Deck 17: Two-Way Between-Subjects Analysis of Variance

Question 1

The critical F value for degrees of freedom (1,76)is 3.96.

The joint effects of Variable A and Variable B on the DV is tested using the F ratio for the _____ effect.

A)main
B)simple
C)interaction
D)total

Answer 1

C

Question 2

F(2,21)= 45.00,p< .05,with eta² = .18.
According to the above F statement,the value computed for the F ratio is:

A)2
B)21
C)45.00
D).18

Answer 2

C

Question 3

Assume the following is a population means table:
Using your knowledge of general patterns of plotted means in a two-way ANOVA,does there appear to be a main effect of variable B in this example?

A)Yes
B)No
C)Not enough information

Answer 3

A

Question 4

Assume the following is a population means table:
Using your knowledge of general patterns of plotted means in a two-way ANOVA,does there appear to be a main effect of variable A in this example?(Hint: Graphing the means might help. )

A)Yes
B)No
C)Not enough information

Question 5

When examining a plot of population means for a two-way ANOVA,what is the simplest way to tell if there is an interaction?

A)The two lines will NOT cross.
B)The two lines will be parallel.
C)The two lines will NOT be parallel.
D)There will be a curve in both lines.

Question 6

How many groups of individuals would be included in a 4 x 2 factorial design?

A)2
B)4
C)6
D)8

Question 7

Factorial designs can be used to study

A)the joint effects of two dependent variables on an independent variable.
B)the joint effects of two independent variables on a dependent variable.
C)the effect of a single dependent variable with two or more levels on an independent variable
D)the effect of a single independent variable with two or more levels on a dependent variable.

Question 8

In a two-way between-subjects analysis of variance,how many sets of statistical hypotheses are examined?

A)one set,which includes one null and one alternative hypothesis
B)two sets,which includes a null and alternative hypothesis for both Factor A and B
C)three sets,one for each main effect and one for the interaction effect
D)four sets,one for each main effect,one for the interaction,and one for the error term

Question 9

F(2,21)= 45.00,p< .05,with eta² = .18.
If this was an F statement for a main effect of factor A with 3 levels,what would need to be reported next in a research report?

A)The results of a Tukey HSD procedure
B)The results of a modified Bonferroni procedure
C)The results of a power analysis
D)The results of the group mean comparisons

Question 10

If the ANOVA method is used to test for differences between means,then why is it called an "analysis of variance"?

A)Because the amount differences among the set of group means is determined by calculating the variance of those group means.
B)Because means and variances are basically the same thing.
C)Because statisticians feel it is important to have multiple names for the same thing.
D)Because the differences between means is determined by averaging the variances.

Question 11

Assume the following is a population means table:
Using your knowledge of general patterns of plotted means in a two-way ANOVA,does there appear to be an interaction in this example?

A)Yes
B)No
C)Not enough information

Question 12

Note: The critical F value for degrees of freedom (1,76)is 3.96.
The test for the "main effect" of Variable B focuses on the difference between the _________.

A)marginal means 10.2 and 6.5
B)marginal means 9.8 and 6.9
C)cell means 12.1 and 7.5
D)cell means 12.1 and 8.3

Question 13

Mean square within (MS_WITHIN)can be defined as

A)variability due to the manipulation of the IV and disturbance variables.
B)variability due to the manipulation of the IV.
C)variability due to individual differences only (e.g.,analogous to the within subjects ANOVA..
D)variability in the data due to sampling error,disturbance variables,and individual differences.

Question 14

A classmate describes her study as follows: "I have to independent variables,one has three levels and the other has two levels.I will be randomly assigning people to one of the study groups,exposing them to one level of each independent variable,then testing them on my dependent variable." Which type of statistical analysis would be most appropriate?

A)two-way mixed model analysis of variance
B)one-way repeated measures analysis of variance.
C)3 X 2 within-subjects analysis of variance.
D)3 X 2 between-subjects analysis of variance.

Question 15

In a two-way between-subjects ANOVA,a factor is another name for

A)an independent variable.
B)each level of an independent variable.
C)two or more independent variables.
D)a disturbance variable.

Question 16

What is one of the main advantages of the two-way between-subjects factorial design?

