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Chapter 15Introduction to the Analysis of Variance

MULTIPLE CHOICE

1. The null hypothesis in the one-way ANOVA asserts that ____.

a. the within groups variance estimate is an estimate of the population variance

b. 1 = 2 = 3 = k

c. the between group variance estimate and the within group variance estimate are both estimates of the same population variance

d. the within group sum of squares is equal to the between group sum of squares

e. b and c

ANS: E PTS: 1

2. Which of the following increase(s) as the difference between the group means increases?

a. sB2

b. Fobt

c. tobt

d. all of the above

ANS: D PTS: 1

3. Which of the following is (are) assumption(s) underlying the use of the F test?

a. the raw score populations are normally distributed

b. the variances of the raw score populations are the same

c. the mean of the populations differ

d. a and b

e. all of the above

ANS: D PTS: 1

4. The parameter being estimated in the analysis of variance is the ____.

a. sample mean

b. variance of the H0 populations

c. sample variance

d. mean of the H0 populations

e. Fobt

ANS: B PTS: 1

5. If its assumptions are met, the analysis of variance technique is appropriate when ____.

a. two or more factors are varied

b. several levels of a single independent variable are compared

c. three or more groups are involved

d. all of the above

ANS: D PTS: 1

6. As the differences between the group means increases, ____.

a. sB2 increases

b. Fobt decreases

c. tobt decreases

d. all of the above

e. none of the above

ANS: A PTS: 1

7. If SST = 20 and SSB = 14, SSW = ____.

a. 34

b. 6

c. 6

d. need more information

ANS: B PTS: 1

8. The F ratio increases as ____.

a. the variability between means increases relative to the variability within groups

b. the variability between means decreases relative to the variability within groups

c. the total variability increases

d. the total variability decreases

e. the variability within groups remains the same

ANS: A PTS: 1

9. Which of the following is (are) true about the F distribution?

a. it has no negative values

b. it is positively skewed

c. there are a family of F curves uniquely determined by df(numerator) and df(denominator)

d. the mean of the F distribution equals 0

e. all of the above

f. a and b

g. a, b and c

ANS: G PTS: 1

10. A major limitation of a two group design is that ____.

a. we cant run enough subjects

b. very often, two groups are insufficient for a clear interpretation

c. the population parameters may not be applicable

d. the means between groups may not differ

ANS: B PTS: 1

11. When analyzing data from experiments that involve more than two groups ____.

a. doing t tests on all possible pairs of means decreases the probability of making Type I errors

b. doing t tests on all possible pairs of means increases the probability of making Type I errors

c. it is generally permissible to do t tests between all possible pairs of means and use Students t distribution

d. doing t tests on all possible pairs of means increases the probability of making Type II errors

ANS: B PTS: 1

12. The alternative hypothesis for which Fobt is appropriate in the one-way ANOVA is ____.

a. always nondirectional

b. never nondirectional

c. sometimes directional

d. evaluated with a one-tailed probability value

e. a and b

f. b and d

ANS: E PTS: 1

13. The alternative hypothesis evaluated by Fobt in the one-way ANOVA states that ____.

a. all conditions have the same effect

b. one or more of the conditions have different effects

c. 1 = 2 = 3 = k

d. 1 2 3 k

e. b and d

ANS: B PTS: 1

14. Which of the following is(are) true?

a. df for sW2 = N k

b. df for sB2 = k 1

c. dfT = N 1

d. all of the above

ANS: D PTS: 1

15. The one-way ANOVA partitions the total variability into ____.

a. SSW and SSB

b. sW2 and sB2

c. SSW and SST

d. SSB and sB2

ANS: A PTS: 1

16. Which of the following would cause Fobt to increase?

a. an increase in the difference between the means

b. an increase in the within-groups variability

c. an increase in the magnitude of the independent variables effect

d. a and b

e. a and c

ANS: E PTS: 1

17. If dfB = 2 and dfW = 14, using = 0.05, Fcrit = ____.

a. 19.42

b. 4.60

c. 3.74

d. 6.51

ANS: C PTS: 1

18. sB2 is a measure of ____.

a. 2 alone

b. 2 + the effects of the independent variable

c. the variability between the means

d. b and c

ANS: D PTS: 1

Exhibit 15-1

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory.

