Question 1

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.

Accepted Answer

This is the standard practice for summarizing any type of two-way ANOVA.

Question 2

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.07,p < .05 (R²= .18).

Accepted Answer

The summary includes all necessary information, including the statistical analysis (F ratio and p-value) and the reference to the dependent variable (comprehension level).

Question 3

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

Accepted Answer

Simple main effect tests are used to analyze significant interactions, not significant main effects, to understand the nature of the interaction.

Question 4

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.

Accepted Answer

If both the main effects and interaction are not significant, it means that there are no significant differences between the groups on any of the variables. Therefore, there would be no need to conduct post hoc or simple main effect tests to determine where the differences lie.

Question 5

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

Accepted Answer

The significance of main effects in a two-way ANOVA does not guarantee the significance of the interaction effect. Main effects and interaction effects test different hypotheses and can be significant independently of each other.

Question 6

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

Accepted Answer

The answer of A two-way between-subjects ANOVA is appropriate for...

Question 7

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.

Accepted Answer

In a two-way between-subjects ANOVA, the degrees of freedom for each factor are determined by the number of levels of each factor minus one. If there are 12 groups formed by the combination of levels from two factors, and if the degrees of freedom for the factors are 3 and 4, this would imply the factors have 4 and 5 levels respectively (since degrees of freedom = number of levels - 1). However, 4 levels of one factor and 5 levels of another would result in 20 groups (4x5), not 12. Therefore, it is not possible for a study with 12 groups to have factors with 3 and 4 degrees of freedom in a two-way between-subjects ANOVA.

Question 8

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

Accepted Answer

This is true. In a 2 F1F1F1S1F1F1F10 3 design, each factor (A, B, and S) has two levels (F1 and F2), leading to a total of 2x2x2 = 8 cells. Therefore, there are 8-1 = 7 degrees of freedom for error, and 2 degrees of freedom for the AxB interaction.

Question 9

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).

Accepted Answer

The degrees of freedom for an F-test should include two numbers: the degrees of freedom for the numerator and the degrees of freedom for the denominator. The summary only provides one degree of freedom (16), which is incorrect.

Question 10

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

Accepted Answer

The answer of Mean square error is the denominator for...

Question 11

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

Accepted Answer

Simple main effect tests are used to analyze the differences within each level of another factor, specifically when there is an interaction effect present, not for analyzing the main effects directly. They help in understanding how the levels of one factor affect the outcome at each level of another factor, indicating the nature of the interaction.

Question 12

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

Accepted Answer

This statement is true. A significant interaction in a factorial ANOVA indicates that the effect of one independent variable on the dependent variable is not consistent across all levels of the other independent variable. Therefore, it is possible for at least one pair of cell means (i.e., the mean of the dependent variable for a particular combination of levels of the independent variables) to significantly differ from one another.

Question 13

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.

Accepted Answer

For a two-way between-subjects ANOVA with 12 groups, there are a total of 11 degrees of freedom for each factor (one less than the number of groups). It is possible to have 2 and 3 degrees of freedom for each factor if the group sizes are different across the 2 levels of each factor, resulting in unequal cell sizes.

Question 14

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

Accepted Answer

Effect size can and should be computed for both interactions and main effects. This is important in determining the practical significance of the results found in statistical analysis.

Question 15

Omega-squared corrects for the number of groups and the size of error in an analysis of variance test;eta-squared does not.

Accepted Answer

Omega-squared is a more accurate measure of effect size than eta-squared because it takes into account the size of the error term and is biased less by the number of groups being compared. Eta-squared, on the other hand, does not take into account the size of the error term and is more affected by the number of groups being compared.

Question 16

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.

Accepted Answer

A two-way between-subjects ANOVA is appropriate when participants are randomly assigned to different combinations of levels for two factors.

Question 17

The denominator of the formula for eta-squared is   for both main effects and the interaction.

Accepted Answer

The denominator of the formula for eta-squared is always the total sum of squares (SS_total), which is the same for both the main effects and the interaction. It is not represented by the code provided.

Question 18

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

Accepted Answer

This statement does not make logical sense in the context of a 2x4 between-subjects ANOVA. The number of degrees of freedom associated with an interaction depends on the number of cells in the design, not the specific nature of the variables involved.

Question 19

Eta-squared is a more powerful estimate of effect size than R².

Accepted Answer

Eta-squared and R² are both measures of effect size, but neither is inherently more powerful; they are used in different contexts. Eta-squared is used in ANOVA, while R² is used in regression analysis.

Question 20

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.

Accepted Answer

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

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