Question 1

Which of the following is not true if Fobs for the interaction in a two-factor between-subjects analysis of variance is statistically significant?

Accepted Answer

If Fobs for the interaction in a two-factor between-subjects analysis of variance is statistically significant, it means that there is a significant difference between the simple effects of factors A and B at different levels. However, there is no evidence to suggest that the simple effects of factors A and B are different from their main effects. Therefore, option D is not true.

Question 2

The null hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is H0:.

Accepted Answer

The answer of The null hypothesis for the interaction of...

Question 3

If factor A produces a main effect in a two-factor between-subjects analysis of variance, then will increase in value relative to MSError.

Accepted Answer

If factor A produces a main effect, it means that there is a significant difference in the means of the groups created by varying levels of factor A. This difference contributes to the variance between the groups, which is captured in the numerator of the F-ratio for factor A. Therefore, the increase in variance between the groups will be reflected in an increase in MSA relative to MSError. The other choices (B and C) refer to the other factor and the interaction, respectively, and are not relevant to the main effect of factor A.

Question 4

If the independent variables interact in a two-factor between-subjects analysis of variance, then will increase in value relative to MSError.

Accepted Answer

When there is interaction between independent variables in a two-factor between-subjects ANOVA, the increase in value relative to MSError is reflected in the interaction term, which is the product of MS for factor A and factor B (MSA × B). Therefore, the correct answer is Choice C. Neither MS for factor A (MSA) nor MS for factor B (MSB) on their own reflect the increase in value relative to MSError caused by the interaction.

Question 5

If factor B produces a main effect in a two-factor between-subjects analysis of variance, then will increase in value relative to MSError.

Accepted Answer

If factor B produces a main effect, then the MSB (mean square between groups for factor B) will show a significant difference between the levels of factor B. The MSB value will be larger than MSError, indicating that the variability between the groups of factor B is greater than the variability within the groups. Therefore, increase in value relative to MSError corresponds to MSB only.

Question 6

H0 is rejected if Fobs in a two-factor between-subjects analysis of variance is its corresponding critical value.

Accepted Answer

In a two-factor between-subjects analysis of variance, the null hypothesis (H0) is rejected if the observed F-value (Fobs) is equal to or larger than its corresponding critical value. This indicates that there is a statistically significant difference between the groups being compared.

Question 7

The following values of Fobs occurred in a two-factor between-subjects analysis of variance: F(1, 28) for factor A = 3.47, F(1, 28) for factor B = 4.29, and F(1, 28) for the interaction of factors A and B = 4.10. Fcrit(1, 28) = 4.20 for alpha = .05. In this experiment you would H0 for factor A, H0 for factor B, and H0 for the interaction of factors A and B.

Accepted Answer

For factor A, Fobs (3.47) is less than Fcrit (4.20), so we fail to reject H0. 
For factor B, Fobs (4.29) is greater than Fcrit (4.20), so we reject H0. 
For the interaction of A and B, Fobs (4.10) is less than Fcrit (4.20), so we fail to reject H0. Therefore, the best choice is C because we fail to reject H0 for factor A and the interaction of A and B, but reject H0 for factor B.

Question 8

The F statistic for interaction in a two-factor between-subjects analysis of variance is formed by dividing MSError into.

Accepted Answer

The F statistic for interaction in a two-factor between-subjects ANOVA is calculated by dividing the mean square for the interaction (MSA × B) by the mean square error (MSError). Therefore, the correct answer is B. None of the other options involve the mean square for the interaction.

Question 9

The MSB term in a two-factor between-subjects analysis of variance responds to the systematic variation due to factor B and.

Accepted Answer

The MSB (Mean Square Between) term in a two-factor ANOVA accounts for the systematic variation due to factor B and the sampling error.

Question 10

If MSA = 4.00, MSB = 10.00, MSA × B = 6.00, and MSError = 2.00 in a two-factor between-subjects analysis of variance, then Fobs for factor A = , Fobs for factor B = ,
And Fobs for the interaction of factors A and B =.

Accepted Answer

The observed F value (Fobs) for a factor or interaction in an ANOVA is calculated by dividing the mean square (MS) of that factor or interaction by the mean square error (MSError). For factor A, Fobs = MSA / MSError = 4.00 / 2.00 = 2.00. For factor B, Fobs = MSB / MSError = 10.00 / 2.00 = 5.00. For the interaction of factors A and B, Fobs = MSA×B / MSError = 6.00 / 2.00 = 3.00.

