Question 1

In a two-factor ANOVA for an independent-measures study,all of the F-ratios use the same denominator.

Accepted Answer

In a two-factor ANOVA for an independent-measures study, all of the F-ratios use the same denominator, which is the variability of the residuals or error term. This is because the denominator represents the amount of variation in the dependent variable that cannot be explained by the independent variables, and this is the same regardless of which factor is being tested.

Question 2

A two-factor analysis of variance with two levels of factor A and three levels of factor B involves six separate hypothesis tests.

Accepted Answer

A two-factor analysis of variance (ANOVA) with two levels of factor A and three levels of factor B involves testing for three main effects and interactions: the main effect of factor A, the main effect of factor B, and the interaction effect between factors A and B, not six separate hypothesis tests.

Question 3

A two-factor study compares 2 levels of factor A and 2 levels of factor B with a sample of n = 20 participants in each treatment condition.If the results are evaluated with a two-factor ANOVA,all the F-ratios will have df = 1,76.

Accepted Answer

The degrees of freedom for the F-ratios in a two-factor ANOVA are (df between groups, df within groups). In this case, there are 2 levels of each factor, so there are 1 degree of freedom between groups for each factor and 1 degree of freedom for the interaction. The within-groups degrees of freedom are calculated as (n - 1) * (number of groups), which is (20 - 1) * (2 * 2) = 76. Therefore, the degrees of freedom for all the F-ratios will be (1, 76).

Question 4

Individual treatment conditions are also referred to as cells.

Accepted Answer

This is true. In some research designs, individual participants are randomly assigned to different treatment conditions, which are referred to as cells in the research design matrix.

Question 5

If a researcher expects that a new teaching technique will be more effective for children who are more than 10 years old than it is for younger children,then the researcher is predicting an interaction between the teaching technique and age.

Accepted Answer

An interaction effect means that the effect of one variable (in this case, the teaching technique) on an outcome (learning) depends on the level of another variable (in this case, age). If the researcher expects that the teaching technique would be more effective for older children, then this suggests an interaction effect.

Question 6

A two-factor experimental design means that the researcher must measure two separate scores for each subject.

Accepted Answer

A two-factor experimental design refers to an experiment that investigates the effects of two independent variables on a dependent variable, not necessarily measuring two separate scores for each subject.

Question 7

A two-factor,independent-measures research study with two levels of factor A and three levels of factor B with n = 10 participants in each treatment condition would require a total of 60 participants.

Accepted Answer

A two-factor independent-measures research study with two levels of factor A and three levels of factor B and n = 10 participants in each treatment condition would require a total of 60 participants. This is because each combination of Factor A and Factor B requires its own treatment group with 10 participants, and there are a total of 6 combinations (2 x 3 = 6), thus requiring 60 participants in total.

Question 8

If the F-ratios for factor A and factor B both have df = 1,36,then the F-ratio for the interaction will also have df = 1,36.

Accepted Answer

This is true. The degrees of freedom for the interaction term in a two-factor ANOVA are calculated as the product of the degrees of freedom for each factor. Therefore, if both factor A and factor B have df = 1,36, then the interaction term will also have df = 1 * 36 = 36.

Question 9

For an independent-measures two-factor experiment,the bigger the differences between the sample means,the more likely it is that at least one of the F-ratios will be significant.

Accepted Answer

In an independent-measures two-factor experiment, the F-ratios are used to test for the significance of the main effects and interaction effects of the two factors. If there are larger differences between the sample means, then the variability due to the effect of the factors is also larger, which increases the F-ratio and makes it more likely to be significant. Therefore, the statement is true.

Question 10

For a two-factor analysis of variance,the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.

Accepted Answer

Each F-ratio in a two-factor ANOVA tests for the significance of one particular factor, while holding the other factor constant. Therefore, the significance of any specific F-ratio is independent of the significance of the other F-ratios, as they test for different sources of variation.

Question 11

A two-factor study compares three different treatment conditions (factor 1)for males and females (factor 2).In this study,the main effect for gender is determined by the overall mean score for the males (averaged over the three treatments)and the corresponding overall mean score for the females.

Accepted Answer

The statement accurately describes how to determine the main effect for gender in a two-factor study. By comparing the overall mean score for males to the overall mean score for females, we can determine whether there is a significant difference between the two genders regardless of which treatment condition they were in.

Question 12

Obtaining a significant interaction means that both factors A and B have significant main effects.

Accepted Answer

Obtaining a significant interaction means that the effect of one factor depends on the level of the other factor, regardless of whether both factors have significant main effects. In other words, it is possible to have a significant interaction without significant main effects, and vice versa.

Question 13

A two-factor,independent-measures research study with two levels of factor A and two levels of factor B would require two separate groups of participants.

Accepted Answer

A two-factor, independent-measures study with two levels for each factor would require four separate groups of participants, one for each combination of the levels of factors A and B.

Question 14

If the A x B interaction is significant,then at least one of the two main effects also must be significant.

Accepted Answer

A significant A x B interaction means that the effect of one factor depends on the level of the other factor, but it does not necessarily mean that either of the main effects (A or B) must be significant on their own.

Question 15

A two-factor study compares two levels of factor A and three levels of factor B with a sample of n = 5 participants in each treatment condition.This study will use a total of 25 participants.

Accepted Answer

A two-factor study with two levels of factor A and three levels of factor B with a sample of n = 5 participants in each treatment condition will use a total of (2 x 3 x 5) = 30 participants, not 25.

Question 16

A two-factor analysis of variance produces an F-ratio for factor A that has df = 3,36.This analysis is comparing three different levels of factor A.

Accepted Answer

The degrees of freedom for factor A (df = 3) suggest that there are four levels of factor A, not three, because the degrees of freedom for a factor in ANOVA are calculated as the number of levels minus one (n - 1).

Question 17

A researcher predicts that a special training course will be highly effective for females but will have little or no effect for males.This researcher is predicting an interaction between training and gender.

Accepted Answer

An interaction between training and gender implies that the effect of the training will depend on the gender of the participants. In this case, the researcher predicts that the training will be highly effective for females but have no effect for males, which indicates an interaction effect.

Question 18

A two-factor study compares two different treatment conditions (factor 1)for males and females (factor 2).In this study,the males have an average score of 20 in the first treatment and an average of 25 in the second.The females average 35 in the first treatment and 45 in the second.For this study,there is no interaction.

Accepted Answer

An interaction effect in a two-factor study occurs when the effect of one factor on the outcome variable differs depending on the level of the other factor. Here, the difference in scores between the two treatments is not consistent across genders (males show a difference of 5 points between treatments, while females show a difference of 10 points), indicating an interaction between treatment condition and gender.

Question 19

A new laundry detergent is supposed to be equally superior to the leading brand in both hot and cold water.If the new detergent works as predicted,then there should be an interaction between the brand of detergent and the temperature of the water.

Accepted Answer

If the new detergent is equally superior in both hot and cold water, there would not be an interaction effect between detergent brand and water temperature; the effect of the detergent would be consistent across temperatures.

Question 20

If the F-ratio for factor A has df = 1,40 and the F-ratio for factor B has df = 3,40,then the F-ratio for the interaction must have df = 2,40.​

Accepted Answer

The F-ratio for the interaction does not necessarily have to have df = 2,40. The degrees of freedom for the interaction depend on the design of the study and cannot be determined simply by knowing the degrees of freedom for the main effects (factor A and B).

Quiz 14: Two-Factor Analysis of Variance Independent Measures