Question 1

For a research study with two levels of factor A,three 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 df value for factor A is equal to the number of levels of factor A minus 1, which is 2-1 = 1. 
The total df value is equal to the total number of observations minus 1, which is 2x3x5 - 1 = 29. 
Therefore, the df values for the F-ratio evaluating the main effect for factor A is 1, 24.

Question 2

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 between the two factors?​
A)​There must be 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 fact that there are significant main effects for both factor A and B does not provide enough information to determine the significance of the interaction between the two factors. A significant interaction would only be concluded if there was additional statistical analysis that explicitly tested for the interaction between the two factors. Therefore, it is not possible to make any conclusion about the significance of the interaction based on the provided information.

Question 3

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? 
A)​20
B)​30
C)​40
D)​50

Accepted Answer

D

Question 4

Which of the following not used in an F-ratio for the two-factor analysis of variance? A)MS_A B)MS_AxB C)MS_{between treatments} D)MS_{within treatments}

Accepted Answer

In a two-factor ANOVA, the F-ratio is calculated using MS_A, MS_B, MS_AxB, and MS_{within treatments}. MS_{between treatments} is not a term used in this context.

Question 5

If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?​
A)​Either the main effect for factor A or the main effect for factor B is also significant.
B)​Both the main 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 in a two-factor ANOVA indicates how the effect of one factor varies across the levels of the other factor, but it does not directly inform about the significance of the main effects of either factor. Main effects can be significant or not, regardless of the interaction effect.

Question 6

If the mean and variance are computed for each sample in an independent-measures two-factor experiment,then which 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 and small sample variances tend to produce large F-ratios in a two-factor ANOVA because the F-ratio is designed to measure the ratio of between-group variance to within-group variance. Large differences among sample means increase the numerator (indicating more variance between groups due to the treatment effect), and small variances within each sample decrease the denominator (indicating less random or error variance), both of which contribute to a larger F-ratio.

Question 7

If the results of a two-factor experiment are presented in a line graph,then what pattern appears in the graph if there is an interaction?​
A)​The lines in the graph are not straight (bent).
B)​The lines are separated by a space.
C)​The lines are parallel.
D)​The lines move toward each other or cross.

Accepted Answer

When there is an interaction, the lines representing the two factors will move toward each other or cross. This indicates that the effect of one factor depends on the level of the other factor. If the lines are parallel, it suggests that there is no interaction and the effects of the two factors are independent of each other. Bent lines or spaces between lines do not necessarily indicate an interaction.

Question 8

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

Accepted Answer

A main effect is the mean difference among the levels of one factor. It represents the overall effect of that factor on the dependent variable, regardless of the levels of the other factor. This can be calculated by averaging the scores for each level of the factor and comparing them.

Question 9

How many separate groups of participants would be needed for an independent-measures,two-factor study with three levels of factor A and 4 levels of factor B?​
A)​3
B)​4
C)​7
D)​12

Accepted Answer

For independent-measures, two-factor study with 3 levels of factor A and 4 levels of factor B, the total number of participants needed would be the product of the levels of both factors. Thus, the total number of participants needed would be 3 x 4 = 12. Therefore, the answer is D.

Question 10

A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication.In this two-factor study,factor A is medication versus no medication and factor B is male versus female.The medicine is expected to reduce blood pressure for both males and females,but it is expected to have a much greater effect for males.What pattern of results should be obtained if the medication works as predicted?​
A)​A significant main effect for factor A (medication)
B)​A significant interaction
C)​A significant main effect for factor A and a significant interaction
D)​An insignificant main effect for factor A (medication)

Accepted Answer

If the medication works as predicted, there should be a significant main effect for factor A (medication) because the medication is expected to reduce blood pressure. However, there should also be a significant interaction between factors A and B because the medication is expected to have a much greater effect for males. Therefore, the pattern of results expected is a significant main effect for factor A and a significant interaction, which is the choice C.

Question 11

Two variables are said to interact when ____.​
A)​the effect of one independent variable depends on the levels of the second variable
B)​both variables are equally influenced by a third factor
C)​the two variables are differentially affected by a third variable
D)​both variables produce a change in the subjects' scores

Accepted Answer

Variables are said to interact when the effect of one independent variable depends on the levels of the second variable. In other words, the effect of one variable on the dependent variable changes depending on the level of the second variable. This is also known as a moderation effect.

Question 12

In a two-factor experiment with two levels of factor A and two 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)​main effects for both A and B, and an interaction

Accepted Answer

The fact that there is a substantial difference between one of the treatment means and the other three indicates the presence of a main effect for one of the factors (either A or B). The fact that the other three means are essentially identical suggests that there is no main effect for the other factor. However, the fact that the treatment means are not all the same suggests the presence of an interaction between the two factors. Therefore, the correct answer is D, which states that there are main effects for both factors (A and B) and an interaction between them.

