Question 1

It is appropriate to conduct a t-Test separately for each paired comparison in a post hoc test.

Accepted Answer

A t-Test for each paired comparison in a post hoc test increases the risk of Type I error (false positives) due to multiple comparisons. Adjusted methods like Bonferroni or Tukey's HSD are recommended to control for this risk.

Question 2

Post hoc tests can be employed regardless of whether the F-ratio is significant for the overall data across the multiple groups.

Accepted Answer

Post hoc tests are used to conduct multiple comparisons between group means after an ANOVA has indicated a significant F-ratio, suggesting differences among the group means. If the F-ratio is not significant, it implies there is no evidence of difference among the group means, and thus, post hoc tests are generally not necessary.

Question 3

Suppose a study comparing three group means has 50 cases per group.Which of the following statements is correct about its degrees of freedom (df).

Accepted Answer

The overall within-groups degrees of freedom is calculated as the total number of cases minus the number of groups: (50 cases/group * 3 groups) - 3 groups = 147.

Question 4

MANOVA should be used when more than one dependent variable is involved in an analysis of variance

Accepted Answer

MANOVA is a multivariate analysis of variance that can handle multiple dependent variables at the same time. It is used when there are two or more continuous dependent variables that are related to one or more independent variables. MANOVA can provide information on the effect of the independent variable(s) on the dependent variables as well as the interaction between them.

Question 5

Suppose a study finds a MSBG of 8 and a MSWG o4.The F-Ratio would be:

Accepted Answer

The F-Ratio is calculated by dividing the mean square between groups (MSBG) by the mean square within groups (MSWG). So, F = MSBG / MSWG = 8 / 4 = 2.0.

Question 6

A two-factor ANOVA is conducted to evaluate the effectiveness of exposure therapy in treating civilians and combat veterans who have PTSD.Both groups of clients are randomly assigned to receive either exposure therapy or routine care.A significant interaction effect is found in the two-factor ANOVA.Which of the following interpretations is most appropriate in light of these results?

Accepted Answer

The significant interaction effect suggests that the comparative effectiveness of the two treatment conditions (exposure therapy vs. routine care) depends on whether the clients are civilians or combat veterans. This means that we cannot simply conclude that exposure therapy is more effective than routine care or vice versa without taking into account the client group being treated. Additionally, we cannot conclude that both treatments are equally effective because the interaction effect suggests that their effectiveness varies depending on the client group. Therefore, choice C is the most appropriate interpretation.

Question 7

A post hoc test is conducted to make multiple comparisons between the mean scores of three groups of clients in a child guidance center.Group A receives play therapy, only.Group B receives family therapy, only.Group C receives both play and family therapy.The significance level is .05.The p value for the difference between Groups A and B is .66.The p value for the difference between Groups A and C is .01.The p value for the difference between Groups B and C is .01.Which of the following interpretations is most appropriate in light of these results?

Accepted Answer

Since the p value for the difference between Groups A and C is significant at .01, we can conclude that play therapy alone is not as effective as the combination of play and family therapy. Similarly, the p value for the difference between Groups B and C is also significant at .01, indicating that family therapy alone is not as effective as the combination of play and family therapy. Therefore, the combination of play and family therapy appears to be more effective than either therapy alone. The non-significant p value for the difference between Groups A and B suggests that there is no significant difference in effectiveness between play therapy and family therapy alone. Thus, option D is the most appropriate interpretation of these results.

Question 8

The F-ratio:

Accepted Answer

All of the options are true statements about the F-ratio. The F-ratio reflects the variation among the means of several groups in relation to the variation within the groups, contains a numerator that consists of the variation between the means of each group divided by the between groups degrees of freedom, and contains a denominator that consists of the variation in the dependent variable among the individual cases within each group divided by the within groups degrees of freedom.

Question 9

An analysis of covariance (ANCOVA) is conducted for a study using the pretest and posttest scores of two groups.The F-ratio is statistically significant.What does this mean?

Accepted Answer

The significant F-ratio means that there is a significant difference between the two groups on the posttest scores when the effects of the pretest scores are controlled. It does not necessarily indicate significant differences on the pretest scores or both the pretest and posttest scores.

Question 10

ANOVA results without post hoc tests tell us only that there is a statistically significant difference somewhere among the multiple groups being compared -- not which particular comparisons of group means are statistically significant.

Accepted Answer

ANOVA results without post hoc tests can only determine if there is a significant difference somewhere among the groups being compared, but cannot identify which specific comparisons of group means are significant.

Question 11

In a study comparing 4 group means, the number of the between groups degrees of freedom is:

Accepted Answer

The between groups degrees of freedom is equal to the number of groups minus one, so in this case it is 4-1=3. A) is incorrect because the total sample size does not give information about between group differences. B) is incorrect because there are more than one group being compared. D) is incorrect because the number of between groups degrees of freedom is not the same as the number of groups being compared.

Question 12

In a study comparing 4 group means, the F-ratio is statistically significant.This means that:

Accepted Answer

A statistically significant F-ratio means that there is a significant difference between at least two of the group means. It does not necessarily mean that there is a significant difference between all four group means. Option C is incorrect because a significant F-ratio usually indicates that the variation between groups is greater than the variation within groups, not the other way around. Option A is incorrect because it goes beyond what the F-ratio can tell us.

Question 13

A two-factor ANOVA identifies the main effect of each independent variable on the dependent variable as well as any interaction effect between the two of them on the dependent variable.

Accepted Answer

A two-factor ANOVA examines the main effects of each independent variable on the dependent variable and the interaction effect of both independent variables on the dependent variable. Therefore, the statement is true.

Question 14

The F -ratio will increase when the within group variation increases.

Accepted Answer

The F-ratio decreases when the within-group variation increases because the F-ratio is calculated as the ratio of the between-group variance to the within-group variance.

Question 15

It is appropriate to use ANOVA when:

Accepted Answer

ANOVA is appropriate when we want to compare the means of three or more groups. It is not suitable for nominal level dependent variable or when the dependent variable has three or more categories. The independent variable may or may not be at the ratio level of measurement.

Question 16

The degrees of freedom for the numerator in the F -ratio is one less than the number of groups being compared.

Accepted Answer

This statement is true. The degrees of freedom for the numerator in the F-ratio is equal to the number of groups being compared minus 1.

Question 17

The ANCOVA procedure examines whether there are significant differences among groups on posttest scores when the effects of the pretest scores or other interval or ratio level variables are controlled.

Accepted Answer

ANCOVA stands for analysis of covariance and it is used to determine whether there are differences in the means of three or more groups while controlling for one or more continuous variables that are not dependent on the grouping variable. In other words, it adjusts for the effects of covariates (such as pretest scores) to better isolate the effect of the independent variable (such as the intervention).

Question 18

ANOVA can be used only when comparing two means.

Accepted Answer

ANOVA can be used to compare means between more than two groups. It is a statistical test that compares the variance of the means between groups to the variance within groups. The result of the ANOVA test can help determine if there is a significant difference between the means of the groups being compared.

Question 19

When evaluating the effectiveness of an intervention, it would be appropriate to conduct a multiple analysis of variance (MANOVA) when:

Accepted Answer

A MANOVA is appropriate when there is more than one dependent variable, when we want to avoid inflating the probability of a Type 1 error, and when the dependent variables are correlated with one another in such a way that an intervention will not have significant effects on any one of them alone, but will have a significant effect on a linear combination of them. Therefore, all of these are valid reasons for conducting a MANOVA.

Quiz 15: Analysis of Variance