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

Question 1

A repeated-measures ANOVA with n = 5 subjects has df within₋treatment equal to 12.What is the value for dfₑᵣᵣₒᵣ for this analysis?

A)8
B)16
C)48
D)Insufficient information to find dferror

Answer 1

8

Question 2

In the first stage of a repeated-measures ANOVA,total degrees of freedom is partitioned into _________________.

A)error df and between-subjects df
B)within-treatments df and between-subjects df
C)between-treatments df and between-subjects df
D)between-treatments df and within-treatments df

Answer 2

between-treatments df and within-treatments df

Question 3

A repeated-measures ANOVA has $\text { SSwithin }$ treatments = 26 and $S S _ { \text {between } }$ subjects = 12.For this analysis,what is the value for SS_error?

A)12
B)14
C)26
D)38

Answer 3

14

Question 4

The repeated-measures ANOVA is a two-stage process.Which of the following accurately describes what happens during this process?

A)The first stage removes individual differences from the numerator of the F-ratio, and the second stage removes individual differences from the denominator.
B)The first stage removes individual differences from the numerator.
C)The second stage removes individual differences from the denominator.
D)None of these

Question 5

For the following data,what is SS_total?
$$\begin{array}{l}\text { Treatments }\\\begin{array} { c c c c c c } \text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \\\text { A } & 3 & 4 & 5 & 12 & G = 27 \\\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \\\text { C } & 2 & 1 & 6 & 9 &\end{array}\\\begin{array} { c c c } T = 6 & T = 6 & T = 15\end{array}\\S S = 2 \quad S S = 6 \quad S S = 2\end{array}$$

A)28
B)18
C)10
D)6

Question 6

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,what are the degrees of freedom for the repeated-measures F-ratio?

A)2, 6
B)2, 9
C)2, 11
D)3, 11

Question 7

For the following data,what is $S S _ { \text {between } }$ subjects? $$\begin{array} { l c c l c l } & { \text { Treatments } } \\\text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \\\hline \text { A } & 3 & 4 & 5 & 12 & G = 27 \\\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \\\text { C } & 2 & 1 & 6 & 9 & \\& T = 6 & T = 6 & T = 15 & & \\& S S = 2 & S S = 6 & S S = 2 & &\end{array}$$

A)2
B)3
C)6
D)12

Question 8

A repeated-measures study uses a sample of n = 15 participants to evaluate the mean differences among four treatment conditions.In the analysis of variance for this study,what is the value for df between treatment?

A)3
B)4
C)5
D)59

Question 9

A researcher reports an F-ratio with df = 2,40 from a repeated-measures ANOVA.How many treatment conditions were compared in this experiment?

A)2
B)3
C)4
D)41

Question 10

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the numerator of the F-ratio?

A)They do not exist because the same individuals participate in all treatments.
B)They are measured and subtracted out in the second stage of the analysis.
C)Individual differences contribute to the variance in the numerator.
D)None of the other options accurately describes individual differences in the numerator.

Question 11

A researcher uses a repeated-measures ANOVA to test for mean differences among three treatment conditions using a sample of n = 10 participants.What are the df values for the F-ratio from this analysis?

A)3, 9
B)2, 9
C)3, 18
D)2, 18

Question 12

What is the correct denominator for the repeated-measures F-ratio?

A)MSerror
B)MSwithin
C)MSbetween subjects
D)MSbetween treatments

Question 13

A researcher reports an F-ratio with df = 2,40 from a repeated-measures ANOVA.How many subjects participated in this experiment?

A)44
B)41
C)63
D)21

Question 14

When using the Scheffé post hoc test for a repeated-measures ANOVA,the denominator for the F ratio should be _____.

A)MSerror
B)MSbetween subjects
C)MSwithin
D)MSbetween treatment

Question 15

In a repeated-measures ANOVA,the variability within treatments is divided into two components.What are they?

A)Between-subjects variance and error variance
B)Between-subjects variance and between-treatments variance
C)Between-treatments variance and error variance
D)Total variability and error variance

Question 16

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the denominator of the F-ratio?

A)They do not exist because the same individuals participate in all treatments.
B)They are measured and subtracted out in the second stage of the analysis.
C)Individual differences contribute to the variance in the denominator.
D)None of the other options accurately describes individual differences in the denominator.

Question 17

The following table shows the results of a repeated-measures analysis of variance comparing two treatment conditions with a sample of n = 12 participants.Note that several values are missing in the table.What is the missing value for SSₜₒₜₐₗ?

A)45
B)47
C)80
D)148

Question 18

In a repeated-measures analysis of variance,how does the magnitude of the mean differences from one treatment to another contribute to the F-ratio?

A)The mean differences add to the numerator of the F-ratio.
B)The mean differences add to the denominator of the F-ratio.
C)The mean differences add to both the numerator and the denominator of the F-ratio.
D)The sample mean differences do not influence the F-ratio.

Question 19

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,the participant totals (the P values)are 3,6,9,and 6.What is the value for $S S _ { \text {between } }$ subjects?

A)2
B)3
C)6
D)10

Question 20

For the following data,what are the df values for the repeated-measures F-ratio? $$\begin{array} { l c c l c l } { \text { Treatments } } \\\text { Subject } & \text { I } & \text { II } & \text { III } & \text { P-totals } & \\\hline \text { A } & 3 & 4 & 5 & 12 & G = 27 \\\text { B } & 1 & 1 & 4 & 6 & \Sigma X ^ { 2 } = 109 \\\text { C } & 2 & 1 & 6 & 9 & \\& T = 6 & T = 6 & T = 15 & & \\& S S = 2 & S S = 6 & S S = 2 & &\end{array}$$

A)2, 4
B)2, 6
C)3, 4
D)3, 6

Question 21

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 22

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 23

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 24

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 = _____.

