Deck 12: Introduction to Analysis of Variance

Question 1

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

Answer 1

B

Question 2

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

Answer 2

C

Question 3

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

Answer 3

B

Question 4

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 5

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 6

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

Question 7

An analysis of variance comparing three treatment conditions produces df_total = 32.If the samples are all the same size, how many individuals are in each sample.

A)9
B)10
C)11
D)It is impossible for the samples to be the same size if df_total = 32.

Question 8

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 9

What is stated by the alternative hypothesis (H₁) for an ANOVA?

A)There are no differences between any of the population means.
B)At least one of the population means is different from another mean.
C)All of the population means are different from each other.
D)None of the other 3 choices is correct.

Question 10

An analysis of variance comparing three treatment conditions produces df_within = 21.If the samples are all the same size, how many individuals are in each sample.

A)6
B)7
C)8
D)It is impossible for the samples to be the same size if df_within = 21.

Question 11

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 12

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

Question 13

What is stated by the null hypothesis (H₀) for an ANOVA?

A)There are no differences between any of the population means.
B)At least one of the population means is different from another mean.
C)All of the population means are different from each other.
D)None of the other 3 choices is correct.

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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 19

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 20

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 21

In 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 22

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

Question 23

In analysis of variance, what is a factor?

A)a dependent variable
B)an independent (or quasi-independent) variable
C)a treatment mean
D)a treatment total

Question 24

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 25

If an analysis of variance is used for the following data, what would be the effect of changing the value of M₂ to 20?

Question 26

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment.Note that several values are missing in the table.What is the missing value for the F-ratio?

Question 27

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 the above.

Question 28

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

Question 29

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 30

A research report concludes that there are significant differences among treatments, with "F(2, 27) = 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 31

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 32

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 = 5.50, then 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 33

For an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment, which of the following identifies the correct df for the F?ratio?

A)1, 18
B)1, 19
C)2, 18
D)2, 19

Question 34

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 35

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 36

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 37

An independent-measures research study compares three treatment conditions using a sample of n = 5 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)1
B)5
C)10
D)15

Question 38

The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 7 participants in each treatment.Note that several values are missing in the table.What is the missing value for SS_total?

Question 39

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 40

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

Question 41

SS_within measures the size of the sample variances.

Question 42

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

Question 43

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

Question 44

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

Question 45

For 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 46

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

Question 47

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 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

For an ANOVA comparing three treatment conditions, rejecting the null hypothesis is equivalent to concluding that all three treatment means are different.

Question 55

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 56

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 57

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

Question 58

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

Question 59

The distribution of F-ratios is negatively skewed.

Question 60

Post tests are only needed if H₀ is rejected in an ANOVA comparing more than 2 treatments.

Question 61

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 62

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

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

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

Question 65

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

Question 66

An ANOVA for k = 3 treatments has MS_between = 10.For this ANOVA, SS_between = 20.

Question 67

The F-ratio for an analysis of variance comparing three treatments with n = 10 in each treatment would have df = 2, 29.

Question 68

In an analysis of variance, if all other factors are held constant, the larger the sample variances, the bigger the value for the F-ratio.