Deck 13: Repeated-Measures Analysis of Variance Anova

Question 1

A repeated-measures analysis of variance produces SS_total = 40 and SS_{within treatments} = 10.For this analysis,what is SS_{between treatments}?​

A)​30
B)​40
C)​50
D)​10

Answer 1

​30

Question 2

A repeated-measures ANOVA has SS_{within treatments} = 26 and SS_{between subjects} = 12.For this analysis,what is the value for SS_error?​

A)12​
B)​14
C)​26
D)​38

Answer 2

​14

Question 3

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 mean differences are subtracted from the numerator of the F-ratio.

Answer 3

​The mean differences add to the numerator of the F-ratio.

Question 4

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

A)​8
B)​16
C)​17
D)​48

Question 5

A repeated-measures study uses a sample of n = 10 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 subjects}?​

A)9​
B)​27
C)​36
D)​39

Question 6

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 SS_{between subjects}?​

A)2​
B)​3
C)​6
D)​10

Question 7

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 8

For independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.What happens to the individual differences in the numerator of the F-ratio for repeated-measures ANOVA?​

A)​They do not exist because the same individuals participate in all of the treatments.
B)​They are measured and subtracted out in the analysis process.
C)​They contribute to the variance in the numerator.
D)​They are amplified in the numerator of the ratio.

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

A researcher obtains an F-ratio with df = 3,12 from an ANOVA for a repeated-measures research study.How many subjects participated in the research study?​

A)​4
B)​5
C)​6
D)​13

Question 11

A repeated-measures analysis of variance produces SS_{within treatments} = 84 and SS_{between subjects} = 20.For this analysis,what is the value of SS_error?​

A)​16
B)​24
C)​64
D)​104

Question 12

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 13

A repeated-measures ANOVA produces SS_{between treatments} = 30 and MS_{between treatments} = 10.In this analysis,how many treatment conditions are being compared?​

A)​3
B)​4
C)​5
D)​20

Question 14

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

A)​MS_error
B)​MS_within
C)​MS_{between subjects}
D)​MS_{between treatments}

Question 15

For independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.What happens to the individual differences in the denominator of the F-ratio for repeated-measures ANOVA?​

A)​They do not exist because the same individuals participate in all of the treatments.
B)​They are measured and subtracted out in of the analysis process.
C)​They contribute to the variance in the denominator.
D)​They are amplified in the denominator of the ratio.

Question 16

A repeated-measures research study uses n = 8 subjects.If the within-treatment df for the ANOVA is 21,what is the value for the error df?​

A)​7
B)​13
C)​14
D)​18

Question 17

The results from a repeated-measures ANOVA are reported as,F(3,24)= 3.75,p < .05.For this study,how many treatment conditions were compared?​

A)​2
B)​3
C)​4
D)​28

Question 18

The repeated-measures ANOVA is a two-stage process.Which statement accurately describes the second stage of this process?​

A)​The second stage adds individual differences to the denominator.
B)​The second stage adds individual differences to the numerator.
C)​The second stage removes individual differences from the denominator.
D)​The second stage removes individual differences from the numerator.

Question 19

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 treatments}?​

A)​3
B)​4
C)5​
D)​59

Question 20

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 21

For a repeated-measures ANOVA,which of the following is computed differently,compared to an independent-measures ANOVA?​

A)​total SS
B)​between treatment SS
C)​within treatment SS
D)​the denominator of the F ratio

Question 22

The results of a repeated-measures ANOVA are reported as follows,F(3,27)= 1.12,p > .05.How many treatments were compared?​

A)​3
B)​4
C)​27
D)​28

Question 23

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)​17

Question 24

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

A)?54
B)?24
C)?18
D)?6

Question 25

The following table shows the results of a repeated-measures analysis of variance comparing three treatment conditions with a sample of n = 10 participants.Note that several values are missing in the table.What is the missing value for the F-ratio?? $$\begin{array} { l c l l l } \text { Source } & \text { SS } & \text { df } & \text { MS } \\\hline \text { Between } & 28 & \mathrm { xx } & \mathrm { xx } & F = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & & \\\quad \text { Bet. Sub. } & 16 & \mathrm { xx } & \\\quad \text { Error } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx }\end{array}$$

A)?4
B)?7
C)?10
D)?14

Question 26

​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)​16

Question 27

For the following data,what is SS_{between subjects}?​Treatments

A)​2
B)​3
C)​6
D)​12

Question 28

For the following data,what is SS_total?​Treatments

A)​28
B)​18
C)​10
D)​6

Question 29

For the following data,what are the df values for the repeated-measures F-ratio?Treatments

A)​2, 4
B)​2, 6
C)​3, 4
D)​3, 6

Question 30

The following table shows the results of a repeated-measures ANOVA.Based on this table,what is the value for ?²,the percentage of variance accounted for by the treatments??? $$\begin{array} { l c c c l } \text { Source } & \text { SS } & \text { df } & \text { MS } \\\text { Between } & 22 & 2 & 11 & F = 5.50 \\\text { Within } & 58 & 21 & & \\\quad \text { Bet. Sub. } & 0 & 7 & & \\\quad \text { Error } & 28 & 14 & 2 & \\\text { Total } & 80 & 23 &\end{array}$$

