Deck 12: Analysis of Variance: One-Way Between-Subjects Design

Question 1

For an analysis of variance,the term "one-way" refers to ______.

A) the number of factors in the design
B) the number of statistical tests in the design
C) the number of ways that the data can be analyzed
D) the direction that the traffic should follow on a road

Answer 1

the number of factors in the design

Question 2

Using a between-subjects ANOVA design,______.

A) n-k participants are each observed one time
B) n participants are observed k times
C) data are not analyzed between groups
D) the same participants are observed in each group

Answer 2

n-k participants are each observed one time

Question 3

The degrees of freedom for the between-groups variability are called ______.

A) degrees of freedom numerator
B) degrees of freedom denominator
C) degrees of freedom between groups
D) degrees of freedom numerator and degrees of freedom between groups

Answer 3

degrees of freedom numerator and degrees of freedom between groups

Question 4

Which of the following is an assumption for computing a one-way between-subjects ANOVA?

A) The population being sampled from is normally distributed.
B) Participants were selected to participate using a random procedure.
C) One observation has no effect on the likelihood of another observation.
D) All of these.

Question 5

Which of the following statements is the appropriate way to read the degrees of freedom for an ANOVA with 10 participants in each of four groups?

A) 3 or 36 degrees of freedom
B) 3 and 36 degrees of freedom
C) 4 and 10 degrees of freedom
D) 4 and 36 degrees of freedom

Question 6

The term "between-subjects" refers to ______.

A) observing the same participants in each group
B) observing different participants one time in each group
C) the type of post hoc test conducted
D) the type of effect size estimate measured

Question 7

Without changing the value of error variance,the ______ the between-groups variability,the more likely we are to retain the null hypothesis.

A) larger
B) smaller

Question 8

The degrees of freedom for error is called ______.

A) degrees of freedom error
B) degrees of freedom denominator
C) degrees of freedom within groups
D) all of these

Question 9

The source of variability associated with error variance in the one-way between-subjects ANOVA is called ______.

A) between-groups variability
B) within-groups variability
C) degrees of freedom
D) between-groups variability and within-groups variability

Question 10

A researcher measures attractiveness ratings of a male confederate among 30 women who were told the confederate was either single,dating,or married (n = 10 per group).What are the degrees of freedom for error for the one-way between-subjects ANOVA?

A) 2
B) 3
C) 27
D) 28

Question 11

A researcher assigned participants (n = 8 per group)to read vignettes describing a person engaging in either a helpful,hurtful,or neutral act.Different participants were assigned to each group and asked to rate how positively they viewed the person described in the vignette.What is the critical value for the one-way between-subjects ANOVA at a .05 level of significance?

A) 3.07
B) 3.44
C) 3.47
D) 4.32

Question 12

ANOVA stands for ______.

A) analysis of variety
B) analysis of variable attributes
C) analysis of variance
D) association of novel operating variable analyses

Question 13

A researcher conducts a study in which k = 4 and n = 22 in each group.What are the degrees of freedom for the one-way between-subjects ANOVA?

A) (3, 84)
B) (4, 88)
C) (4, 22)
D) (3, 18)

Question 14

What is the minimum number of groups that can be observed using the one-way between-subjects ANOVA design?

A) 1
B) 2
C) 3
D) 4

Question 15

A researcher conducts a study in which k = 6 and n = 6 per group.What are the critical values for the one-way between-subjects ANOVA at a .05 level of significance?

A) 3.70
B) 3.47
C) 2.53
D) 2.42

Question 16

A researcher notes that the variability attributed to difference between group means is quite large.Which source of variation is the researcher referring to?

A) between persons
B) within groups
C) between groups
D) error

Question 17

A researcher conducts a study in which k = 5 and N = 80.What are the degrees of freedom between groups for the one-way between-subjects ANOVA?

A) 4
B) 5
C) 75
D) 395

Question 18

A lowercase k is used to denote ______ using a one-way ANOVA.

