Deck 12: Introduction to Analysis of Variance

Question 1

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis,what is df_between?

A)1
B)2
C)3
D)Cannot be determined without additional information

Answer 1

B

Question 2

For an ANOVA comparing three treatment conditions,what is stated by the alternative hypothesis (H₁)?

A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Answer 2

B

Question 3

An analysis of variances produces df_total = 29 and df_within = 27.For this analysis,how many treatment conditions are being compared?

A)1
B)2
C)3
D)Cannot be determined without additional information

Answer 3

C

Question 4

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df_total?

A)2
B)11
C)33
D)35

Question 5

When comparing more than two treatment means,why should you use an analysis of variance instead of using several t tests?

A)Using several t tests increases the risk of a Type I error.
B)Using several t tests increases the risk of a Type II error.
C)The analysis of variance is more likely to detect a treatment effect.
D)There is no advantage to using an analysis of variance instead of several t tests.

Question 6

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and $\Sigma$ X² = 94.For this study,what is SS_total?

A)10
B)24
C)34
D)68

Question 7

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df_{within treatments}?

A)2
B)11
C)33
D)35

Question 8

In an analysis of variance,differences caused by treatment effects contribute to which of the following variances?

A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Question 9

In an ANOVA,what is represented by the letter T?

A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The number of scores in the total research study

Question 10

An analysis of variances produces df_between = 3 and df_within = 24.If each treatment has the same number of participants,then how many participants are in each treatment?

A)6
B)7
C)8
D)9

Question 11

In an ANOVA,what is represented by the letter N?

A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The number of scores in the total research study

Question 12

An analysis of variance produces SS_total = 80 and SS_within = 30.For this analysis,what is SS_between?

A)30
B)50
C)110
D)Cannot be determined without additional information

Question 13

On average,what value is expected for the F-ratio if the null hypothesis is false?

A)0
B)1.00
C)Between 0 and 1.00
D)Much greater than 1.00

Question 14

On average,what value is expected for the F-ratio if the null hypothesis is true?

A)0
B)1.00
C)k - 1
D)N - k

Question 15

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and $\Sigma$ X² = 94.For this study,what is SS_between?

A)10
B)24
C)34
D)68

Question 16

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and $\Sigma$ X² = 94.For this study,what is SS_within?

A)10
B)24
C)34
D)68

Question 17

For an ANOVA comparing three treatment conditions,what is stated by the null hypothesis (H₀)?

A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Question 18

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df _{between treatments}?

A)2
B)11
C)33
D)35

Question 19

In an analysis of variance,differences between participants contribute to which of the following variances?

A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Question 20

In analysis of variance,what is measured by the MS values?

A)Sample variance
B)Population variance
C)The average distance from one mean to another
D)The total variability for the set of N scores

Question 21

Which of the following describes a typical distribution of F-ratios?

A)Symmetrical with a mean of zero
B)Positively skewed with all values greater than or equal to zero
C)Negatively skewed with all values greater than or equal to zero
D)Symmetrical with a mean equal to df_between

Question 22

A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment.The F-ratio for this analysis would have what df values?

A)df = 2,11
B)df = 2,33
C)df = 2,35
D)df = 2,36

Question 23

A researcher reports an F-ratio with df = 1,24 for an independent-measures experiment.If all the treatments had the same number of participants,then how many individuals were in each treatment?

A)11
B)12
C)13
D)14

Question 24

An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment.If all three treatments have the same total,T₁ = T₂ = T₃,what is SS_between?

A)0
B)1.00
C)10(3)
D)Cannot be determined from the information given

Question 25

For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment,what is the critical value for the F-ratio using α = .05?

A)3.88
B)3.49
C)3.74
D)3.34

Question 26

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS₂ to 100? Sample Data

A)Increase SS_within and increase the size of the F-ratio M₁ = 15 M₂ = 25
B)Increase SS_within and decrease the size of the F-ratio SS₁ = 90 SS₂ = 70
C)Decrease SS_within and increase the size of the F-ratio
D)Decrease SS_within and decrease the size of the F-ratio

Question 27

An analysis of variance produces SS_between = 30,SS_within = 60,and an F-ratio with df = 2,15.For this analysis,what is the F-ratio?