19. Refer to Exhibit 15-1. SSB = ____.

a. 94.2

b. 96.0

c. 96.5

d. 97.4

ANS: C PTS: 1

20. Refer to Exhibit 15-1. SSW = ____.

a. 62.25

b. 59.75

c. 56.65

d. 57.00

ANS: B PTS: 1

21. Refer to Exhibit 15-1. sB2 = ____.

a. 48.250

b. 50.145

c. 51.254

d. 45.750

ANS: A PTS: 1

22. Refer to Exhibit 15-1. sW2 = ____.

a. 6.813

b. 6.558

c. 6.702

d. 6.639

ANS: D PTS: 1

23. Refer to Exhibit 15-1. Fobt = ____.

a. 8.31

b. 7.30

c. 7.27

d. 6.45

ANS: C PTS: 1

24. Refer to Exhibit 15-1. Using = 0.05, Fcrit = ____.

a. 8.02

b. 4.26

c. 19.38

d. 4.46

ANS: B PTS: 1

25. Refer to Exhibit 15-1. Using = 0.05, what do you conclude?

a. reject H0; the drug has the same effect on memory at all levels

b. reject H0; the drug does not have the same effect on memory at all levels

c. retain H0; we cannot conclude that the drug affects memory

d. accept H0; the drug has no effect on memory

ANS: B PTS: 1

26. Refer to Exhibit 15-1. Estimate the size of the effect. = ____.

a. 0.5109

b. 0.5210

c. 0.5100

d. 0.4328

ANS: A PTS: 1

27. Refer to Exhibit 15-1. Estimate the size of the effect. 2 = ____.

a. 0.6524

b. 0.6176

c. 0.6318

d. 0.6034

ANS: B PTS: 1

Exhibit 15-2

A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient.

Cognitive/Behavioral

Therapy Relaxation

Therapy Attention-Placebo

Group

5

6

8

4

7 6

8

10

9

7 8

10

9

10

9

28. Refer to Exhibit 15-2. SSB = ____.

a. 27.53

b. 26.13

c. 23.67

d. 28.60

ANS: B PTS: 1

29. Refer to Exhibit 15-2. SSW = ____.

a. 19.60

b. 16.80

c. 18.80

d. 22.80

ANS: D PTS: 1

30. Refer to Exhibit 15-2. sB2 = ____.

a. 14.30

b. 13.76

c. 13.07

d. 11.84

ANS: C PTS: 1

31. Refer to Exhibit 15-2. sW2 = ____.

a. 1.40

b. 1.90

c. 1.57

d. 1.88

ANS: B PTS: 1

32. Refer to Exhibit 15-2. Fobt = ____.

a. 10.21

b. 8.44

c. 8.20

d. 6.88

ANS: D PTS: 1

33. Refer to Exhibit 15-2. Using = 0.05, Fcrit = ____.

a. 3.98

b. 19.41

c. 6.93

d. 3.88

ANS: D PTS: 1

34. Refer to Exhibit 15-2. Using = 0.05, what do you conclude?

a. reject H0; there is no difference among the treatments

b. reject H0; at least one of the treatments differs from at least one of the others

c. retain H0; we cannot conclude that there is a difference among the treatments

d. accept H0; we cannot conclude that there is a difference among the treatments

ANS: B PTS: 1

35. Refer to Exhibit 15-2. Estimate the size of the effect. = ____.

a. 0.5226

b. 0.4824

c. 0.4393

d. 0.4658

ANS: C PTS: 1

36. Refer to Exhibit 15-2. Estimate the size of the effect. 2 = ____.

a. 0.5530

b. 0.5034

c. 0.6232

d. 0.5341

ANS: D PTS: 1

37. The total degrees of freedom for an experiment with n1 = 10, n2 = 12, and n3 = 10 is ____.

a. 2

b. 32

c. 31

d. 29

ANS: C PTS: 1

38. Which of the following is(are) illegal values for Fobt?

a. 1.00

b. 0.96

c. 2.97

d. b and c

ANS: C PTS: 1 MSC: WWW

39. What is the value of Fcrit for an experiment with k = 3, n1 = n2 = n3 = 10 subjects, and = 0.01?

a. 5.45

b. 4.51

c. 3.35

d. 5.49

ANS: D PTS: 1

Exhibit 15-3

The following questions pertain to the data below.

