Deck 14: Analysis of Variance: Two-Way Between-Subjects Factorial Design

Question 1

Using an A * B ANOVA,a researcher concludes that Factor A is significant,independent of Factor B. In this study, this researcher found a significant ______.

A) main effect of Factor A
B) main effect of Factor B
C) A * B interaction
D) post hoc test

Answer 1

main effect of Factor A

Question 2

A researcher has participants complete a survey regarding their level of restraint when eating.Participants were assigned to groups based on their current health status (lean,overweight,obese)and gender (male,female).What type of factorial design is most appropriate for this study?

A) a 1-between, 1-within factorial design
B) a between-subjects factorial design
C) a within-subjects factorial design
D) none; this is not a factorial design

Answer 2

a between-subjects factorial design

Question 3

Each of the following is a type of two-way ANOVA,except ______.

A) a 2-between factorial design
B) a 1-between, 1-within factorial design
C) a 2-within factorial design
D) a 1-between factorial design

Answer 3

a 1-between factorial design

Question 4

A researcher computes a two-way between-subjects ANOVA and finds a significant A * B interaction and two main effects.Which significant effect should typically be analyzed first?

A) the significant main effect for one factor
B) the significant main effect for both factors
C) the significant interaction
D) no effect needs to be analyzed further

Question 5

Which of the following is a reason why it can be necessary to include two factors in the same statistical design?

A) you want to observe two groups in the same statistical design
B) you want to analyze the main effects of a factor
C) your hypothesis may require that you observe two factors
D) you want to minimize the number of participants observed in your study

Question 6

Which of the following describes a research design in which one factor could be a between-subjects factor,and the second factor could be a within-subjects factor?

A) the effects of ones' sex (male, female) and season of birth on rates of schizophrenia
B) the effects of ones' socioeconomic status and education level on their overall life satisfaction
C) the effects of ones' income level on their resiliency in the face of each of three cognitively-challenging tasks
D) the effects of ones' handedness (right, left) and class year (freshman to senior) on their intelligence scores

Question 7

A researcher observes the same participants across the levels of one factor and different participants across the levels of a second factor.What type of factorial design is most appropriate for this study?

A) a 1-between, 1-within factorial design
B) a between-subjects factorial design
C) a within-subjects factorial design
D) none; this is not a factorial design

Question 8

A researcher computes a 2 * 3 factorial ANOVA.In this example,how many interactions can be observed?

A) 1
B) 2
C) 3
D) 6

Question 9

For an analysis of variance,the term "two-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 traffic should follow on a road

Question 10

Which of the following correctly identifies each source of variation in the two-way between-subjects ANOVA?

A) two between-groups, one within-groups, and error
B) two within-groups, one between-groups, and error
C) two interactions, one main effect, and error
D) two main effects, one interaction, and error

Question 11

A ______ is the combination of one level from each factor.

A) factor
B) cell
C) main effect
D) interaction

Question 12

Using a two-way between-subjects ANOVA with Factor A (gender: male,female)and Factor B (type of employment: blue collar,white collar),a researcher found that scores for men and women significantly varied across the levels of the second factor (type of employment).In this study,the researcher found a significant ______.

A) main effect of Factor A
B) main effect of Factor B
C) A * B interaction
D) post hoc test

Question 13

Which source of variation,if significant,is typically analyzed first?

A) a main effect
B) the interaction

Question 14

There are ______ factors in a 2 *3 ANOVA design.

A) 2
B) 3
C) 5
D) 6

Question 15

Which of the following hypotheses identifies a prediction that requires that two factors we observed in the same statistical design?

A) Eating slowly will reduce total caloric intake during a meal.
B) Mood will improve most when people consume foods that are high in sugar and fat.
C) Intense exercise will increase cravings for high calorie foods.
D) The closer a food is to a participant, the more of that food they will consume.

Question 16

There are ______ cells or groups in a 3 * 4 ANOVA design.

A) 3
B) 4
C) 7
D) 12

Question 17

The complexity of the two-way ANOVA differs from that of the t tests and the one-way ANOVAs in that,______.