A) the number of groups in a study
B) the number of participants in a study
C) the number of levels of the factor in a study
D) the number of groups in a study and the number of levels of the factor in a study

Question 19

A researcher compares differences in positivity between participants in a low-,middle-,or upper-middle-class family.If she observes 15 participants in each group,then what are the degrees of freedom for the one-way between-subjects ANOVA?

A) (2, 12)
B) (3, 43)
C) (2, 42)
D) (3, 12)

Question 20

Without changing the value of error variance,the ______ the between-groups variability,the more likely we are to reject the null hypothesis.

A) larger
B) smaller

Question 21

A researcher conducts two studies on self-perception.In Study 1,24 participants rate how positively they view themselves (on a 5-point scale)in one of three groups (n = 8 per group).In Study 2,the researcher conducts a similar study,except that k = 3 and n = 8.If SS_BG = 28 and SS_E = 42 in both studies,then in which study will the decision be to reject the null hypothesis at a .05 level of significance for a one-way between-subjects ANOVA?

A) Study 1
B) Study 2
C) both
D) none

Question 22

Which of the following post hoc tests is associated with the least power to detect an effect?

A) Fisher's LSD test
B) Tukey's HSD test
C) Studentized Newman-Keuls
D) none; each post hoc test is associated with the same power to detect an effect

Question 23

A researcher randomly assigned 32 children to observe a short clip depicting either their favorite superhero,a parent,a teacher,or no person at all (n = 8 per group).If SS_BG = 30 and SS_E = 104,then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?

A) reject the null hypothesis.
B) retain the null hypothesis.
C) there is not enough information to answer this question

Question 24

Which of the following post hoc tests is associated with the greatest power to detect an effect?

A) Schaffé test
B) Tukey's HSD test
C) Bonferroni test
D) Fisher's LSD test

Question 25

When the variability attributed to between groups is equal to the variability attributed to error,then the value of the test statistic for a one-way between-subjects ANOVA is ______.

A) equal to 0
B) equal to 1
C) significant at any sample size
D) undefined in that the test statistic cannot be computed in this case

Question 26

Computing a one-way between-subjects ANOVA is appropriate when ______.

A) different participants are observed one time in each of two or more groups for one factor
B) the same participants are observed in each of two or more groups for one factor
C) the levels of one or more factors are manipulated
D) all of the above

Question 27

A researcher conducts two studies on child health.In Study 1,30 children consume either a low-,moderate-,or high-fat meal (n = 10 per group).In Study 2,the researcher conducts the same study,except that a No Meal control group is added,with n = 10 in each group.If F_obt = 3.11 in both studies,then in which study will the decision be to reject the null hypothesis at a .05 level of significance for a one-way between-subjects ANOVA?

A) Study 1
B) Study 2
C) both
D) none

Question 28

A researcher measures differences in recall between male and female participants following a romantic movie clip.If different participants were in each group,then what type of statistical design is appropriate for this study?

A) a two-independent-sample t test
B) a one-way between-subjects ANOVA
C) a two-way between-subjects ANOVA
D) a two-independent-sample t test and a one-way between-subjects ANOVA

Question 29

Homogeneity of variance is an assumption for the one-way between-subjects ANOVA.What does this assumption mean?

A) that the population being sampled from is normally distributed
B) that participants are randomly selected to participate in a sample
C) that the variance is equal in each population from which samples are selected
D) that one observation has no effect on the likelihood of another observation

Question 30

A researcher computes the following one-way between-subjects ANOVA table for a study where k = 3 and n = 12.State the decision at a .05 level of significance.(Hint: Complete the table first.)

A) reject the null hypothesis
B) retain the null hypothesis
C) there is not enough information to answer this question

Question 31

A researcher randomly assigned N = 16 rodents to experience one of four levels of shock (n = 4 per group)following the illumination of a visual cue.If SS_BG = 24 and SS_E = 48,then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?

A) reject the null hypothesis
B) retain the null hypothesis
C) there is not enough information to answer this question

Question 32

A professor compared differences in class grades between students in their freshman,sophomore,junior,and senior years of college.If different participants were in each group,then what type of statistical design is appropriate for this study?