A)30/60 = 0.50
B)60/30 = 2.00
C)15/4 = 3.75
D)4/15 = 0.27

Question 28

For an analysis of variance comparing four treatments,MS_between = 12.What is the value of SS_between?

A)3
B)4
C)36
D)48

Question 29

In an analysis of variance,which of the following is not true?

A)SS_total = SS_between + SS_within
B)df_total = df_between + df_within
C)MS_total = MS_between + MSS_within
D)All three choices are true.

Question 30

If an analysis of variance is used for the following data,what would be the effect of changing the value of M₁ to 20? Sample Data

A)Increase SS_between and increase the size of the F-ratio M₁ = 15 M₂ = 25
B)Increase SS_between and decrease the size of the F-ratio SS₁ = 90 SS₂ = 70
C)Decrease SS_between and increase the size of the F-ratio
D)Decrease SS_between and decrease the size of the F-ratio

Question 31

An analysis of variance produces SS_between = 40 and MS_between = 20.In this analysis,how many treatment conditions are being compared?

A)2
B)3
C)4
D)20

Question 32

An independent-measures research study compares three treatment conditions using a sample of n = 10 in each treatment.For this study,the three sample means are M₁ = 1,M₂ = 2,and M₃ = 3.For the ANOVA,what value would be obtained for SS_between?

A)2
B)10
C)20
D)30

Question 33

A researcher reports an F-ratio with df = 2,18 from an independent-measures research study.Based on the df values,how many treatments were compared in the study,and what was the total number of subjects participating in the study?

A)2 treatments and 19 subjects
B)2 treatments and 20 subjects
C)3 treatments and 21 subjects
D)3 treatments and 22 subjects

Question 34

In general,what factors are most likely to reject the null hypothesis for an ANOVA?

A)Small mean differences and small variances
B)Small mean differences and large variances
C)Large mean differences and small variances
D)Large mean differences and large variances

Question 35

In an analysis of variance,which of the following is determined the size of the sample variances?

A)SS_between
B)SS_within
C)df_between
D)df_within

Question 36

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS₁ to 50? Sample Data

A)Increase SS_within and increase the size of the F-ratio M₁ = 10 M₂ = 20
B)Increase SS_within and decrease the size of the F-ratio SS₁ = 90 SS₂ = 70
C)Decrease SS_within and increase the size of the F-ratio
D)Decrease SS_within and decrease the size of the F-ratio

Question 37

An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.For this study,the three samples have SS₁ = 10,SS₂ = 20,and SS₃ = 15.What value would be obtained for MS_within?

A)45/14
B)45/12
C)10/2
D)10/3

Question 38

In an analysis of variance,which of the following is determined by the size of the sample mean differences?

A)SS_between
B)SS_within
C)df_between
D)df_within

Question 39

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment.If the data produce an F-ratio of F = 4.60,which of the following is the correct statistical decision?

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

Question 40

Which of the following is expected if the null hypothesis is true for an analysis of variance?

A)SS_between should be about the same size as SS_total
B)SS_between should be about the same size as SS_within
C)MS_between should be about the same size as MS_total
D)MS_between should be about the same size as MS_within

Question 41

If an analysis of variance is used for the following data,what would be the effect of changing the value of M₂ to 25? Sample Data

A)Increase SS_between and increase the size of the F-ratio M₁ = 10 M₂ = 20
B)Increase SS_between and decrease the size of the F-ratio SS₁ = 90 SS₂ = 70
C)Decrease SS_between and increase the size of the F-ratio
D)Decrease SS_between and decrease the size of the F-ratio

Question 42

For an analysis of variance comparing four treatment means with a separate sample of n = 8 participants in each treatment,the F-ratio will have df = 3,31.