A) two factors can be observed using the two-way ANOVA, but not using the t tests and the one-way ANOVAs
B) an interaction can be observed using the two-way ANOVA, but not using the t tests and the one-way ANOVAs
C) three hypothesis are made with one statistical test using the two-way ANOVA, but not using the t tests and the one-way ANOVAs
D) all of these

Question 18

A researcher computes a two-way between-subjects ANOVA and finds a significant main effect of Factor A and an A *B interaction.Which significant effect should typically be analyzed first?

A) the significant main effect
B) the significant interaction
C) No effect needs to be analyzed further.

Question 19

A researcher assigns participants to one of three groups (Group A,B,or C)and then observes each group for two days (Days 1 and 2).What type of factorial design is most appropriate for this study?

A) a 1-between, 1-within factorial design
B) a between-subjects factorial design
C) a within-subjects factorial design
D) none; this is not a factorial design

Question 20

Not including the total variation,how many sources of variation are measured in a two-way between-subjects ANOVA?

A) 2
B) 3
C) 4
D) 5

Question 21

A professor compares the exam grades of students based on whether they have a learning disability (yes,no)and where they sit in the classroom (in the front,middle,or back row).Different participants were observed in each group.What type of statistical design is appropriate for this study?

A) one-way between-subjects ANOVA
B) one-way within-subjects ANOVA
C) two-way between-subjects ANOVA
D) one-way within-subjects ANOVA and two-way between-subjects ANOVA

Question 22

A simple main effect test is appropriate for analyzing which significant result?

A) a significant main effect, where k = 2
B) a significant main effect, where k > 2
C) a significant interaction
D) all of these

Question 23

A researcher computes a 3 * 4 between-subjects ANOVA.What are the degrees of freedom for Factor A for this study?

A) 2
B) 3
C) 6
D) 12

Question 24

A researcher measures differences in recall between participants watching a regular or a 3-D movie clip with a romance,drama,or action theme.Different participants were observed in each group.What type of statistical design is appropriate for this study?

A) one-way between-subjects ANOVA
B) one-way within-subjects ANOVA
C) two-way between-subjects ANOVA
D) one-way within-subjects ANOVA and two-way between-subjects ANOVA

Question 25

A researcher computes a 3 * 4 between-subjects ANOVA and finds one significant main effect and a significant interaction.What is typically the next appropriate step?

A) compute pairwise comparisons for the main effect
B) compute simple main effect tests for the main effect
C) compute pairwise comparisons for the interaction
D) compute simple main effect tests for the interaction

Question 26

A researcher randomly measures social adjustment among children from different family backgrounds (levels of Factor A: divorced,married,single)who engaged in one of five social activities (Factor B).For this study,10 children were observed in each group.If SS_A = 10,MS_B = 12,SS_AXB = 48,and SS_E = 405,then which effect was significant at a .05 level using the two-way between-subjects ANOVA?

A) Factor A (family backgrounds)
B) Factor B (social activities)
C) the A* B interaction
D) there were no significant effects

Question 27

A researcher conducts a 2* 4 between-subjects ANOVA in which 12 participants were observed in each group.If SS_A = 18 and SS_E = 264,then what is the decision for Factor A at a .05 level of significance using the two-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 28

Which of the following is NOT an assumption for computing a two-way between-subjects ANOVA?

A) The population being sampled from is normally distributed.
B) Participants were selected using a random procedure.
C) One observation has no effect on the likelihood of another observation.
D) There is homogeneity of variance and homogeneity of covariance.

Question 29

A researcher computes a 4 * 4 between-subjects ANOVA and finds two significant main effects and a significant interaction.What is typically the next appropriate step?

A) compute pairwise comparisons for each main effect
B) compute simple main effect tests for each main effect
C) compute pairwise comparisons for the interaction
D) compute simple main effect tests for the interaction

Question 30

A researcher conducts a 2 * 4 between-subjects ANOVA in which 12 participants were observed in each group.If SS_B = 18 and SS_E = 264 for this study,then what is the decision for Factor B at a .05 level of significance?