A) a two-independent-sample t test
B) a one-way between-subjects ANOVA
C) a two-way between-subjects ANOVA
D) a two-independent-sample t test and a one-way between-subjects ANOVA

Question 33

Which of the following is not a post hoc test for a one-way between-subjects ANOVA?

A) $\eta$ ²
B) Fisher's LSD test
C) Tukey's HSD test
D) Bonferroni test

Question 34

A researcher measures differences in romantic feelings among adolescent and adult males.If different participants were in each group,then what type of statistical design is appropriate for this study?

A) a two-independent-sample t test
B) a one-way between-subjects ANOVA
C) a two-way between-subjects ANOVA
D) a two-independent-sample t test and a one-way between-subjects ANOVA

Question 35

Following a significant one-way between-subjects ANOVA in which k > 2,what is the next appropriate step?

A) summarize the data; no further tests are required
B) interpret the data; no further tests are required
C) conduct post hoc tests
D) summarize the data and interpret the data; no further tests are required

Question 36

A researcher divides participants into groups that will engage in low,moderate,or intense levels of exercise.The total calories consumed by participants following the exercise are then recorded.What type of statistical design is appropriate for this study?

A) a related-samples t test
B) a two-independent-sample t test
C) a one-way between-subjects ANOVA
D) a two-independent-sample t test and a one-way between-subjects ANOVA

Question 37

In a study with three groups and 13 participants in each group,the sum of squares for the within-groups source of variation is 18.What is the value for the mean square within groups in this study?

A) 2
B) 3
C) 9
D) 0.5

Question 38

A researcher computes the following one-way between-subjects ANOVA table.State the decision at a .05 level of significance.(Hint: Complete the table first.)

A) reject the null hypothesis
B) retain the null hypothesis
C) there is not enough information to answer this question

Question 39

In a study with four groups and 10 participants in each group,the sum of squares for the between-groups source of variation is 60.What is the value for the mean square between groups in this study?

A) 10
B) 15
C) 20
D) 1.67

Question 40

A researcher assigns 21 adolescents to rate the likability of a person described in a vignette as having one of three personality traits.An equal number of participants are assigned to each group.If F_obt = 4.08 for this study,then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?

A) reject the null hypothesis
B) retain the null hypothesis
C) there is not enough information to answer this question

Question 41

Which measure of proportion of variance tends to overestimate the size of an effect in a population?

A) $\eta$ ²
B) $\omega$ ²
C) none of these

Question 42

Which of the following is a measure of proportion of variance for a one-way between-subjects ANOVA?

A) $\eta$ ²
B) $\omega$ ²
C) estimated Cohen's d
D) $\eta$ ² and $\omega$ ²

Question 43

An ANOVA is used when samples are selected from two or more populations and when two or more samples are selected from the same population.

Question 44

A one-way between-subjects ANOVA is conducted to test for mean differences between the levels of two or more factors.

Question 45

There are two sources of variation in a one-way between-subjects ANOVA: one attributed to differences between groups and one attributed to error.

Question 46

Post hoc tests are computed ______.

A) prior to conducting a hypothesis test.
B) to determine which set of degrees of freedom can be attributed to the variability between groups
C) following a significant ANOVA test to make pairwise comparisons
D) to determine if groups means differ, even for tests in which the decision is to retain the null hypothesis

Question 47

The degrees of freedom total for a one-way between-subjects ANOVA is the total sample size minus one.

Question 48

How does $\omega$ ² for the one-way between-subjects ANOVA correct for the fact that $\eta$ ² tends to be a biased estimate of effect size?

A) It corrects for the size of error by including MS_E in the formula.
B) It includes the degrees of freedom between groups (df_BG) in the formula.
C) It accounts for the number of groups that were observed.
D) All of these.

Question 49

A researcher measures mating displays among 12 birds randomly assigned to be in the presence of no cue,an auditory cue,or a visual cue.The degrees of freedom for this one-way between-subjects ANOVA is 2 and 9 degrees of freedom.

Question 50

An analysis of variance is a statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means,where the variance in one or more populations is unknown.

