Deck 14: Two-Factor Analysis of Variance

Question 1

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

Answer 1

D

Question 2

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

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

Answer 2

A

Question 3

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

Answer 3

B

Question 4

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 5

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 AxB interaction?

A)df = 2, 40
B)df = 3, 40
C)df = 4, 40
D)df = 7, 40

Question 6

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 7

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

Question 8

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 9

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

Question 10

How many separate F-ratios are used in a two-factor ANOVA?

A)one overall F?ratio
B)two separate F?ratios
C)three separate F?ratios
D)four separate F?ratios

Question 11

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 12

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 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

Question 14

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

Question 15

Which of the following is used to calculate the degrees of freedom for the A x B interaction?

A)df_{bet.treatments} - df_A - df_B
B)df_A - df_B
C)df_within - (df_A + df_B)
D)df_{bet.treatments} - df_within

Question 16

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 17

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 18

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

Question 19

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 20

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.

Question 21

The following table shows the results of a repeated-measures ANOVA.Based on this table, what is the value for $\eta$ ² for factor A?

A) $12 / 36$
B) $12 / 96$
C) $12 / 99$
D) $12 / 120$

Question 22

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)none of the above.

Question 23

If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then 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

Question 24

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?

Question 25

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 AxB interaction?

Question 26

For the following data, what is the value of SS_B?

Question 27

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 main effects?

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.

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_within?

Question 30

For the following data, what is the value of SS_{bet.treatments}?

Question 31

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?

Question 32

For a two-factor study with 2 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 33

For a two-factor study with 2 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 34

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 B?

A)10
B)20
C)30
D)60

Question 35

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.

Question 36

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

Question 37

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 5 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 overall 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 38

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)there is a space separating the lines
C)the lines are parallel
D)the lines move toward each other or cross

Question 39

For a two-factor study with 2 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 value of SS_{between treatments}?

A)10
B)40
C)50
D)300

Question 40

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

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

Question 41

A two-factor ANOVA consists of three separate hypothesis tests.

Question 42

A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.

Question 43

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 44

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 45

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 46

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

Question 47

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 48

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 49

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

Question 50

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.

Question 51

A two-factor, independent-measures research study with 2 levels of factor A and 3 levels of factor B with n = 10 participants in each treatment condition would require a total of 60 participants.

Question 52

A two-factor study compares 2 levels of factor A and 3 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 53

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 54

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 55

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

Question 56

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

Question 57

A two-factor, independent-measures research study with 2 levels of factor A and 2 levels of factor B would require 2 separate groups of participants.

Question 58

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

Question 59

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 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 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 62

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

Question 63

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 parfticipants' scores.

Question 64

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 65

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 66

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 67

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 68

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 69

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 70

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