Deck 14: Two-Factor Analysis of Variance Independent Measures

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

Answer 1

​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.

Answer 2

​You cannot make any conclusion about the significance of the interaction.

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

Answer 3

​50

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}

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.

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

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.

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

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

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)

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

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

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

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

Question 15

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

A)​factor
B)​level
C)​comparison
D)​stage

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

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

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

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

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.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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}

Question 27

​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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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.

Question 40

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

Question 41

In a two-factor ANOVA for an independent-measures study,all of the F-ratios use the same denominator.

Question 42

A two-factor analysis of variance with two levels of factor A and three levels of factor B involves six separate hypothesis tests.

Question 43

A two-factor study compares 2 levels of factor A and 2 levels of factor B with a sample of n = 20 participants in each treatment condition.If the results are evaluated with a two-factor ANOVA,all the F-ratios will have df = 1,76.

Question 44

Individual treatment conditions are also referred to as cells.

Question 45

If a researcher expects that a new teaching technique will be more effective for children who are more than 10 years old than it is for younger children,then the researcher is predicting an interaction between the teaching technique and age.

Question 46

A two-factor experimental design means that the researcher must measure two separate scores for each subject.

Question 47

A two-factor,independent-measures research study with two levels of factor A and three levels of factor B with n = 10 participants in each treatment condition would require a total of 60 participants.

Question 48

If the F-ratios for factor A and factor B both have df = 1,36,then the F-ratio for the interaction will also have df = 1,36.

Question 49

For an independent-measures two-factor experiment,the bigger the differences between the sample means,the more likely it is that at least one of the F-ratios will be significant.

Question 50

For a two-factor analysis of variance,the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.

Question 51

A two-factor study compares three different treatment conditions (factor 1)for males and females (factor 2).In this study,the main effect for gender is determined by the overall mean score for the males (averaged over the three treatments)and the corresponding overall mean score for the females.

Question 52

Obtaining a significant interaction means that both factors A and B have significant main effects.

Question 53

A two-factor,independent-measures research study with two levels of factor A and two levels of factor B would require two separate groups of participants.

Question 54

If the A x B interaction is significant,then at least one of the two main effects also must be significant.

Question 55

A two-factor study compares two levels of factor A and three levels of factor B with a sample of n = 5 participants in each treatment condition.This study will use a total of 25 participants.

Question 56

A two-factor analysis of variance produces an F-ratio for factor A that has df = 3,36.This analysis is comparing three different levels of factor A.

Question 57

A researcher predicts that a special training course will be highly effective for females but will have little or no effect for males.This researcher is predicting an interaction between training and gender.

Question 58

A two-factor study compares two different treatment conditions (factor 1)for males and females (factor 2).In this study,the males have an average score of 20 in the first treatment and an average of 25 in the second.The females average 35 in the first treatment and 45 in the second.For this study,there is no interaction.

Question 59

A new laundry detergent is supposed to be equally superior to the leading brand in both hot and cold water.If the new detergent works as predicted,then there should be an interaction between the brand of detergent and the temperature of the water.

Question 60

If the F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40,then the F-ratio for the interaction must have df = 2,40.​

Question 61

If a two-factor study has two levels of factor A,and three levels of factor B,then df_{between.treatments} = 5.

Question 62

For an independent-measures two-factor analysis of variance,all of the F-ratios use the same denominator.​

Question 63

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns,with a separate sample in each of the matrix cells.Using this matrix structure,describe what is meant by the "main effect" for each factor and the "interaction" between factors.

Question 64

For an independent-measures two-factor experiment,the bigger the values for the sample variances,the more likely it is that at least one of the F-ratios will be significant.​

Question 65

What are the assumptions for the two-factor ANOVA?

Question 66

Whenever a two-factor experiment results in a significant interaction,you should be cautious about interpreting the main effects because an interaction can distort,conceal,or exaggerate the main effects of the individual factors.

Question 67

If a two-factor ANOVA results in a significant main effect for factor A and a significant A x B interaction,explain why you should be cautious in interpreting the effect of factor A.

Question 68

If the F-ratios for factor A has df = 1,36 and the F-ratio for the interaction has df = 2,36,then the F-ratio for factor B will also have df = 2,36.

Question 69

It often is possible to reduce the variance in an independent-measures design by using a participant variable such as age or gender as a second factor.

Question 70

The following data were obtained from a two-factor independent-measures experiment with n = 5 participants in each treatment condition.​ ​
a. State the hypotheses for each of the three separate tests included in the two-factor ANOVA.
b. Calculate degrees of freedom and locate the critical region for each of the three tests.
c. Calculate the three F-ratios.
d. State a conclusion for each test.

Question 71

If the results of a two-factor ANOVA show no main effect for factor A and no significant interaction,then it is safe to conclude that factor A has no effect on the participants' scores.

Question 72

The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with two levels of factor A,three levels of factor B,and n = 8 participants in each treatment condition
a. Fill in all missing values in the table. (Hint: Start with the df column.)
b. Compute η² (the percentage of variance accounted for) for each of the main effects and for the interaction.​

Question 73

In a two-factor ANOVA,MS_{between treatments} = MS_A + MS_B + MS_AxB.

Question 74

If the results of a two-factor ANOVA show no main effect for factor A but show a significant interaction,then the results indicate that factor A has no effect on the subjects' scores.

Question 75

A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 10 participants in each treatment condition.For this study,the F-ratio for factor A has df = 2,54.