Question 1

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 different participants are randomly assigned to each combination of levels for two factors, making it suitable for analyzing the data in this scenario.

Question 2

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 3

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

Accepted Answer

It is appropriate to compute effect size for both interactions and main effects. Effect size provides a measure of the strength of the relationship between variables or the magnitude of differences between groups, which is important for interpreting the practical significance of findings.

Question 4

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 summary lacks clarity on what the degrees of freedom (16) refer to, typically denoted as F(df1, df2) in APA format, and the unusual code "R² = .12" is not a standard way to report effect size or any other statistical outcome in APA format.

Question 5

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

Accepted Answer

Mean square error is the denominator for all tests using a two-way between-subjects ANOVA because it represents the variability within the groups, which is used to estimate the error variance.

Question 6

$\omega$² corrects for the number of groups and the size of error in an analysis of variance test; $\eta$² does not.

Accepted Answer

The symbols in the code refer to different components of an ANOVA test. "F1F1F1S1" represents between-group variation, "F1F1F10S1" represents within-group variation, "U1P12" represents the number of groups and sample size, and "S1S1P0" represents the size of error. The symbol "" in the second code does not represent any component of an ANOVA test, so it cannot correct for the number of groups and size of error.

Question 7

The denominator of the formula for $\eta$² is SS_T for both main effects and the interaction.

Accepted Answer

The denominator for eta squared ($\eta^2$) is the total sum of squares (SS_T) for both main effects and interaction in ANOVA, representing the total variability in the data.

Question 8

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

Accepted Answer

A two-way between-subjects ANOVA is used to analyze differences in the combination of levels for exactly two factors, not more than two.

Question 9

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 10

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

This statement is true. Simple main effect tests are used to further understand the nature of an interaction by examining the differences in mean scores of one factor at each level of a second factor.

Question 11

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

Accepted Answer

A 2x4 between-subjects ANOVA has (2-1)*(4-1) = 3 degrees of freedom for the interaction, not 8.

Question 12

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

Accepted Answer

In a 2 F1F1F1S1F1F1F10 design, there are 2 between-subjects factors (F1F1F1S1 and F1F1F10) and 3 between-subjects levels (hence the 3 in the design notation). An interaction between F1F1F1S1 and F1F1F10 would have 2 degrees of freedom, as it would involve the combination of the levels of both factors. Therefore, the statement is true.

Question 13

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 statement is true. When reporting the results of a two-way ANOVA, it is important to include information on the test statistic, degrees of freedom, and p-value for each significant main effect and interaction. This information allows the reader to evaluate the magnitude and significance of the effects being tested.

Question 14

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

Accepted Answer

Simple main effect tests are specifically used to analyze a significant interaction by examining the effects of one independent variable at each level of another independent variable, not for analyzing a significant main effect.

Question 15

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

Accepted Answer

A significant interaction implies that the effect of one variable on the dependent variable is dependent on the level of the other variable. This can lead to differences in the cell means, and a significant interaction indicates that at least one of these differences is statistically significant. Therefore, option A is correct.

Question 16

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 main effects and interaction are not significant in a two-way between-subjects ANOVA, it indicates that there aren't any significant differences between the groups. Hence, post hoc tests and simple main effect tests are unnecessary in such cases.

Question 17

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.77,p < .05 (R² = .18)."

Accepted Answer

The summary correctly includes the key components of a significant main effect in APA format. It includes the variable name, degree of freedom, F-value, p-value, and a measure of effect size (represented by the R² statistic).

Question 18

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 19

$\eta$² is a more powerful estimate of effect size than R².

Accepted Answer

The notation provided does not correspond to any standard notation for statistical measures or effect size estimation, making it impossible to determine the power of the estimate without a clear definition of the terms.

Question 20

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

If a study has 12 groups, then it can be designed as a 2x6, 3x4, 4x3, or 6x2 factorial design. Each of these designs can be analyzed using a two-way between-subjects ANOVA with 2 and 3 degrees of freedom for each factor. Therefore, it is possible for a study with 12 groups to have 2 and 3 degrees of freedom for a two-way between-subjects ANOVA.

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

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.

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.

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

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)."

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

$\omega$ ² corrects for the number of groups and the size of error in an analysis of variance test; $\eta$ ² does not.

The denominator of the formula for $\eta$ ² is SS_T for both main effects and the interaction.

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

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

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.

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

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

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.

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

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

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.

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.77,p < .05 (R² = .18)."

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

$\eta$ ² is a more powerful estimate of effect size than R².

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.

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

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.

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.

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

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)."

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

ω\omegaω 2 corrects for the number of groups and the size of error in an analysis of variance test; η\etaη 2 does not.

The denominator of the formula for η\etaη 2 is SST for both main effects and the interaction.

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

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

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.

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

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

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.

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

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

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.

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.77,p < .05 (R2 = .18)."

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

η\etaη 2 is a more powerful estimate of effect size than R2.

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.

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)."

$\omega$ ² corrects for the number of groups and the size of error in an analysis of variance test; $\eta$ ² does not.

The denominator of the formula for $\eta$ ² is SS_T for both main effects and the interaction.

The following APA summary of a significant main effect is correctly stated: "The main effect of comprehension level was significant,F(2,30)= 3.77,p < .05 (R² = .18)."

$\eta$ ² is a more powerful estimate of effect size than R².