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

Question 31

A researcher is using a repeated-measures design to test for mean differences among four treatment conditions.If the data for this study consist of 10 scores in each treatment,then how many subjects participated in the study?​

A)​4
B)​10
C)​40
D)​50

Question 32

When using the Scheffe' post hoc test for a repeated-measures ANOVA,the denominator for the F ratio should be ____.​

A)​MS error
B)​MS between subjects
C)​MS within
D)​MS between treatment

Question 33

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,and the SS values within each treatment are SS₁ = 2,SS₂ = 2 and SS₃ = 6.What is the value for SS_error?​

A)2​
B)​4
C)​6
D)​10

Question 34

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 df_total = ____.​

A)27​
B)​28
C)​29
D)​30

Question 35

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

A)​between subjects and error
B)​between subjects and between treatments
C)​between treatments and error
D)​total variability and error

Question 36

The results of a repeated-measures ANOVA are reported as follows,F(2,24)= 1.12,p > .05.How many individuals participated in the study?​

A)​25
B)​13
C)​12
D)​7

Question 37

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 SS_total?? $$\begin{array} { l l l l l } \text { Source } & \text { SS } & \text { df } & \text { MS } \\\text { Between } & \mathrm { xx } & \mathrm { xx } & 12 & \mathrm {~F} = 4.00 \\\text { Within } & \mathrm { xx } & \mathrm { xx } & & \\\quad \text { Bet. Sub. } & 35 & \mathrm { xx } & & \\\text { Error } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } \\\text { Total } & \mathrm { xx } & \mathrm { xx } &\end{array}$$

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

Question 38

For the following data,SS_{between subjects} is equal to 6.What is the SS value for the error term?​Treatments

A)​4
B)​6
C)​12
D)​16

Question 39

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

Question 40

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

Question 41

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

Question 42

Based on the results of a repeated-measures ANOVA,a researcher reports F(4,20)= 2.57,p > .05.For this ANOVA,the null hypothesis was rejected.

Question 43

In a repeated-measures ANOVA the variability caused by systematic individual differences must be measured and subtracted out of the between-treatments variability in the numerator of the F-ratio.

Question 44

Variability caused entirely by random and unsystematic factors comprises the error variance.

Question 45

For the repeated-measures ANOVA,SS_{within treatments} = SS_{between subjects} + SS_error.

Question 46

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

Question 47

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 48

A repeated-measures ANOVA produces SS_{between treatments} = 30 and SS_total = 60.For this study,the percentage of variance accounted for by the treatments is η2 = 30/60 = 0.50.

Question 49

A repeated-measures study uses a sample of n = 10 participants to evaluate the mean differences among three treatment conditions.The F-ratio for the repeated-measures ANOVA will have df = 2,18.

Question 50

Individual differences refer to participant characteristics such as age,personality,and gender that vary from one person to another.

Question 51

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 52

The repeated-measures ANOVA begins the same way as the independent-measures ANOVA,with the total variability partitioned into between-treatment and within-treatment components.

Question 53

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 df_error = 7.

Question 54

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 55

For a repeated-measures study,df_{between treatments}= 3 and df_total = 27.This means that there were n = 7 participants in the study.

Question 56

A researcher reports the results of an ANOVA for a repeated-measures study as "F(2,12)= 7.84,p < .01." This study used a sample of n = 13 participants.

Question 57

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 58

A repeated-measures study comparing three treatment conditions with a sample of n = 10 participants would produce an F-ratio with df = 2,18.

Question 59

In a repeated-measures ANOVA,individual differences are measured by SS_{between subjects}.

Question 60

For a repeated-measures ANOVA,n = 5,k = 4,and error SS= 24.Therefore,MS_error = 2.

Question 61

One advantage of the repeated-measures ANOVA is that it eliminates "individual differences" as a source of variability.Explain why there are no individual differences in the numerator and in the denominator of the F-ratio.

Question 62

Explain why MS_within is not an appropriate error term (denominator)for the repeated-measures F-ratio.

Question 63

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 64

A repeated-measures study compares three treatments with a sample of n = 12 subjects.For the analysis of variance,df_error = 33.

Question 65

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 66

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 67

One major difference between the independent_measures ANOVA and the repeated_measures ANOVA is that SS_total is calculated differently for each type of ANOVA.

Question 68

A researcher conducts a repeated-measures study comparing three treatment conditions with a sample of n = 12 participants.The results are evaluated with a repeated-measures ANOVA and an incomplete summary table follows.Provide the missing values.(Hint: Begin with values for df).​ _____________________________________________

Question 69

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

Question 70

The following data were collected from a repeated-measures study.Perform an ANOVA and then analyze the data with a t test.Use the .05 level of significance for both.​

Question 71

For a repeated-measures ANOVA,if SS_{between subjects} = 40 and SS_{within treatments} = 70,then SS_error = 30.

Question 72

The first stage of a repeated-measures ANOVA is identical to the analysis in an independent-measures ANOVA.

Question 73

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 be F = 16.

Question 74

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 75

The following data were collected from a repeated-measures study.
a. Determine if there are any significant differences among the four treatments. Use the .05 level of significance.
b. Compute the percentage of variance explained by the treatment effects (η²).​Treatments