40. Refer to Exhibit 15-3. What is the value of Fobt?

a. 5.67

b. 6.53

c. 1.95

d. 3.26

ANS: B PTS: 1 MSC: WWW

41. Refer to Exhibit 15-3. What is the value of Fcrit? Use = 0.05.

a. 5.14

b. 4.76

c. 4.46

d. 4.07

ANS: A PTS: 1 MSC: WWW

42. Refer to Exhibit 15-3. What is your conclusion? Again use = 0.05.

a. retain H0

b. reject H1

c. reject H0

d. accept H0

ANS: C PTS: 1 MSC: WWW

43. Refer to Exhibit 15-3. Using , the estimated size of effect is ____.

a. 22.6% of the variability

b. 52.8% of the variability

c. 43.6% of the variability

d. 55.1% of the variability

ANS: D PTS: 1 MSC: WWW

44. Refer to Exhibit 15-3. Using 2, what is the estimated size of effect?

a. 0.7232

b. 0.6852

c. 0.6582

d. 0.6312

ANS: B PTS: 1 MSC: WWW

45. What is the value of SST if SSB = 236 and SSW = 54?

a. 290

b. 182

c. 4.37

d. 100

ANS: A PTS: 1

46. By doing multiple t tests when there are more than 2 experimental groups we increase the risk of making what kind of mistake?

a. accepting H0

b. Type I error

c. Type II error

d. all of the above

ANS: B PTS: 1 MSC: WWW

47. If s12 = 10, s22 = 15, and s32 = 12, and n1 = n2 = n3, then sW2 equals ____.

a. cannot be determined from information given

b. 37.0

c. 12.33

d. 3.51

ANS: C PTS: 1 MSC: WWW

48. If s12 = 9, s22 = 6, s32 = 8, and n1 n2 n3, then sW2 equals ____.

a. cannot be determined from information given

b. 7.667

c. 2.77

d. 23.0

ANS: A PTS: 1

49. If = 46, = 50, = 92 and n1 = n2 = n3, what is the value of ?

a. cannot be determined from information given

b. 50.0

c. 188.0

d. 62.67

ANS: D PTS: 1

50. If SSW = 126, N = 28, k = 4, then what is the value of sW2?

a. cannot be determined from information given

b. 5.25

c. 42.0

d. 4.667

ANS: B PTS: 1

51. If dfB = 3 and dfT = 29 and Fobt = 3.15, what would you conclude using = 0.05?

a. reject H0

b. reject H1

c. retain H0

d. retain H1

ANS: A PTS: 1

52. If k = 2 and tobt = 2.95, what would the value of Fobt be for an independent groups design?

a. 2.95

b. 8.70

c. 1.72

d. 0.05

ANS: B PTS: 1

53. If sB2 = 27.9 and sW2 = 54.2, what is the value of Fobt?

a. impossible result, there must be an error

b. 1.94

c. 0.51

d. 2.76

ANS: C PTS: 1

54. If SST = 96, SSW = 47, and SSB = 68, what would you conclude?

a. reject H0

b. retain H0

c. cannot be determined from information given

d. there must be an error in the calculations

ANS: D PTS: 1

55. A priori comparisons ____.

a. are planned in advance of the experiment

b. often arise out of theory and prior research

c. may be done without obtaining a significant Fobt in the one-way ANOVA

d. all of the above

ANS: D PTS: 1

56. In doing planned comparisons, we use ____.

a. the t test for independent groups, unaltered

b. the t test for independent groups with sW2 in the denominator

c. df equal to those of sW2

d. b and c

ANS: D PTS: 1

57. When doing planned comparisons, ____.

a. there is no correction for the inflated Type I error probability

b. a different number of df are used which corrects for the inflated Type I error probability

c. tobt is reduced to correct for the inflated Type I error probability

d. a different sampling distribution is used to correct for the inflated Type I error probability