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

Question 31

A researcher computes two 2* 2 between-subjects ANOVAs.In Study 1,he observes eight participants in each cell; in Study 2,he observes 12 participants in each cell.Which study is associated with a larger value for degrees of freedom for the A * B interaction?

A) Study 1
B) Study 2
C) both studies have the same degrees of freedom for the A * B interaction

Question 32

A researcher computes a 2 * 4 between-subjects ANOVA.What are the degrees of freedom for Factor B for this study?

A) 2
B) 3
C) 4
D) 8

Question 33

A researcher computes a 2 * 3 between-subjects ANOVA in which six participants are observed in each cell.What are the degrees of freedom error for this study?

A) 71
B) 60
C) 30
D) 36

Question 34

A researcher computes a 2 * 3 between-subjects ANOVA test in which 11 participants were observed in each condition.If F = 5.20 for both main effect tests and the A * B interaction test,then the decision for each test

A) will be significant for both main effects and the A * B interaction
B) will be significant for Factor A, but not Factor B
C) will be significant for Factor B and the A * B interaction
D) there is not enough information to answer this question

Question 35

A researcher computes a 3 * 5 between-subjects ANOVA.What are the degrees of freedom for the A * B interaction for this study?

A) 2
B) 4
C) 8
D) 15

Question 36

The denominator of the test statistic for the main effects and interaction in a two-way between-subjects ANOVA ______.

A) is equal to 0
B) is equal to mean square error
C) is equal to mean square between groups
D) is a measure of variance for differences between groups

Question 37

A researcher computes the following 2 * 3 between-subjects ANOVA,in which 11 participants were observed in each group.Which effect was significant at a .05 level of significance using the two-way between-subjects ANOVA?

A) one of the main effects only
B) Factor A and the A * B interaction
C) Factor B and the A * B interaction
D) there were no significant effects

Question 38

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

A) different participants are assigned to each group or cell
B) the same participants are observed across groups or cells
C) the levels of two or more factors are manipulated
D) different participants are assigned to each group or cell and the levels of two or more factors are manipulated

Question 39

A researcher records the amount of time spent studying by male and female college students in a dormitory versus a library setting.Different participants were observed in each group.What type of statistical design is appropriate for this study?

A) one-way between-subjects ANOVA
B) one-way within-subjects ANOVA
C) two-way between-subjects ANOVA
D) one-way within-subjects ANOVA and two-way between-subjects ANOVA

Question 40

The statistical procedure used to analyze the simple main effects of an interaction is called ______.

A) a simple main effect test
B) a pairwise comparison
C) the proportion of variance
D) estimated Cohen's d

Question 41

When the same participants are observed in each cell or group,we use the two-way between-subjects ANOVA to analyze the data.

Question 42

The means and standard error or standard deviations measured in a study can be summarized in,______.

A) a figure
B) a table
C) the main text of a report
D) all of these

Question 43

An estimate of effect size with the two-way ANOVA is typically reported for ______.

A) a significant main effect test
B) a significant interaction test
C) a significant main effect test and a significant interaction test
D) none; effect size is not reported for the two-way ANOVA

Question 44

Homogeneity of co-occurrence is one assumption for computing a two-way between-subjects ANOVA.

Question 45

The assumptions for a two-way between-subjects ANOVA apply only to main effect tests,and not the interaction test.

Question 46

For the effects of a two-way between-subjects ANOVA,which values must be known to compute effect size using $\omega$ ²?

A) mean squares
B) sum of squares
C) degrees of freedom
D) all of these

Question 47

Using the two-way mixed ANOVA,different participants are observed at each level of the between-subjects factor,and the same participants are observed across the levels of the within-subjects factor.

Question 48

To summarize any type of two-way ANOVA using APA format,we report each of the following except the,______.

A) test statistic
B) critical values
C) p value
D) degrees of freedom

Question 49

Using a two-way between-subjects ANOVA,we compute hypothesis tests for two main effects and one interaction.

Question 50

If an interaction and a main effect are significant for a two-way between-subjects ANOVA,then the main effect must be analyzed first.

