,36 suggests 2 levels of factor A (since 1+1=2) and for factor B, df = 2,36 suggests 3 levels of factor B (since 2+1=3), matching option B.

Question 4

A repeated-measures experiment compares three treatment conditions with a sample of n = 10 participants.If the data are analyzed with ANOVA,the analysis would have dfₜₒₜₐₗ = _____.

Accepted Answer

For a repeated-measures ANOVA, the total degrees of freedom (df_total) is calculated as df_total = n – 1. In this case, with a sample size of n = 10, df_total = 9. However, since there are three treatment conditions, the degrees of freedom for the treatments (df_treatments) is equal to k – 1, where k is the number of treatment conditions. Therefore, df_treatments = 3 – 1 = 2. Finally, the degrees of freedom for the error term (df_error) is calculated as df_error = df_total – df_treatments = 9 – 2 = 7. Thus, the ANOVA would have df_total = 9, df_treatments = 2, and df_error = 7, for a total of df_total + df_treatments + df_error = 9 + 2 + 7 = 18 + 11 = 29 degrees of freedom.

Question 5

The following data represent the means for each treatment condition in a two-factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?
 B1 B2

Accepted Answer

The answer of The following data represent the means for...

Question 6

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 AxB interaction.Based on this information,how many levels of factor B were compared in the study?

Accepted Answer

The degrees of freedom for the AxB interaction (df = 2,30) indicate that there are 3 levels of factor B. This is because the degrees of freedom for an interaction term are calculated by multiplying the degrees of freedom of the factors involved (dfA+1)*(dfB+1) - 1, where dfB = 2 suggests 3 levels of B (since df = number of levels - 1).

Question 7

If the mean and variance are computed for each sample in an independent-measures,two-factor experiment,which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

Accepted Answer

Large differences between sample means indicate that the treatment effects are substantial, while small sample variances suggest that the data points within each group are close to their group mean, leading to clearer distinctions between the groups. This combination tends to produce large F-ratios in a two-factor ANOVA, indicating significant effects.

Question 8

The following data represent the means for each treatment condition in a two-factor experiment.Note that one mean is not given.What value for the missing mean would result in no main effect for factor B?
 B1 B2

Accepted Answer

The answer of The following data represent the means for...

Question 9

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 AxB interaction?

Accepted Answer

The degrees of freedom for the AxB interaction are calculated by multiplying the degrees of freedom of factor A by those 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 10

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?

Accepted Answer

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

Question 11

How many separate groups of participants would be needed for an independent-measures,two-factor study with 3 levels of factor A and 4 levels of factor B?

Accepted Answer

In an independent-measures, two-factor study, each participant is assigned to only one cell in the design, resulting in four groups for each combination of the two factors. Therefore, the total number of separate groups of participants needed in this study would be the product of the number of levels of factor A (3) and the number of levels of factor B (4), which is 12.

Question 12

A repeated-measures analysis of variance for a study comparing three treatment conditions with a sample of n = 10 participants,produces an F-ratio of F = 5.40.For this result,which of the following is the correct statistical decision?

Accepted Answer

The F-ratio of 5.40 is likely significant at α = .05 but not at α = .01, given typical critical values for F-distribution with small sample sizes.

Question 13

A repeated-measures ANOVA produced an F-ratio of F = 4.00 with df = 1,14.If the same data were analyzed with a repeated-measures t test,what would be the df value for the t statistic?

Accepted Answer

The degrees of freedom (df) for a repeated-measures t-test is calculated based on the number of subjects minus one. Given that the repeated-measures ANOVA has df = 14 for the within-subjects effect, this indicates there are 15 subjects (since df = N - 1 for within-subjects designs, where N is the number of subjects). Therefore, for a repeated-measures t-test, the df would also be 14, matching the within-subjects df from the ANOVA.

Question 14

For a research study with 2 levels of factor A,3 levels of factor B,and n = 5 in each treatment condition,what are the df values for the F-ratio evaluating the main effect for factor A?

Accepted Answer

The degrees of freedom for the main effect of factor A is 1 (since there are 2 levels of factor A, df = 2 - 1 = 1). The error term's degrees of freedom is calculated by the total number of observations minus the number of treatment conditions. With 2 levels of A, 3 levels of B, and 5 observations per treatment, there are 2*3*5 = 30 total observations and 2*3 = 6 treatment conditions. Thus, df for the error term is 30 - 6 = 24.

Question 15

The following table shows the results of a repeated-measures ANOVA.Based on this table,what is the value for n²,the percentage of variance accounted for by the treatments? $$\begin{array} { l c c c c } 
\text { Source } & \text { SS } & \text { df } & \text { MS } & \
\text { Between } & 22 & 2 & 11 & F = 5.50 \
\text { Within } & 58 & 21 & & \
\text { Bet. Sub. } & 30 & 7 & & \
\text { Error } & 28 & 14 & 2 & \
\text { Total } & 80 & 23 & &
\end{array}$$

Accepted Answer

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

Question 16

In a two-factor ANOVA,which of the following is not computed directly but rather is found by subtraction?

Accepted Answer

In a two-factor ANOVA, the interaction term SSAxB (the interaction between factor A and factor B) is not computed directly but is found by subtraction from the total SS after accounting for the main effects (SSA and SSB) and the error.

Question 17

For an experiment involving 3 levels of factor A and 3 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?

Accepted Answer

The degrees of freedom for the AxB interaction is calculated as (levels of A - 1) * (levels of B - 1). Here, (3-1)*(3-1) = 4. The total degrees of freedom is calculated as (total number of observations - number of groups), which is (3*3*8 - 9) = 63. Thus, the df for the AxB interaction is 4, 63.

Question 18

For an experiment involving 2 levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition,what is the value for dfwᵢthᵢn?

Accepted Answer

The answer of For an experiment involving 2 levels of...

Question 19

A repeated-measures ANOVA produced an F-ratio of F = 4.00 with df = 1,14.If the same data were analyzed with a repeated-measures t test,what value would be obtained for the t statistic?

Accepted Answer

The t statistic is the square root of the F-ratio when comparing the same data in a repeated-measures design, so $t = \sqrt{F} = \sqrt{4.00} = 2$.

Question 20

A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition.How many participants are needed for the entire study?

Accepted Answer

In a two-factor study with two levels of factor A and three levels of factor B, there are a total of 2 x 3 = 6 treatment conditions. Since there are n = 5 participants in each condition, the total number of participants needed is 6 x 5 = 30.

Quiz 13: Repeated-Measures and Two-Factor Analysis of Variance