ANS: A PTS: 1

58. A posteriori or post hoc comparisons ____.

a. are planned before the experiment

b. are often decided on after the data are collected

c. require a significant Fobt before they may be conducted

d. b and c

e. all of the above

ANS: B PTS: 1

59. Which of the following is(are) statistical test(s) for doing post hoc comparisons?

a. HSD test

b. Newman-Keuls test

c. independent t test

d. two group one-way ANOVA

e. a and b

f. all of the above

ANS: E PTS: 1

60. The HSD test ____.

a. maintains the comparison-wise error rate at alpha

b. maintains the experiment-wise Type I error rate at alpha

c. is used for a priori comparisons

d. all of the above

e. b and c

ANS: B PTS: 1

61. Using the HSD test, if there are 16 df associated with sW2, and = .05 and the number of groups = 3, Qcrit = ____.

a. 4.13

b. 3.00

c. 3.65

d. 4.79

ANS: C PTS: 1

62. Using the Newman-Keuls test, if the number of means encompassed is 3, = .05, and there are 20 df associated with sW2, Qcrit = ____.

a. 3.58

b. 2.95

c. 4.02

d. 4.64

ANS: A PTS: 1

63. Within a single experiment, the value of Qcrit changes from comparison-to-comparison in the ____.

a. t test for independent groups

b. HSD test

c. Newman-Keuls test

d. all of the above

ANS: C PTS: 1

64. Orthogonal comparisons are a type of ____.

a. a posteriori comparisons

b. planned comparisons

c. regression analysis

d. none of the above

ANS: B PTS: 1

Exhibit 15-4

An investigator conducts an experiment involving the effects of three levels of a drug on memory. Subjects are randomly assigned to one of three conditions. A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory.

65. Refer to Exhibit 15-4. Assume you wanted to compare drug levels 2 and 3 using planned comparisons and a nondirectional H1. The obtained value of the appropriate statistic is ____.

a. Qobt = 4.46

b. tobt = 3.16

c. tobt = 3.15

d. tobt = 0.55

ANS: B PTS: 1

66. Refer to Exhibit 15-4. The appropriate df = ____.

a. 11

b. 6

c. 9

d. 7

ANS: C PTS: 1

67. Refer to Exhibit 15-4. Using = .05, the critical value is ____.

a. 2.262

b. 1.833

c. 2.228

d. 3.95

e. 3.20

ANS: A PTS: 1

68. Refer to Exhibit 15-4. Using = .05, what is your conclusion?

a. accept H0; the drug has the same effect at these levels

b. retain H0; we cannot conclude the drug has a different effect at these levels

c. reject H0; the groups are not significantly different

d. reject H0; the drug has different effects at these levels

ANS: D PTS: 1

69. Refer to Exhibit 15-4. Assume you are going to do a post hoc comparison between drug levels 2 and 3 using the HSD test. The obtained value of the appropriate statistic is ____.

a. tobt = 3.16

b. Qobt = 4.46

c. Qobt = 4.46

d. Qobt = 5.25

ANS: B PTS: 1

70. Refer to Exhibit 15-4. Using = .05, the appropriate critical value is ____.

a. 2.179

b. 3.20

c. 3.95

d. 5.43

ANS: C PTS: 1

71. Refer to Exhibit 15-4. Using = .05, what is your conclusion?

a. retain H0; we cannot conclude the drug has a different effect at these levels

b. reject H0; the drug has different effects at these levels

c. retain H0; the drug has the same effect at these levels

d. reject H0; the groups are not significantly different

ANS: B PTS: 1

72. Refer to Exhibit 15-4. Assume you are going to do a post hoc comparison between drug levels 2 and 3 using the Newman-Keuls test. The obtained value of the appropriate statistic is ____.