A)Participants participate in all groups.
B)The joint effect of two variables can be examined.
C)Sample size requirements are quite small.
D)Normally distributed data is not requireD.

Question 17

In the two-way ANOVA,which of the following sources of variability is NOT a component of the sum of squares between?

A)within group variability
B)variability due to the first independent variable
C)variability due to the second independent variable
D)variability due to the interaction effect

Question 18

When examining a plot of population means for a two-way ANOVA,what should you conclude if the two lines completely overlap and have zero slope?

A)There is a main effect of A only.
B)There is a main effect of B only.
C)There is an interaction effect only.
D)There are no main effects or an interaction.

Question 19

How many levels of variable A are there in a 3 X 3 factorial design?

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

Question 20

How many groups are there in a 3 X 3 factorial design?

A)3
B)6
C)9
D)2

Question 21

Which of the following is not a requirement for use of a two-way between-subjects factorial ANOVA?

A)The dependent variable is quantitative in nature.
B)The independent variables are each between-subjects in nature.
C)The dependent variable must be measured on a nominal level
D)The independent variables are combined to form a factorial design.

Question 22

When dealing with sample data,the existence of a given population main effect or interaction can be affirmed only by a:

A)visual inspection of sample means
B)visual inspection of slopes
C)significant statistical test

Question 23

Two statistical procedures used to determine the nature of the interaction are

A)simple main effects analysis and least squares analysis of variance.
B)simple main effects analysis and interaction comparisons.
C)interaction comparisons and modified Bonferroni procedure.
D)least squares analysis of variance and modified Bonferroni procedure.

Question 24

If a researcher suspects that the strength of the relationship in the population is .30 for the main effect of factor A,.10 for factor B,and .07 for the interaction effect as indexed by eta-squared,what sample size should she use per cell in a study involving three levels of factor A,five levels of factor B,and an alpha level of .05 in order to achieve a power of at least .80 for each effect?

A)2
B)7
C)9
D)13
E)23

Question 25

When dealing with population means,if the lines in a graph are _____,this suggests the presence of an interaction.

A)not parallel
B)parallel
C)curvilinear
D)none of these

Question 26

In the modified Bonferroni procedure used for interaction comparisons,to be statistically significant,the largest F ratio must yield a p value

A)less than the overall alpha level divided by the total number of interaction comparisons.
B)less than the overall alpha level divided by the total number of levels of factor A
C)greater than the overall alpha level
D)none of these

Question 27

Dr.Fleet is interested in studying the effect of gender,years of undergraduate college (0-4 years),and marital status (single,married,divorced,or widowed.on the annual income of residents of the northeastern United States.She would have ____ groups of subjects to study.

A)4
B)40
C)2
D)6

Question 28

Two-way factorial designs allow us to study:

A)main effects
B)interaction effects
C)a and b

Question 29

The F test statistic for a main effect of factor A of a 2 x 2 factorial ANOVA is determined by which of the following formulas?

A)MS_A/df_A
B)MS_A/SS_A
C)MS_A/MS_{WITHIN GROUP}
D)SS_A/df_{WITHIN GROUP}

Question 30

The sum of squares between in a two-way between-subjects analysis of variance can be partitioned into:

A)SS_A + SS_B
B)SS_A + SS_B + SS_AxB
C)SS_A + SS_ERROR
D)none of these

Question 31

Dr.Fleet is interested in studying the effect of gender,years of undergraduate college (0-4 years),and marital status (single,married,divorced,or widowed.on the annual income of residents of the northeastern United States.Which of the following describes a design that she might use?

A)2 x 2 factorial design
B)2 x 5 x 4 factorial design
C)2 x 2 repeated-measures design
D)2 x 2 x 2 factorial design

Question 32

If a researcher suspects that the strength of the relationship in the population is .25 for the main effect of factor A,.03 for factor B,and .15 for the interaction effect as indexed by eta-squared,what sample size should she use per cell in a study involving four levels of factor A,two levels of factor B,and an alpha level of .05 in order to achieve a power of at least .95 for each effect?

A)7
B)12
C)25
D)53
E)211

Question 33

The joint effect of two independent variables on a dependent variable is indicated by the ____ effect when a two-way factorial analysis is used.

