Question 1

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

Accepted Answer

The F tests for two-way between-subjects ANOVA assume that the scores in each population are normally distributed. This assumption is necessary to ensure that the F test statistic accurately reflects the differences between the means of the populations being compared. Heterogeneous variances and skewed distributions can affect the accuracy of the F test, but they are not assumptions of the test itself.

Question 2

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

Accepted Answer

Inspecting the sample means would help determine the nature of the relationship. A statistically significant main effect means that there is a difference between the means of the two levels of the factor. By inspecting the sample means, one can see which level has the higher mean value, indicating the direction of the effect.

Question 3

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

Accepted Answer

When a statistically significant main effect is found in a factorial ANOVA for a factor with three or more levels, post-hoc tests like the Tukey HSD test are used to determine which specific group means are significantly different from each other.

Question 4

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

Accepted Answer

The answer of The F ratio formed by SS_A/SS_WITHIN is...

Question 5

Interaction comparisons focus on _____ within a factorial design.
A)simple main effects
B)a priori effects
C)main effects
D)2 X 2 subtables

Accepted Answer

The answer of Interaction comparisons focus on _____ within a...

Question 6

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

Accepted Answer

The F test is more robust to violations of normality and homogeneity of variance assumptions when the sample sizes are equal and relatively large. When the sample sizes are small, the F test may not be robust to violations of these assumptions. When the sample sizes are unequal, the F test may be affected by the assumption of equal variances.

Question 7

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

Accepted Answer

The F test assumes equal variance across groups and normality of the data. When the sample sizes are highly different across groups, the test becomes less robust to violations of these assumptions, particularly to non-normality and variance heterogeneity. Therefore, the robustness of the F test diminishes in this case.

Question 8

The nature of an interaction can be determined by ___. A)eta² B)interaction comparisons C)simple main effects D)both b and c

Accepted Answer

The nature of an interaction can be determined through interaction comparisons, which involve examining the differences between groups at each level of the other independent variable. Simple main effects can also be used to determine the nature of an interaction by analyzing the effects of one independent variable at a specific level of the other independent variable. Therefore, both option B and C are correct.

Question 9

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

Accepted Answer

Examining all possible 2x2 subtables can inflate the experimentwise error rate, which is the probability of making one or more Type I errors across multiple comparisons.

Question 10

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

Accepted Answer

F tests can still perform well even if there are small deviations from normality assumption or homogeneity of variance, as long as the sample sizes are equal and the violations are not too severe. Therefore, the F tests are robust to violations of both assumptions, and the correct answer is C.

Question 11

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

Accepted Answer

Statisticians generally recommend the use of interaction comparisons over simple main effects analysis to determine the nature of a statistically significant interaction effect. This is because interaction comparisons provide a more direct and informative test of the nature of the interaction, while simple main effects analysis can only provide an examination of the marginal effects at each level of the independent variable, and not the combination of the variables.

Question 12

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

Accepted Answer

In Tukey's procedure, two population means are considered different if the difference between their sample means is greater than the critical difference.

Question 13

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

Accepted Answer

The modified Bonferroni procedure can control for an inflated Type I error rate in interaction comparisons. This procedure involves adjusting the alpha level for multiple comparisons by dividing it by the number of comparisons being made, which reduces the likelihood of making a Type I error. Tukey HSD and corrected F ratio are not appropriate for controlling for Type I error rate in interaction comparisons.

Question 14

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

Accepted Answer

After a 2 x 2 factorial ANOVA, the strength of the relationship can be indicated by measuring the effect size through eta-squared (η²) which represents the proportion of variance in the dependent variable that can be attributed to the independent variable(s). Therefore, the best choice is C, which represents eta-squared. The other options are not relevant in this context.

Question 15

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

Accepted Answer

When we have a statistically significant main effect with three or more levels, we need to conduct post-hoc tests to determine the nature of the relationship. Tukey HSD (Honestly Significant Difference) test is a commonly used post-hoc test for multiple comparisons that can be used in this situation. It allows us to determine which group means differ significantly from each other. Therefore, option A is the best choice.

Question 16

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

Accepted Answer

The answer of If the cells of a 2 x...

Question 17

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

Accepted Answer

A main effect with only two levels can be analyzed similarly to an independent groups t-test, as it involves comparing the means of two groups.

Question 18

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

Accepted Answer

As the number of groups increases, it becomes more difficult to maintain homogeneity of population variances, which can lead to increased heterogeneity of variances. This violates the assumption of homoscedasticity, which can result in biased estimates of the standard errors and affect the statistical significance of the results.

Question 19

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.

Accepted Answer

A between-groups factorial ANOVA differs from a between-groups one-way ANOVA in that it uses two or more independent variables instead of just one. Option A is incorrect because a between-groups factorial ANOVA can use only one dependent variable. Option B is incorrect because a negative F score cannot be produced in any ANOVA.

Question 20

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

Accepted Answer

Eta-squared is the appropriate measure for assessing the strength of the relationships for the three sources of between-group variability, which include the overall effect size, the effect size for the treatment groups, and the effect size for the differences among the treatment groups. It is commonly used in ANOVA and can provide a standardized measure of effect size, making it easier to compare the strength of relationships across different studies. Options A, B, and C are not commonly used measures for assessing between-group variability in ANOVA.

Quiz 16: Two-Way Between-Subjects Analysis of Variance

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

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 ____.

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 ____.

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

Interaction comparisons focus on _____ within a factorial design.

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

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.

The nature of an interaction can be determined by ___.

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 _.

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

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

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.

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

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.

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

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

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.

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

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

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