a. tobt = 3.16

b. Qobt = 4.46

c. Qobt = 3.30

d. Qobt = 5.25

ANS: B PTS: 1

73. Refer to Exhibit 15-4. The df = ____.

a. 8

b. 6

c. 9

d. 11

ANS: C PTS: 1

74. Refer to Exhibit 15-4. Using = .05, the critical value is ____.

a. 2.179

b. 3.20

c. 3.95

d. 4.60

ANS: B PTS: 1

75. Refer to Exhibit 15-4. Using = .05, what do you conclude?

a. retain H0; we cannot conclude the drug has a different effect at these levels

b. reject H0; the drug has different effects at these levels

c. retain H0; the drug has the same effect at these levels

d. reject H0; the groups are not significantly different

ANS: B PTS: 1

76. When doing multiple comparisons, which method is the most powerful?

a. planned comparisons

b. the Newman-Keuls test

c. the HSD test

d. they are all equally powerful

ANS: A PTS: 1

Exhibit 15-5

A clinical psychologist is interested in comparing the effectiveness of short term relaxation and cognitive-behavioral therapy in treating mild depression. An experiment is conducted in which 15 patients with mild depression are randomly selected and assigned 5 each to a relaxation therapy group, a cognitive/behavioral therapy group, and an attention placebo group. Therapy is administered until the patient is judged no longer depressed or until 10 treatment sessions have elapsed. The following data is obtained. Scores are the number of sessions for each patient.

Cognitive/Behavioral

Therapy Relaxation

Therapy Attention-Placebo

Group

5

6

8

4

7 6

8

10

9

7 8

10

9

10

9

77. Refer to Exhibit 15-5. Assume you wanted to compare cognitive/behavioral therapy with relaxation therapy, using planned comparisons and a nondirectional H1. The obtained value of the appropriate statistic is ____.

a. Qobt = 3.15

b. tobt = 2.29

c. tobt = 2.22

d. tobt = 0.55

ANS: B PTS: 1

78. Refer to Exhibit 15-5. The appropriate df = ____.

a. 14

b. 6

c. 12

d. 7

ANS: C PTS: 1

79. Refer to Exhibit 15-5. Using = .05, the critical value is ____.

a. 2.179

b. 1.782

c. 2.681

d. 2.145

ANS: A PTS: 1

80. Refer to Exhibit 15-5. Using = .05, what is your conclusion?

a. accept H0; the two therapies are equal in effectiveness

b. retain H0; we cannot conclude the two therapies differ in effectiveness

c. reject H0; the groups are not significantly different

d. reject H0; the two therapies appear to be differentially effective

ANS: D PTS: 1

81. Refer to Exhibit 15-5. Assume you are going to do a post hoc comparison between cognitive behavioral therapy and relaxation therapy, using the HSD test. The obtained value of the appropriate statistic is ____.

a. tobt = 2.23

b. Qobt = 3.24

c. Qobt = 3.15

d. Qobt = 5.25

ANS: B PTS: 1

82. Refer to Exhibit 15-5. Using = .05, the appropriate critical value is ____.

a. 2.179

b. 3.08

c. 3.77

d. 5.05

ANS: C PTS: 1

83. Refer to Exhibit 15-5. Using = .05, what is your conclusion?

a. retain H0; we cannot conclude the two therapies differ in effectiveness

b. reject H0; the two therapies appear to differ in effectiveness

c. retain H0; the two therapies have the same effectiveness

d. reject H0; the two therapies are not significantly different

ANS: A PTS: 1

84. Refer to Exhibit 15-5. Assume you are going to do a post hoc comparison between cognitive/behavioral therapy and relaxation therapy, using the Newman-Keuls test. The obtained value of the appropriate statistic is ____.