A)27
B)28
C)29
D)30

Question 25

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

A)10
B)15
C)30
D)40

Question 26

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 27

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

Question 28

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

A)20
B)30
C)40
D)50

Question 29

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 30

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 31

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

Question 32

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?

A)Reject the null hypothesis with either α = .05 or α = .01
B)Reject the null hypothesis with α = .05 but not with α = .01
C)Fail to reject the null hypothesis with either α = .05 or α = .01
D)There is not enough information to determine the correct decision.

Question 33

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?

A)1
B)14
C)15
D)Cannot determine without more information

Question 34

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 35

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? $$\begin{array} { l c c c c } \text { Source } & \text { SS } & \text { df } & \text { MS } & \\\text { Between } & 22 & 2 & 11 & F = 5.50 \\\text { Within } & 58 & 21 & & \\\text { Bet. Sub. } & 30 & 7 & & \\\text { Error } & 28 & 14 & 2 & \\\text { Total } & 80 & 23 & &\end{array}$$

A)22/30
B)22/50
C)22/58
D)22/80

Question 36

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

A) $S S _ { \text {between } }$ treatments
B)SSA
C)SSB
D)SSAxB

Question 37

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 38

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?

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

Question 39

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

Question 40

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 41

For the repeated-measures analysis,the F-ratio,on average,is expected to be zero when H₀ is true.

Question 42

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 43

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 44

The denominator of the repeated-measures F-ratio is intended to measure differences that exist without any systematic treatment effect or any systematic individual differences.

Question 45

Because the repeated-measures ANOVA removes variance caused by individual differences,it usually is more likely to detect a treatment effect than the independent-measures ANOVA is.

Question 46

The F-ratio for a repeated-measures ANOVA has df = 1,15.The research study used a total of n = 16 participants.

Question 47

For the following data,what is the value of $\text { SSwithin }$ ?
B1 B2

A)10
B)20
C)40
D)60

Question 48

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 these

Question 49

The following table shows the results of a two-factor ANOVA.Based on this table,what is the value for ² for factor A?
$$\begin{array} { c c r r l } \text { Source } & \text { SS } & \text { df } & \text { MS } & \\ \text { Between } & 36 & 3 & & \\\text { A } & 12 & 1 & 12 & F = 4.00 \\\text { B } & 3 & 1 & 3 & F = 1.00 \\\text { AxB } & 21 & 1 & 21 & F = 7.00 \\\text { Within } & 84 & 28 & 3 & \\\text { Total } & 120 & 31 & &\end{array}$$

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

Question 50

In the second stage of the repeated-measures ANOVA,individual differences are removed from the denominator of the F-ratio.

Question 51

For the following data,what is the value of SSB?
B1 B2

A)0
B)10
C)20
D)40

Question 52

A repeated-measures study uses a sample of n = 10 participants to evaluate the mean differences among three treatment conditions.For this study,df between subjects = 18.

Question 53

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 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

Question 54

The following table shows the results of a two-factor analysis of variance with 2 levels of factor A,3 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? $$\begin{array} { c r r r l } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \\\text { Between } & 80 & \mathrm { xx } & & \\\text { A } & 8 & \mathrm { xx } & \mathrm { xx } & F = \mathrm { xx } \\\text { B } & \mathrm { xx } & \mathrm { xx } & 20 & F = \mathrm { xx } \\\text { AxB } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & F = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \\\text { Total } & 176 & \mathrm { xx } & &\end{array}$$

A)2
B)4
C)8 F = xx
D)16

Question 55

The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.

Question 56

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 treatment?

A)3
B)4
C)5
D)6

Question 57

For a repeated-measures design,the differences between treatments may be caused by a treatment effect or by sampling error (random factors),but they cannot be caused by individual differences.

Question 58

A repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences between two treatment conditions.The analysis of variance for this study will have dfₑᵣᵣₒᵣ = 7.

Question 59

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 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 60

For a repeated-measures study,if there are no systematic treatment effects (H₀ is true),then the numerator and denominator of the F-ratio are both measuring the same sources of variance.

Question 61

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 62

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 63

A repeated-measures study has n = 8 participants and k = 3 treatments.For this study,dfₑᵣᵣₒᵣ= 21.

Question 64

A repeated-measures t test produces a t statistic of t = 4.00 with df = 12.If the same data were evaluated with a repeated-measures ANOVA,the F-ratio would have df = 2,12.

Question 65

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 66

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

Question 67

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 68

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 69

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

Question 70

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 uses a total of 25 participants.

Question 71

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

Question 72

The F-ratio for a repeated-measures ANOVA has df = 2,16.The research study compared 3 treatments with a sample of n = 8 participants.

Question 73

The result of a repeated-measures ANOVA stated that F(3,21)= 4.57,p < .05.The study used a sample of n = 7 participants.

Question 74

If a two-factor study has 2 levels of factor A and 3 levels of factor B,then
df between treatment = 5.

Question 75

For a repeated-measures study,df between treatment= 3 and dfₜₒₜₐₗ = 27.This means that there were n = 7 participants in the study.

Question 76

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 77

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 78

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 79

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

Question 80

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.