Question 43

F-ratios are always greater than or equal to zero.

Question 44

If an analysis of variance produces a value of F = 1.00,then all of the samples have exactly the same mean.

Question 45

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12)= 4.00.If the researcher had used an ANOVA to evaluate the data,what F-ratio would be obtained?

A)F(1,12)= 2.00
B)F(1,12)= 16.00
C)F(1,11)= 2.00
D)F(1,11)= 16.00

Question 46

A research report concludes that there are significant differences among treatments,with "F(2,24)= 8.62,p < .01." If the same number of participants was used in all of the treatment conditions,then how many individuals were in each treatment?

A)7
B)9
C)10
D)30

Question 47

In an analysis of variance,MS_total = MS_between + MS_within.

Question 48

For an ANOVA,when the null hypothesis is true,the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.

Question 49

If an analysis of variance produces a value of F = 0,then all of the samples have exactly the same mean.

Question 50

For an independent-measures ANOVA comparing four treatment conditions,df_between = 3.

Question 51

If an analysis of variance produces SS_{between treatments} = 30 and MS_{between treatments} = 10,then the ANOVA is comparing four treatment conditions.

Question 52

For an independent-measures ANOVA with n = 10 participants in each treatment condition,df_within = 9.

Question 53

An F-ratio near 1.00 is an indication that the null hypothesis is likely to be true.

Question 54

For an analysis of variance comparing three treatment means,H₀ states that all three population means are the same and H₁ states that all three population means are different.

Question 55

What is the purpose for post tests?

A)To determine whether or not a Type I error was committed
B)To determine how much difference exists between the treatments
C)To determine which treatments are significantly different
D)None of these

Question 56

For an analysis of variance comparing three treatment means with a separate sample of n = 10 participants in each treatment,df_total = 29.

Question 57

The distribution of F-ratios is negatively skewed.

Question 58

SS_within measures the size of the sample variances.

Question 59

The larger the differences among the sample means,the larger the numerator of the F-ratio will be.

Question 60

A researcher uses an ANOVA to evaluate the mean difference between two treatments and obtains F(1,22)= 4.00.If the researcher had used an independent-measures t test to evaluate the data,what t value would be obtained?

A)t(22)= 2.00
B)t(22)= 16.00
C)t(23)= 2.00
D)t(23)= 16.00

Question 61

Post tests are only needed if H₀ is rejected in an ANOVA comparing more than two treatments.

Question 62

After an ANOVA,a researcher computes ² to evaluate effect size and obtains ² = 0.50.If the ANOVA had SS_total = 100,then SS_within = SS_between = 50.

Question 63

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.If all the samples were the same size,then each sample had n = 7 participants.

Question 64

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study used a total of 31 participants.

Question 65

Effect size for analysis of variance is measured by η²,which equals SS_between divided by SS_within.

Question 66

An ANOVA comparing two treatment conditions produces SS_within = 80 and SS_between = 50.For these data, $\eta$ ²= 25/80.

Question 67

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study compared three treatments.

Question 68

In analysis of variance,large sample variances reduce the likelihood of rejecting the null hypothesis.

Question 69

SS_between measures the size of the mean differences from one treatment to another.

Question 70

A researcher conducts an ANOVA to evaluate the mean difference between two treatments using the data from an independent-measures study and obtains F = 4.00.If the researcher had used an independent-measures t test,then t would be t = 2.00.

Question 71

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments.If the t statistic has df = 12,then an ANOVA evaluating the same data would produce an F-ratio with df = 1,11.

Question 72

An ANOVA is used to determine whether significant difference exist,and post tests are used to determine exactly which treatment means are significantly different.

Question 73

Describe the circumstances in which post tests are used,and explain why these tests are necessary.

Question 74

Post tests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.

Question 75

If an analysis of variance produces SS_between = 20 and SS_within = 40,then η² = 0.50.

Question 76

For an ANOVA,if SS_between = 40 and SS_within = 60,then η² = 40/100.