Question 13

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 14

How many separate samples would be needed for a two-factor,independent-measures research study with 3 levels of factor A and 3 levels of factor B?​
A)​3
B)​6
C)​9
D)​10

Accepted Answer

In a two-factor independent-measures research study with 3 levels of factor A and 3 levels of factor B, each level of factor A must be paired with each level of factor B to form separate samples. This results in a total of 9 separate samples needed for the study.

Question 15

In analysis of variance,each independent variable is referred to as a ____.​
A)​factor
B)​level
C)​comparison
D)​stage

Accepted Answer

In analysis of variance, each independent variable is referred to as a factor. Factors are the variables being tested in an experiment to determine their effect on the outcome. They are the inputs or explanatory variables that are manipulated to see the impact on the response variable. Levels refer to the different values or categories within a factor. Comparisons can be made between levels, but they do not refer to independent variables themselves. Stage is not a relevant term in the context of analysis of variance.

Question 16

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? 
A)10​
B)​20
C)​30
D)​40

Accepted Answer

If the missing mean was 20, then the means for each level of factor A would be 20, 40, and 60. Likewise, the means for each level of factor B would be 20, 30, and 40. If there is no interaction between factors A and B, then the difference between the means of factor A at each level of factor B should be the same. In this case, the differences are 20-20=0, 40-30=10, and 60-40=20. These differences are all different, indicating an interaction between factors A and B. Therefore, the missing mean must be adjusted until the differences between the means of factor A at each level of factor B are approximately equal, which occurs when the missing mean is 20.

Question 17

In a line graph showing the results from a two-factor experiment,the levels of factor B are presented on the X-axis and separate lines are used to display the means for A1 and A2.If the points on the line for A1 are consistently five points higher than the corresponding point on the line for A2,what pattern of results is indicated?​
A)​no indication of an interaction
B)​an indication of an A-effect
C)​an indication of an A-effect but no indication of an interaction
D)​an indication of an interaction but no indication of an A-effect

Accepted Answer

The consistent difference of five points between the lines for A1 and A2 indicates an A-effect, meaning that factor A has a significant effect on the outcome. However, there is no indication of an interaction because the difference between the lines does not vary depending on the level of factor B. Therefore, the correct choice is C, which indicates an A-effect but no interaction.

Question 18

For an experiment involving two levels of factor A and three levels of factor B with a sample of n = 5 in each treatment condition,what is the value for df_{within treatments}? A)20 B)24 C)29 D)30

Accepted Answer

df_{within treatments} = (a - 1) * (b - 1) * n= (2 - 1) * (3 - 1) * 5= 1 * 2 * 5= 10

Question 19

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

The study has 2 levels of factor A and 3 levels of factor B, creating 2 x 3 = 6 different treatment conditions. With n = 5 participants in each condition, the total number of participants needed is 6 x 5 = 30.

Question 20

In a two-factor ANOVA,what is the implication of a significant AxB interaction?​
A)​At least one of the main effects must also be significant.
B)​Both of the main effects must also be significant.
C)​Neither of the two main effects can be significant.
D)​The significance of the interaction has no implications for the main effects.

Accepted Answer

A significant AxB interaction implies that the effect of one factor depends on the level of the other factor. It does not necessarily imply anything about the significance of the main effects themselves.

Quiz 14: Two-Factor Analysis of Variance Independent Measures

For a research study with two levels of factor A,three 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?

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 between the two factors?

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?

Which of the following not used in an F-ratio for the two-factor analysis of variance?

If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?

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

If the results of a two-factor experiment are presented in a line graph,then what pattern appears in the graph if there is an interaction?

In a two-factor analysis of variance a main effect is defined as the ____.

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

Two variables are said to interact when ____.

In a two-factor experiment with two levels of factor A and two 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?

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

How many separate samples would be needed for a two-factor,independent-measures research study with 3 levels of factor A and 3 levels of factor B?

In analysis of variance,each independent variable is referred to as a ____.

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?

For an experiment involving two levels of factor A and three levels of factor B with a sample of n = 5 in each treatment condition,what is the value for df_{within treatments}?

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?

In a two-factor ANOVA,what is the implication of a significant AxB interaction?

Quiz 14: Two-Factor Analysis of Variance Independent Measures

For a research study with two levels of factor A,three 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?​

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 between the two factors?​

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?

Which of the following not used in an F-ratio for the two-factor analysis of variance?​

If a two-factor analysis of variance produces a statistically significant interaction between the two factors A and B,then what can you conclude about the main effects for A and B?​

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

If the results of a two-factor experiment are presented in a line graph,then what pattern appears in the graph if there is an interaction?​

In a two-factor analysis of variance a main effect is defined as the ____.​

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

Two variables are said to interact when ____.​

In a two-factor experiment with two levels of factor A and two 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?​

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

How many separate samples would be needed for a two-factor,independent-measures research study with 3 levels of factor A and 3 levels of factor B?​

In analysis of variance,each independent variable is referred to as a ____.​