a. tobt = 2.23

b. Qobt = 3.24

c. Qobt = 3.15

d. Qobt = 5.25

ANS: B PTS: 1

85. Refer to Exhibit 15-5. The df = ____.

a. 14

b. 6

c. 12

d. 7

ANS: C PTS: 1

86. Refer to Exhibit 15-5. Using = .05, the critical value is ____.

a. 2.179

b. 3.08

c. 3.77

d. 4.32

ANS: B PTS: 1

87. Refer to Exhibit 15-5. Using = .05, what do you conclude?

a. retain H0; we cannot conclude the two therapies differ in effectiveness

b. reject H0; the two therapies appear to differ in effectiveness

c. retain H0; the two therapies are equal in effectiveness

d. reject H0; the two therapies are not significantly different

ANS: B PTS: 1

88. The value for Qcrit using the HSD test for 6 groups with 6 subjects in each group and = 0.01 is ____.

a. 4.30

b. 4.23

c. 5.24

d. 5.37

ANS: C PTS: 1

89. The harmonic mean when k = 3 and n1 = 5, n2 = 4, and n3 = 7 is ____.

a. 5.06

b. 1.69

c. 0.19

d. 0.06

ANS: A PTS: 1

90. In general the number of planned comparisons should ____.

a. equal k

b. be kept to a minimum

c. equal nk

d. equal zero

ANS: B PTS: 1

91. Which of the following tests hold the experiment-wise error rate at ?

a. HSD test

b. Newman-Keuls

c. F test

d. a and c

ANS: D PTS: 1 MSC: WWW

92. In general, which of the following tests is the most powerful test to detect a difference between group means?

a. a t test for a planned comparison

b. the HSD test

c. the Newman-Keuls test

d. all are equally powerful

ANS: A PTS: 1 MSC: WWW

93. If n = 8 and sW2 = 18.2, what is the value of the denominator for a planned comparison?

a. 4.55

b. 2.27

c. 1.51

d. 2.13

ANS: D PTS: 1

94. Using the Newman-Keuls test, if = 10.2, = 16.1, = 12.6, and = 9.0, the value of Qcrit for the comparison of and with = 0.01 is ____. sW2 has 12 degrees of freedom.

a. 5.05

b. 5.50

c. 4.32

d. 5.84

ANS: C PTS: 1

Exhibit 15-6

For the following problem(s), consider the following information from an experiment to compare differences between the length of time a house paint lasts before it begins to fade. The number of subjects are the same in each group.

95. Refer to Exhibit 15-6. Using the HSD test, the value of Qobt for the testing the difference between and is ____.

a. 5.92

b. 2.29

c. 3.24

d. 1.05

ANS: C PTS: 1 MSC: WWW

96. Refer to Exhibit 15-6. The value of Qcrit for the post hoc comparison of and using the HSD test is ____ at = 0.05.

a. 2.97

b. 3.61

c. 4.00

d. 4.70

ANS: B PTS: 1 MSC: WWW

97. Refer to Exhibit 15-6. The value of Qcrit for the post hoc comparison of and using the Newman-Keuls test is ____ at = 0.05.

a. 2.97

b. 4.07

c. 3.61

d. 4.00

ANS: A PTS: 1 MSC: WWW

98. Refer to Exhibit 15-6. The value of tobt for the planned comparison of and is ____.

a. 4.96

b. 5.82

c. 2.97

d. 4.18

ANS: D PTS: 1 MSC: WWW

TRUE/FALSE

1. Tabled F values are one-tailed probability levels.

ANS: T PTS: 1 MSC: WWW

2. The F distribution has no negative values.

ANS: T PTS: 1

3. Variance ratio is the statistic underlying the F distribution.

ANS: T PTS: 1

4. The F distribution is a family of curves, each uniquely determined by df.

ANS: T PTS: 1

5. The F test is not used when comparing 2 or more estimates of the H0 population variance.

ANS: F PTS: 1

6. The total variability of a set of data can be completely partitioned into the between-groups variability and the within-groups variability.

ANS: T PTS: 1

7. The within-groups variability increases necessarily as the between-groups variability increases.

ANS: F PTS: 1

8. The total variance of a set of data can be completely partitioned into the between-groups variance and the within-groups variance.