Question 51

A researcher conducts a 2 * 3 between-subjects ANOVA.She finds a significant interaction,where SS_AXB = 120 and SS_T = 518.What is the effect size for this test using $\eta$ ²?

A) 0.23
B) 0.43
C) 4.32
D) there is not enough information to answer this question

Question 52

A researcher groups college students in a study based on their year in college (freshman,sophomore,junior,senior)and the type of college they attend (junior,technical,university).He concludes that perceptions of academic cheating are more positive among freshman attending junior college.To reach this conclusion,which statistical test would need to be computed?

A) a two-way between-subjects ANOVA
B) a simple main effect test
C) a post hoc test
D) all of these

Question 53

A complete factorial design is one in which each level of one factor is combined or crossed with each level of the other factor.

Question 54

A two-way ANOVA is a statistical procedure used to test hypotheses concerning the variance of two group means for the levels of one factor.

Question 55

There are two factors and four cells in a 2 * 2 between-subjects ANOVA.

Question 56

For the effects of a two-way between-subjects ANOVA,which values must be known to compute effect size using $\eta$ ²?

A) mean squares
B) sum of squares
C) degrees of freedom
D) all of these

Question 57

For a two-way ANOVA,the ______ should also be reported for each significant hypothesis test and for the simple main effect tests.

A) effect size
B) critical values
C) individual participant data
D) all of these

Question 58

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

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

Question 59

Homogeneity of variance is one assumption for the two-way between-subjects ANOVA.

Question 60

The following is a summary of a significant interaction for a two-way ANOVA: F(2,30)= 2.04,p < .05 ( $\eta$ ² = .15).Assuming the test statistic value is correct,then which of the following must be incorrect in this report?

A) the effect size
B) the degrees of freedom
C) the p value
D) the test statistic

Question 61

A researcher randomly assigns different participants to each combination of levels for two factors.In this example,a two-way between-subjects ANOVA is appropriate to analyze the data.

Question 62

If a study has 12 groups,then it is possible that the degrees of freedom for each factor are 3 and 4 degrees of freedom for a two-way between-subjects ANOVA.

Question 63

It is inappropriate to compute effect size for interactions and main effects.

Question 64

The following APA summary of a significant interaction is correctly stated: "The interaction between playfulness and resiliency was significant,F(16)= 3.07,p < .05 (R² = .12)."

Question 65

Mean square error is the denominator for all tests using a two-way between-subjects ANOVA.

Question 66

$\omega$ ² corrects for the number of groups and the size of error in an analysis of variance test; $\eta$ ² does not.

Question 67

The denominator of the formula for $\eta$ ² is SS_T for both main effects and the interaction.

Question 68

A two-way between-subjects ANOVA is appropriate for analyzing differences in the combination of levels for two or more factors.

Question 69

If each main effect is significant,then the interaction must also be significant for a two-way between-subjects ANOVA.

Question 70

Simple main effect tests are used to analyze a significant interaction by comparing the mean differences of one factor at each level of a second factor.

Question 71

An A * B interaction is associated with 8 degrees of freedom in a 2 * 4 between-subjects ANOVA.

Question 72

An A * B interaction is associated with 2 degrees of freedom in a 2 * 3 between-subjects ANOVA design.

Question 73

To summarize any type of two-way ANOVA,we report the test statistic,the degrees of freedom,and the p value for each significant main effect and interaction.

Question 74

Simple main effect tests are necessary to analyze a significant interaction and a significant main effect.

Question 75

A significant interaction indicates that at least one pair of cell means significantly differs.

Question 76

If both main effects and the interaction are not significant using the two-way between-subjects ANOVA then post hoc tests and simple main effect tests are unnecessary.

Question 77

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.77,p < .05 (R² = .18)."

Question 78

Simple main effect tests are necessary to analyze interactions,not main effects.

Question 79

$\eta$ ² is a more powerful estimate of effect size than R².

Question 80

If a study has 12 groups,then it is possible that the degrees of freedom for each factor are 2 and 3 degrees of freedom for a two-way between-subjects ANOVA.