Question 51

Which of the following post hoc tests uses the t-critical value in the calculation to determine the critical value for the test?

A) Schaffé test
B) Tukey's HSD test
C) SNK test
D) Fisher's LSD test

Question 52

A researcher conducts a study using the one-way between-subjects ANOVA.He computes SS_BG = 120 and SS_E = 200.What is the effect size for this test using $\eta$ ²?

A) 0.60
B) 0.38
C) 1.67
D) there is not enough information to answer this question

Question 53

For a one-way between-subjects ANOVA,a study with 3 and 36 degrees of freedom must have included four groups.

Question 54

A "one-way" ANOVA is associated with one degree of freedom.

Question 55

The following is a summary of a one-way between-subjects ANOVA: F(2,37)= 3.42,p < .05, $\eta$ ²= .12.How many pairwise comparisons need to be made for this ANOVA result?

A) 2
B) 3
C) 4
D) 12

Question 56

A researcher conducts two studies using the one-way between-subjects ANOVA.The sum of squares between groups is larger in Study 1 than in Study 2; the sum of squares total is smaller in Study 1 than in Study 2.Using $\eta$ ²,in which study will the effect size be larger?

A) Study 1
B) Study 2
C) there is not enough information to answer this question

Question 57

A researcher conducts two studies using the one-way between-subjects ANOVA.The sum of squares between groups is smaller in Study 1 than in Study 2; the sum of squares total is the same in both studies.Using $\eta$ ²,in which study will the effect size be larger?

A) Study 1
B) Study 2
C) there is not enough information to answer this question

Question 58

A researcher randomly assigns 24 participants to one of four groups.At a .05 level of significance,the critical value for a one-way between-subjects ANOVA is 3.49.

Question 59

The following is a summary of a one-way between-subjects ANOVA: F(2,37)= 3.42,p < .05, $\eta$ ² = .12.How many participants were observed in this study?

A) 12
B) 37
C) 40
D) 39

Question 60

A "one-way" between-subjects ANOVA is conducted when data are recorded in one group.

Question 61

Two measures of proportion of variance for the one-way between-subjects ANOVA are $\eta$ ² and $\omega$ ².

Question 62

A researcher has the same 18 participants rate 6 pictures (k = 6),each depicting a person with a different body type.The one-way between-subjects ANOVA is the most appropriate test for this design.

Question 63

A significant ANOVA indicates that all pairs of group means significantly differ.

Question 64

All post hoc tests control for the effect size of a significant result.

Question 65

A mean square is a sample variance.

Question 66

The test statistic for a one-way between-subjects ANOVA is the sum of squares between groups divided by the sum of squares error.

Question 67

The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability associated with error.

Question 68

To compute a mean square,we divide the sum of squares by the degrees of freedom for a given source of variation.

Question 69

To conduct a one-way between-subjects ANOVA,we assume that the samples were randomly selected from populations with equal variances,and that participants were independently observed in each group.

Question 70

Cohen's d is the most commonly reported measure of effect size for the one-way between-subjects ANOVA.

Question 71

The test statistic for a one-way between-subjects ANOVA is used to determine whether the variance associated with having different groups is significantly larger than the variance attributed to chance or error.

Question 72

To summarize the results of a one-way between-subjects ANOVA test,we report the test statistic,the degrees of freedom,and the p value.

Question 73

Unlike $\omega$ ²,the formula for $\eta$ ² corrects for the number of groups and the size of error in its estimate of effect size.

Question 74

The same participants are observed in each group using the between-subjects design.

Question 75

A post hoc test is only necessary following a decision to retain the null hypothesis.

Question 76

While it is common to report the result of an ANOVA,researchers rarely report the results of a post hoc test.

Question 77

Violating the assumption of homogeneity of variance tends to increase the likelihood of committing a Type I error.

Question 78

Post hoc tests control for the total alpha level for a series of tests conducted on the same data.

Question 79

Post hoc tests are conducted following a significant one-way between-subjects ANOVA,only when k > 2.

Question 80

$\eta$ ² is often reported as R² for an analysis of variance test.