ANS: F PTS: 1 MSC: WWW

9. In the analysis of variance, the larger Fobt is (df constant), the lower the probability that the results of the experiment are due to chance.

ANS: T PTS: 1

10. When there are only two groups, then tobt2 = Fobt.

ANS: T PTS: 1 MSC: WWW

11. The null hypothesis in the analysis of variance states that 1 = 2 = 3 = k.

ANS: T PTS: 1 MSC: WWW

12. The sampling distribution of F is a family of positively skewed curves each with a mean equal to 0.

ANS: F PTS: 1

13. Fobt = sB2/sW2

ANS: T PTS: 1

14. If Fobt < Fcrit, we reject H0. ANS: F PTS: 1 15. In the one-way ANOVA, it is assumed that the within-groups variance estimate (sW2) is sensitive to the effect of the independent variable. ANS: F PTS: 1 16. SST = SSW + SSB ANS: T PTS: 1 17. The one-way ANOVA assumes 12 = 22 = 32 = k2. ANS: T PTS: 1 18. If F < 1, the independent variable has not had a significant effect. ANS: T PTS: 1 19. The partition of variability is based on the idea that the deviation of each score from the Grand mean is made up of two parts: the deviation of each score from its group mean and the deviation of the other scores in the group from the group mean. ANS: F PTS: 1 20. A significant Fobt value indicates that all the group means are significantly different from each other. ANS: F PTS: 1 MSC: WWW 21. Planned comparisons are the same thing as a priori comparisons. ANS: T PTS: 1 22. When doing planned comparisons, the denominator of the t equation changes for each pair of means compared. ANS: F PTS: 1 23. A posteriori or post hoc comparisons are the same thing. ANS: T PTS: 1 24. With a priori comparisons, there is no correction for the inflated probability of making a Type I error. ANS: T PTS: 1 25. Both the HSD and the Newman-Keuls test use the Studentized Range distributions. ANS: T PTS: 1 MSC: WWW 26. The experiment-wise error rate is the probability of making a Type I error for any of the possible comparisons. ANS: F PTS: 1 MSC: WWW 27. The HSD test uses the tobt statistic. ANS: F PTS: 1 28. It is possible to get significant differences between pairs of means using the Newman-Keuls test that are not significant using the HSD test. ANS: T PTS: 1 29. When using multiple comparisons, a priori comparisons are more powerful than either the HSD or the Newman-Keuls tests. ANS: T PTS: 1 MSC: WWW 30. In using the HSD test, it is necessary to rank order the means. ANS: F PTS: 1 31. When using multiple comparisons, the real issue is between doing the most powerful test and making the fewest Type I errors. ANS: T PTS: 1 MSC: WWW 32. Qcrit is generally the same for the HSD and the Newman-Keuls tests. ANS: F PTS: 1 33. The HSD and Newman-Keuls tests differ in the value they calculate for Qobt. ANS: F PTS: 1 34. The appropriate sampling distribution for the HSD test is the Studentized Range distribution. ANS: T PTS: 1 35. When comparisons are planned in advance of conducting the experiment, you need a significant value for Fobt before you can make the comparisons. ANS: F PTS: 1 36. When doing post hoc comparisons, it is necessary to have a significant value for Fobt before you can make the comparisons. ANS: F PTS: 1 MSC: WWW DEFINITIONS 1. Define a posteriori comparisons. ANS: Answer not provided. PTS: 1 2. Define a priori comparisons. ANS: Answer not provided. PTS: 1 3. Define the analysis of variance. ANS: Answer not provided. PTS: 1 4. Define between-groups sum of squares (SSB). ANS: Answer not provided. PTS: 1 5. Define between-groups variance estimate (sB2). ANS: Answer not provided. PTS: 1 6. Define comparison-wise error rate. ANS: Answer not provided. PTS: 1 7. Define experiment-wise error rate. ANS: Answer not provided. PTS: 1 8. Define eta squared (2). ANS: Answer not provided. PTS: 1 9. Define F test. ANS: Answer not provided. PTS: 1 10. Define Fcrit. ANS: Answer not provided. PTS: 1 11. Define grand mean ( ). ANS: Answer not provided. PTS: 1 MSC: