Question 1

In a two-factor ANOVA,which of the following is not computed directly but rather is found by subtraction? A)SS_{between treatments} B)SS_A C)SS_B D)SS_AxB

Accepted Answer

In a two-factor ANOVA, the interaction sum of squares (SS_AxB) is not computed directly but is found by subtraction from the total sum of squares, after accounting for the main effects (SS_A and SS_B) and the total variation.

Question 2

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?
A)3
B)4
C)7
D)12

Accepted Answer

To calculate the number of separate groups of participants needed for an independent-measures, two-factor study with 3 levels of factor A and 4 levels of factor B, we need to multiply the number of levels of each factor. Therefore, 3 x 4 = 12, which means that there would be 12 separate groups of participants needed for this study.

Question 3

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?
A)2
B)4
C)16
D)Cannot determine without more information

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 4

If a two-factor analysis of variance produces a statistically significant interaction,what can you conclude about the main effects?
A)Either the main effect for factor A or the main effect for factor B is also significant
B)Both the man effect for factor A and the main effect for factor B are significant
C)Neither the main effect for factor A nor the main effect for factor B is significant
D)The significance of the main effects is not related to the significance of the interaction

Accepted Answer

The significance of the interaction effect does not imply anything about the significance of the main effects. Main effects and interaction effects are independent tests in a two-factor ANOVA.

Question 5

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?
A)1
B)2
C)3
D)Cannot be determined without additional information

Accepted Answer

The degrees of freedom for the AxB interaction (2,30) represent the product of the degrees of freedom for both factors A and B. Since the degrees of freedom for factor A is 1, the degrees of freedom for factor B must be 2 (i.e. 2x1=2). This means that factor B has two levels that were compared in the study. Therefore, the answer is C, with three levels of factor A and two levels of factor B.

Question 6

In a two-factor analysis of variance,a main effect is defined as _____.
A)the mean differences among the levels of one factor
B)the mean differences among all treatment conditions
C)the mean difference between the two factors
D)the difference between the largest treatment mean and the smallest treatment mean

Accepted Answer

A main effect is the effect of one independent variable on the dependent variable, ignoring the effects of the other independent variable. Therefore, it is the mean differences among the levels of one factor.

Question 7

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?
A)A main effect for factor A
B)A main effect for factor B
C)An interaction between A and B
D)The pattern would produce main effects for both A and B,and an interaction.

Accepted Answer

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

Question 8

A two-factor research study has 2 levels of factor A and three 3 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

df_{between treatments} = (n-1) = (8-1) = 7. Since factor A has 2 levels and factor B has 3 levels, there are 2*3=6 total treatment conditions. Therefore, there are 6-1=5 degrees of freedom remaining after accounting for the contrast between treatments_and. So, the value for df_{between treatments} is 5.

Question 9

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?
A)2,63
B)4,63
C)6,63
D)8,63

Accepted Answer

The answer of For an experiment involving 3 levels of...

Question 10

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?
A)Large differences between sample means and small sample variances
B)Large differences between sample means and large sample variances
C)Small differences between sample means and small sample variances
D)Small differences between sample means and large sample variances

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 11

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 F-ratio for factor A has 1 numerator degree of freedom, indicating that there is only one level of factor A. The F-ratio for factor B has 2 numerator degrees of freedom, indicating that there are two levels of factor B. Therefore, the correct answer is B with 2 levels of factor A and 3 levels of factor B.

Question 12

For a two-factor experiment with 2 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

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

Question 13

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?
A)1,4
B)1,24
C)1,29
D)2,29

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 14

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?
A)5
B)10
C)25
D)30

Accepted Answer

There are two levels of factor A and three levels of factor B, which means there will be a total of 2 x 3 = 6 treatment conditions. Since there are 5 participants in each treatment condition, the total number of participants needed for the entire study is 6 x 5 = 30. Therefore, the best choice is D.

Question 15

What is the relationship among the separate F-rations 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 answer of What is the relationship among the separate...

Question 16

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 17

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?
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 18

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B.Based on this information,what can you conclude about the interaction?
A)There must by a significant interaction
B)There probably is a significant interaction
C)The interaction cannot be significant
D)You cannot make any conclusion about the significance of the interaction

Accepted Answer

The results only indicate significant main effects for each factor, but do not provide information about the significance (or lack thereof) of the interaction between the two factors. Therefore, it is not possible to make any conclusions about the interaction based solely on the information provided.

Question 19

A repeated-measures ANOVA produced an F-ration 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?
A)1
B)14
C)15
D)Cannot determine without more information

Accepted Answer

The answer of A repeated-measures ANOVA produced an F-ration of...

Question 20

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 df_within? A)20 B)24 C)29 D)30

Accepted Answer

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

Quiz 13: Repeated-Measures and Two-Factor Anova

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

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?

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?

If a two-factor analysis of variance produces a statistically significant interaction,what can you conclude about the main effects?

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?

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

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?

A two-factor research study has 2 levels of factor A and three 3 of factor B with n = 8 participants in each treatment condition.For this study,what is the value for df_{between treatments}?

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?

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?

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 a two-factor experiment with 2 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 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?

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?

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

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 AxB interaction?

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B.Based on this information,what can you conclude about the interaction?

A repeated-measures ANOVA produced an F-ration 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?

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 df_within?