A)main
B)simple
C)significant
D)interaction

Question 34

In a 4 x 2 factorial design,we can test for _____ main effect(s)and _____ interaction(s).

A)4;2
B)8;1
C)2;1
D)1;2

Question 35

In a two-way ANOVA,the _____ is further partitioned into three components,SS_A,SS_B,and SS_AxB.

A)SS_WITHIN
B)SS_TOTAL
C)SS_BETWEEN
D)SS_ERROR

Question 36

When graphing sample means,nonparallel lines may indicate the existence of an interaction,or may indicate sampling error.

Question 37

One statistical technique for analyzing the relationship between a dependent variable and two or more independent variables is ____.

A)rank-order correlation
B)two-way between-subjects analysis of variance
C)repeated measures analysis of variance
D)Kruskal-Wallis analysis of variance

Question 38

The joint effects of two independent variables on a dependent variable can be studied using:

A)factorial designs
B)one-way analysis of variance
C)single-subject designs
D)none of these

Question 39

When there are unequal sample sizes in the cells of a 2 x 2 factorial between subjects design,modification of the ANOVA techniques are necessary because

A)the within-group variability is different in all four groups.
B)the within-group variability is the same in all four groups.
C)the two independent variables are related to each other in the population.
D)the two independent variables are related to each other in the sample.

Question 40

An interaction effect refers to the case where the nature or strength of the relationship between one of the independent variables and the dependent variable differs as a function of the:

A)sample size
B)number of variables
C)dependent variable
D)other independent variable

Question 41

In general,statisticians recommend the use of _____ over _____ in determining the nature of a statistically significant interaction effect.

A)simple main effects analysis;interaction comparisons
B)interaction comparisons;simple main effects analysis
C)eta-squared;interaction comparisons
D)eta-squared;simple main effects analysis

Question 42

After a 2 x 2 factorial ANOVA has been used to determine that a statistically significant relationship exists between the dependent variable and an independent variable,a(n)____ can be calculated to indicate the strength of the relationship.

A)t²
B)Tukey's HSD
C)eta²
D)critical difference

Question 43

If a factorial ANOVA is conducted and a statistically significant main effect is determined for a factor that has three or more levels,the nature of the relationship should be determined by ____.

A)inspecting the sample means
B)calculating eta²
C)calculating a between-groups ANOVA for the significant factor
D)applying the Tukey HSD test

Question 44

When a statistically significant _____ effect has only two levels,the nature of the relationship is determined in the same fashion as for the independent groups t test.

A)interaction
B)simple
C)main
D)a and b

Question 45

The F ratio formed by SS_A/SS_WITHIN is used to test the null hypothesis with respect to:

A)factor A
B)factor B
C)factors A and B
D)none of these

Question 46

A between-groups factorial ANOVA differs from a between-groups one-way ANOVA in which of the following ways?

A)two or more dependent variables are used.
B)a factorial ANOVA may produce a negative F score.
C)two or more independent variables are used.
D)both a and b.

Question 47

As with one-way analysis of variance,under certain conditions the F tests are robust to violations of the _____ assumption.

A)normality
B)homogeneity of variance
C)a and b
D)neither a nor b

Question 48

The strengths of the relationships for the three sources of between-group variability are assessed with:

A)eta
B)r²
C)F²
D)eta-squared

Question 49

The F tests for two-way between-subjects analysis of variance assume that the scores in each population:

A)are normally distributed
B)have heterogeneous variances
C)are positively skewed
D)none of these

Question 50

In the case of highly different sample sizes across groups,the robustness of the F test to non-normality and variance heterogeneity often _____,sometimes considerably so.

A)diminishes
B)increases
C)fluctuates
D)none of these

Question 51

The nature of an interaction can be determined by ___.

A)eta²
B)interaction comparisons
C)simple main effects
D)both b and c

Question 52

The F test is particularly robust to violations of the normality and homogeneity of variance assumptions when sample sizes are _____ and relatively _____.