Question 11

A effect of an independent variable in a factorial design is the effect of that independent variable at of the other independent variable.

Accepted Answer

The answer of A effect of an independent variable in...

Question 12

H0 is not rejected if Fobs in a two-factor between-subjects analysis of variance is its corresponding critical value.

Accepted Answer

In a two-factor between-subjects analysis of variance, the null hypothesis (H0) is not rejected if the observed F-value (Fobs) is less than its corresponding critical value. This is because the critical value is the threshold above which we would consider the observed differences to be statistically significant. If Fobs is less than this threshold, it indicates that the observed differences could be due to chance, and thus, we do not have enough evidence to reject the null hypothesis.

Question 13

The alternative hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is H1:.

Accepted Answer

The alternative hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is that not all means of the combination of A and B are equal to their respective main effects plus the grand mean. This can be expressed as $\left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) \neq 0$ for at least one combination of A and B levels. Thus, the correct choice is C. Options A and B are incorrect because they do not fully capture the specifics of the alternative hypothesis for interaction in a between-subjects ANOVA. Option D expresses a hypothesis of parallelism rather than interaction.

Question 14

If an interaction of the independent variables occurs in a two-factor between-subjects analysis of variance, then the simple effects of a factor will be to each other and to the main effect for that factor.

Accepted Answer

When an interaction occurs, the simple effects of a factor will be unequal to each other and to the main effect for that factor. This is because the effect of one factor on the dependent variable depends on the level of the other factor. Therefore, the simple effects will not be equal. Additionally, the main effect will be different from the simple effects because it represents the overall effect of that factor regardless of the level of the other factor.

Question 15

A two-factor between-subjects analysis of variance is based upon the assumption that the in the populations sampled.

Accepted Answer

A two-factor between-subjects ANOVA assumes that the variances of the scores in each group (defined by the two factors) are equal. This assumption is necessary to ensure that the F ratio, which is used to test for significant main effects and interactions, is valid. If the variances are not equal, then the F ratio may be biased and the results may not be reliable.

Question 16

A simple effect refers to the in a factorial design.

Accepted Answer

A simple effect refers to the effect of one independent variable on the dependent variable at only one level of another independent variable. It allows for a more detailed analysis of the interaction effect in a factorial design.

Question 17

The MSA term in a two-factor between-subjects analysis of variance responds to the systematic variation due to factor A and.

Accepted Answer

MSA (Mean Square for Factor A) in ANOVA measures the systematic variation due to factor A and the random variation due to sampling error.

Question 18

The MSA × B term in a two-factor between-subjects analysis of variance responds to the systematic variation due to the interaction of factors A and B and.

Accepted Answer

The MSA × B term in a two-factor ANOVA represents the interaction effect between factors A and B, and it also includes the sampling error, which is the random variation not explained by the main effects or the interaction.

Question 19

The following values of Fobs occurred in a two-factor between-subjects analysis of variance: F(1, 40) for factor A = 4.76, F(1, 40) for factor B = 3.81, and F(1, 40) for the interaction of factors A and B = 5.03. Fcrit(1, 40) = 4.08 for alpha = .05. In this experiment you would H0 for factor A, H0 for factor B, and H0 for the interaction of factors A and B.

Accepted Answer

For factor A, Fobs (4.76) > Fcrit (4.08), so we reject the null hypothesis for factor A. 
For factor B, Fobs (3.81) < Fcrit (4.08), so we fail to reject the null hypothesis for factor B. 
For the interaction of factors A and B, Fobs (5.03) > Fcrit (4.08), so we reject the null hypothesis for the interaction. Therefore, the best answer is D, where we reject the null hypothesis for factor A and the interaction of factors A and B, but fail to reject the null hypothesis for factor B.

Question 20

A two-factor between-subjects analysis of variance is based upon the assumption that the in the populations sampled are.

Accepted Answer

A two-factor between-subjects analysis of variance assumes that the scores in the populations sampled are normally distributed. This assumption is necessary for valid statistical inference.

Quiz 11: Two-Factor Between-Subjects Analysis of Variance