Deck 12: Introduction to Analysis of Variance

Question 1

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)​The beta estimate is significant.

Answer 1

​At least one of the population means is different from another mean.

Question 2

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

A)​30
B)50​
C)​80
D)​110

Answer 2

50​

Question 3

In an analysis of variance,which statement is false?​

A)​SS_total = SS_between + SS_within
B)​df_total = df_between + df_within
C)​MS_total = MS_between + MSS_within
D)​MS_total = MS_between - df_between

Answer 3

​MS_total = MS_between + MSS_within

Question 4

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

A)​sample variances
B)​population variance
C)​the average distance from one mean to another
D)​the total variability for the set of N scores

Question 5

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)​0

Question 6

Which outcome 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 7

In an 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 8

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 9

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

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

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)7​
B)​8
C)​21
D)​22

Question 11

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)​0

Question 12

When comparing more than two treatment means,should you use an analysis of variance rather than using several t tests,and if so,why?​

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

Question 13

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?? $$\begin{array} { l c c l l } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \\\hline \text { Between } & 20 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & 2 & \\\text { Total } & \mathrm { xx } & \mathrm { xx } & & \\\hline\end{array}$$ ?

A)?16
B)?23
C)?29
D)?56

Question 14

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)​8
B)​9
C)​10
D)​11

Question 15

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?? $$\begin{array} { l c c c c } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \\\hline \text { Between } & 30 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \\\text { Total } & 62 & \mathrm { xx } & & \\\hline\end{array}$$

A)?0.50
B)?3.75
C)?5.00
D)?45.00

Question 16

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 17

What provides a measure of the variance caused by random,unsystematic differences?​

A)​the error term
B)​the F ratio
C)​MS
D)​SS_total

Question 18

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)​The beta estimate is significant.

Question 19

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 20

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 21

In an analysis of variance,which value is determined by the size of the sample variances?​

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

Question 22

If an analysis of variance is used for the following data,what would be the effect of changing the value of M₂ to 20?? $$\begin{array} { l l } \text { Sample Data}\\ \mathrm { M } _ { 1 } = 10 & \mathrm { M } _ { 2 } = 15 \\\mathrm { SS } _ { 1 } = 90 & \mathrm { SS } _ { 2 } = 70 \\\hline\end{array}$$ ??

A)?Increase SS_between and increase the size of the F-ratio.
B)?Increase SS_between and decrease the size of the F-ratio.
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 23

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 24

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 statistical decision is correct?​

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 25

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS₂ to 100?? $$\begin{array} { l l } \text { Sample Data}\\\mathrm { M } _ { 1 } = 15 & \mathrm { M } _ { 2 } = 25 \\\mathrm { SS } _ { 1 } = 90 & \mathrm { SS } _ { 2 } = 70 \\\hline\end{array}$$

A)?Increase SS_within and increase the size of the F-ratio.
B)?Increase SS_within and decrease the size of the F-ratio.
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 26

The percentage of variance accounted for by the treatment effect is usually known as _____ in published reports of ANOVA results.​

A)µ²​
B)​η²
C)​σ²
D)​α²

Question 27

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 28

The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment.Note that several values are missing in the table.What is the missing value for SS_total?? $$\begin{array} { l c c l l } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \\\hline \text { Between } & 20 & \mathrm { xx } & \mathrm { xx } & \mathrm { F } = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & 2 & \\\text { Total } & \mathrm { xx } & \mathrm { xx } & & \\\hline\end{array}$$

A)22?
B)?30
C)?54
D)?74

Question 29

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 30

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 31

The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n = 11 participants in each treatment.Note that several values are missing in the table.What is the missing value for the F-ratio?? $$\begin{array} { l l l l l } \text { Source } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \\\hline \text { Between } & \mathrm { xx } & \mathrm { xx } & 14 & \mathrm {~F} = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \\\text { Total } & 154 & \mathrm { xx } & & \\\hline\end{array}$$

A)?2
B)?7
C)?14
D)?28

Question 32

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS₁ to 50?? $$\begin{array} { l l } \text { Sample Data}\\\mathrm { M } _ { 1 } = 10 & \mathrm { M } _ { 2 } = 15 \\\mathrm { SS } _ { 1 } = 90 & \mathrm { SS } _ { 2 } = 70 \\\hline\end{array}$$ ?

A)Increase SS_within and increase the size of the F-ratio.?
B)?Increase SS_within and decrease the size of the F-ratio.
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 33

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 34

If an analysis of variance is used for the following data,what would be the effect of changing the value of M₁ to 20?? $$\begin{array} { l l } \text { Sample Data}\\\mathrm { M } _ { 1 } = 15 & \mathrm { M } _ { 2 } = 25 \\\mathrm { SS } _ { 1 } = 90 & \mathrm { SS } _ { 2 } = 70 \\\hline\end{array}$$

A)?Increase SS_between and increase the size of the F-ratio.
B)?Increase SS_between and decrease the size of the F-ratio.
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 35

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)​to determine whether or not the sample is normally distributed

Question 36

A researcher uses an 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 which df values?​

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

Question 37

For an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment,what are the correct df values for the F-ratio?​

A)​1, 18
B)​1, 19
C)​2, 18
D)​2, 19

Question 38

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 39

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 40

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 41

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 42

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

Question 43

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

Question 44

The individual conditions or values that make up a factor are called the levels of the factor.

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

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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 53

The between-treatments variance measures the overall differences between treatment conditions.

Question 54

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

Question 55

The within-treatments variance provides a measure of the variability inside each treatment condition.

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

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

Question 58

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

Question 59

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

Question 60

The distribution of F-ratios is negatively skewed.

Question 61

Tukey's HSD test allows one to compute a single value that determines the minimum difference between treatment means that is necessary for significance.

Question 62

A psychologist would like to examine the effects of sugar consumption on the activity level of preschool children.Three samples of children are selected with n = 5 in each sample.One group gets no sugar,one group gets a small dose,and the third group gets a large dose.The psychologist records the activity level for each child.The data from this experiment are presented below.
a. Do these data indicate any significant differences among the three groups? Test with α = .05.
b. Compute η², the percentage of variance accounted for by the treatment.​

Question 63

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

Question 64

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

Question 65

The Scheffé test uses an F-ratio to evaluate the significance of the difference between any two treatment conditions

Question 66

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

Question 67

In general,a post hoc test enables you to go back through the data and compare the individual treatments two at a time,a process known as making pairwise comparisons.​

Question 68

If one of the assumptions for the independent-measures ANOVA has been violated,you can still proceed by transforming the original scores to ranks and then using an alternative statistical analysis known as the Kruskal-Wallis test,which is designed specifically for ordinal data

Question 69

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

Question 70

As one does more and more separate hypothesis tests,the risk of a Type I error accumulates and is called the experiment-wise alpha level.

Question 71

An ANOVA is used to determine whether a significant difference exists between any of the treatments,and post tests are used to determine exactly which treatment means are significantly different.​

Question 72

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 73

Describe the circumstances under which you should use ANOVA instead of t tests,and explain why t tests are inappropriate in these circumstances.

Question 74

What value is expected,on average,for the F-ratio in ANOVA when the null hypothesis is true? Explain why this value is expected.