Question 1

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 recommend the use of interaction comparisons over simple main effects analysis in determining the nature of a statistically significant interaction effect. This is because simple main effects analysis only examines one main effect at a time, while interaction comparisons allow for the examination of the effects of one variable at different levels of the other variable in question. This can provide a more comprehensive understanding of the interaction effect.

Question 2

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

Eta-squared (η²) can be calculated to indicate the strength of the relationship between the dependent variable and an independent variable after a 2 x 2 factorial ANOVA. Eta-squared represents the proportion of variance in the dependent variable that can be attributed to the independent variable(s).

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

The Tukey HSD (Honestly Significant Difference) test is specifically designed to conduct post-hoc comparisons when a main effect in an ANOVA with three or more levels is found to be significant. It helps in determining which specific group means are significantly different from each other.

Question 4

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

When a statistically significant main effect has only two levels, the nature of the relationship is determined in the same fashion as for the independent groups t test because it involves comparing the means of two groups to see if there is a significant difference between them.

Question 5

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 6

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 factorial ANOVA is used when there are two or more independent variables, while a one-way ANOVA only has one independent variable. Therefore, the correct answer is C. Option A is incorrect because ANOVA doesn't require multiple dependent variables. Option B is also false because the F-score cannot be negative in ANOVA.

Question 7

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

The F test for one-way analysis of variance is robust to violations of normality and homogeneity of variance assumptions under certain conditions. Specifically, when sample sizes are equal or nearly equal, and when sample sizes are large, the F test is robust to violations of these assumptions. Therefore, choice C is the best answer as it indicates both options are correct.

Question 8

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 strengths of relationships for the sources of between-group variability, as it indicates the proportion of variance in the dependent variable that is accounted for by the independent variable. None of the other options listed are appropriate for assessing between-group variability.

Question 9

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 analysis of variance assume that the scores in each population are normally distributed.

Question 10

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 is less robust to violations of normality and variance homogeneity when sample sizes across groups are highly different. This is because a smaller sample size can have a larger influence on the F test statistic, making it more susceptible to outliers and non-normality. Therefore, the robustness of the F test to these violations diminishes, sometimes considerably so.

Question 11

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 by both interaction comparisons and simple main effects. Interaction comparisons involve comparing the effects of one independent variable at different levels of the other independent variable. Simple main effects involve analyzing the effect of one independent variable at a specific level of the other independent variable. Both of these methods can help to determine the nature of the interaction.

Question 12

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 robust to violations of normality and homogeneity of variance assumptions when sample sizes are equal and relatively large. When sample sizes are unequal and/or small, violations of these assumptions can greatly impact the accuracy of the test. Therefore, option B is the best choice since it satisfies both conditions.

Question 13

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

Tukey HSD procedure is the best choice when dealing with a statistically significant main effect with three or more levels, as it allows for pairwise comparisons between all levels to determine the nature of the relationship. Informal examination of sample means may provide some insight, but it is not a reliable or formal statistical method. F ratio and t ratio are used for hypothesis testing and comparing two means, respectively, and are not appropriate for determining the nature of a relationship among three or more levels.

Question 14

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 in a factorial design, the probability of unequal variances between these groups increases. This heterogeneity of population variances can lead to problems with statistical analysis and interpretation of results.

Question 15

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 will allow the researcher to determine the direction and magnitude of the main effect for the factor with two levels.

Question 16

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 by adjusting the significance level for each comparison. This procedure is a more conservative version of the original Bonferroni correction, which works by dividing the alpha level by the number of comparisons being made. The modified Bonferroni procedure adjusts the alpha level based on the total number of comparisons being made, as well as the number of interactions being tested. This procedure is effective at controlling for Type I errors while still maintaining reasonable power in the analysis. The other options, Tukey HSD and corrected F ratio, are not appropriate for controlling for inflated Type I error rates in interaction comparisons.

Question 17

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 18

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 19

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

Tukey's procedure is used to determine if the difference between the means of two populations is statistically significant. If the difference between their sample means is greater than the critical difference determined by Tukey's procedure, the populations are considered to be different.

Question 20

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

The strategy of examining all possible 2 X 2 subtables following a significant interaction does not adequately control the experimentwise error rate at alpha (á), increasing the likelihood of making Type I errors across multiple comparisons.

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

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

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 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 ____.

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.

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

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

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

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

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

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 ___.

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

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

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

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 ____.

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

Interaction comparisons focus on _____ within a factorial design.

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

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 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 _.