A)unequal;large
B)equal;large
C)equal;small
D)unequal;small

Question 53

If a statistically significant main effect has three or more levels,then the nature of the relationship is determined using a(n):

A)Tukey HSD procedure
B)informal examination of sample means
C)F ratio
D)t ratio

Question 54

As the number of groups in the factorial design increases,_____ becomes increasingly problematic.

A)homogeneity of population variances
B)heterogeneity of population variances
C)non-normality
D)error variance

Question 55

If a factorial ANOVA is computed and a statistically significant main effect is determined for a factor that has two levels,the nature of the relationship should be determined by ____.

A)inspecting the sample means
B)calculating eta²
C)calculating a t score
D)applying the Tukey HSD test

Question 56

The problem of an inflated Type I error rate can be controlled for interaction comparisons by using a:

A)Tukey HSD
B)modified Bonferroni procedure
C)corrected F ratio
D)none of these

Question 57

Interaction comparisons focus on _____ within a factorial design.

A)simple main effects
B)a priori effects
C)main effects
D)2 X 2 subtables

Question 58

If the cells of a 2 x 2 factorial-design have unequal numbers of subjects in them,then it is common to analyze the data using

A)simple main effects
B)least-squares analysis
C)split-plot analysis
D)nonparametric analysis

Question 59

In a follow-up test,two population means are considered to be different if the difference between their sample means is ____ the critical difference determined by Tukey's procedure.

A)less than
B)greater than
C)greater than or equal to
D)equal to

Question 60

A problem with the strategy of examining all possible 2 X 2 subtables following a significant interaction is that it does not adequately control the _____ at _____.

A)experimentwise error rate;á
B)experimentwise error rate;â
C)Type II error rate;á
D)Type II error rate;â

Question 61

A 2 X 3 factorial design has three independent variables.

Question 62

Due to the role of sampling error,nonequivalent sample means do not necessarily indicate nonequivalent population means.

Question 63

The total sum of squares in two-way between-subjects analysis of variance can be represented as SS_TOTAL = SS_WITHIN + SS_ERROR.

Question 64

A significant main effect means that,collapsing across the levels of the other independent variable,the means for an independent variable are not all equal.

Question 65

An interaction effect refers to the comparison of cell means in terms of whether the relationship between one of the independent variables and the dependent variable differs as a function of the other independent variable.

Question 66

The manner in which we choose to state an interaction is arbitrary.

Question 67

When a main effect for a variable with 3 levels is statistically significant,the nature of the relationship can be determined by examining the group means.

Question 68

The data analysis for a two-way ANOVA is the same regardless of whether group sample sizes are equal or unequal.

Question 69

When dealing with sample data,we can determine the existence of main effects and interactions in populations by mere visual inspection of sample means or slopes of lines in a graph.

Question 70

When dealing with population means,the determination of whether an interaction is present is most readily made by examining the slopes of the lines in a given graph.

Question 71

Not only do factorial designs allow us to assess the interaction between the two independent variables,but they also "remove" the individual and joint effects of these variables from the:

A)between-group variability
B)F ratio
C)within-group variability
D)sum of squares total

Question 72

When data are presented graphically,the presence of an interaction is suggested by parallel lines.

Question 73

When the sample sizes are the same in all cells,the two independent variables are _____ to each other

A)unrelated
B)positively related
C)negatively related

Question 74

An advantage of the two-way ANOVA is that we can study the joint effects of two variables.

Question 75

Assuming there are unequal numbers of subjects in each group,the main effect means can be calculated by taking the sum of the two cells in a given column.

Question 76

Stated informally,the null hypothesis for an interaction effect is that the nature and/or magnitude of the mean differences on the independent variable as a function of the other independent variable differs depending on the level of the dependent variable.

Question 77

The sum of squares between in two-way analysis of variance is partitioned into three components: (1)variability due to the first independent variable, (2)variability due to the second independent variable,and (3)variability due to the interaction of the two independent variables.

Question 78

The principles for detecting main effects and interactions are not readily generalizable from 2 x 2 designs to designs with more than two levels for one or both factors.

Question 79

The two-way between-subjects ANOVA is appropriate for use with a dependent variable that is quantitative or qualitative.

Question 80

Each main effect in a two-way analysis of variance has a null hypothesis and an alternative hypothesis associated with it.