WWW 12. Define the Newman-Keuls test. ANS: Answer not provided. PTS: 1 13. Define estimated omega squared ( ). ANS: Answer not provided. PTS: 1 14. Define one-way analysis of variance, independent groups design. ANS: Answer not provided. PTS: 1 15. Define planned comparisons. ANS: Answer not provided. PTS: 1 16. Define post hoc comparisons. ANS: Answer not provided. PTS: 1 17. Define Qcrit. ANS: Answer not provided. PTS: 1 18. Define Qobt. ANS: Answer not provided. PTS: 1 19. Define sampling distribution of F. ANS: Answer not provided. PTS: 1 MSC: WWW 20. Define simple randomized group design. ANS: Answer not provided. PTS: 1 21. Define single factor experiment, independent groups design. ANS: Answer not provided. PTS: 1 22. Define total variability (SST). ANS: Answer not provided. PTS: 1 23. Define Tukey's HSD test. ANS: Answer not provided. PTS: 1 24. Define within-groups sum of squares (SSW). ANS: Answer not provided. PTS: 1 25. Define within-groups variance estimate (sW2). ANS: Answer not provided. PTS: 1 SHORT ANSWER 1. The analysis of variance is a nondirectional technique and yet it uses a one-tailed evaluation. Is this statement correct? If so, how can you explain this apparent contradiction? ANS: Answer not provided. PTS: 1 MSC: WWW 2. The analysis of variance technique analyzes the variability of the data. Yet a significant F value indicates there is at least one significant mean difference between the conditions. How does analyzing the variability of the data allow conclusions about the means of the conditions? ANS: Answer not provided. PTS: 1 3. Describe the sampling distribution of F. ANS: Answer not provided. PTS: 1 4. This question was a duplicate and has been removed from the ExamView test bank. To maintain the integrity of the numbering system between the printed copy and ExamView, the question has been marked "do not use on test" in ExamViews question information dialog. ANS: Do Not Use PTS: 1 5. List three variables, not including beta, that affect the power of the ANOVA and state what increases in each do to the power of the ANOVA. ANS: Answer not provided. PTS: 1 6. If an experiment using ANOVA results in a significant F value, it necessarily follows that the IV has had an important effect. Is this true? Explain. ANS: Answer not provided. PTS: 1 7. A researcher conducts an independent groups experiment and analyzes the data with the t test for independent groups. Assume tobt = 2.23. Also assume this result is significant at the 0.05 level. Could this data have been analyzed with one-way, independent groups ANOVA? If so, what do you think the value of Fobt would be? Would the result be significant with the ANOVA analysis too? Explain. ANS: Answer not provided. PTS: 1 8. Which is more powerful, a priori or a posteriori comparisons? Why? ANS: Answer not provided. PTS: 1 MSC: WWW 9. Explain how the Q distributions were developed. How does this compare to the t distributions? ANS: Answer not provided. PTS: 1 10. Which test is more powerful, the Tukey HSD test or the Newman-Keuls test? Explain. ANS: Answer not provided. PTS: 1 11. Give two conditions that should be met before doing a priori comparisons that are not independent. ANS: Answer not provided. PTS: 1 12. Is the Type I error rate higher when doing a priori comparisons or when doing the Tukey HSD test? Explain. ANS: Answer not provided. PTS: 1 13. Write the number of the symbol shown in Column 1 in the space provided to the left of the term in Column 2 that it represents. Column 1 Symbols Column 2 Terms 1. sW2 2. 3. sB2 4. SSW 5. 6. SSB ___ Between-groups sum of squares ___ with-in groups sum of squares ___ indicates the mathematical operations of squaring all scores, then summing the squared values ___ between-groups variance estimate ___ within-groups variance estimate ANS: Answer not provided. PTS: 1 MSC: WWW

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