Chapter Review: Chapter 13 Two-Factor Analysis of Variance

In a two-factor independent-measures ANOVA, when is FA guaranteed to be equal to FB? a. when MSA = MSB b. when SSA = SSB c. both a and b d. none of the above

a. when MSA = MSB

When might removing individual differences in ANOVA not be advantageous in a two-factor design? a. when the treatment effects are reasonably consistent for all of the participants b. when the treatment effects are not consistent across participants c. when the sample sizes are less than 10 d. when the population variances are not equivalent across treatment conditions

b. when the treatment effects are not consistent across participants

For the following table from an experiment testing three treatments, calculate SSbetween subjects. (look up) a. 3.11 b. 6.22 c. 12.44 d. 18.66

b. 6.22

The results from a two-factor ANOVA are presented in the following summary table. Compute η2 to measure the size of the treatment effect. (look up) a. 0.388 b. 0.395 c. 0.605 d. 0.667

c. 0.605

A two-factor ANOVA was calculated with df = 1, 14. If the same data were analyzed with a repeated-measures t test, how many degrees of freedom would be used with the t statistic? a. 2 b. 3 c. 13 d. 14

d. 14

Which of the following is the null hypothesis for a two-factor ANOVA? a. H0: μA1 = μA2 b. H0: μA1 = μA2 or μA2 = μA3 c. H0: μA1 > μA2 d. H0: μA1 - μA2 = μA3

a. H0: μA1 = μA2

Which of the following is a correct calculation for MSwithin treatments in a two-factor ANOVA? a. MSwithin treatments = SSwithin treatments/dfwithin treatments b. MSwithin treatments = SSwithin treatments × dfwithin treatments c. MSwithin treatments = SSwithin treatments + dfwithin treatments d. MSwithin treatments = SSwithin treatments - dfwithin treatments

a. MSwithin treatments = SSwithin treatments/dfwithin treatments

What does a large value for the F-ratio indicate? a. Sample mean differences are greater than expected. b. Sample mean differences are lower than expected. c. Sample mean differences are within the expected range. d. None of the above

a. Sample mean differences are greater than expected.

What happens in the first stage of a two-factor ANOVA? a. The total variability is divided into "between-treatments" and "within-treatments." b. The variability within treatments is divided into "between-subjects" and "error." c. The variability within treatments is divided into the two main effects and the interaction. d. The variability between treatments is divided into the two main effects and the interaction.

a. The total variability is divided into "between-treatments" and "within-treatments."

A researcher runs a two-factor ANOVA on two treatment conditions. The null hypothesis is rejected with F = 9. If the researcher were to run a t test on the same data, what would she find? a. t = 3, and the null hypothesis would be rejected. b. t = 3, and the null hypothesis would fail to be rejected. c. t = 9, and the null hypothesis would be rejected. d. t = 9, but there is not enough information to determine whether the null hypothesis would be rejected.

a. t = 3, and the null hypothesis would be rejected.

Which of the following would be required in a two-factor, independent measures ANOVA test? I. Multiple mean differences II. An experimental study in which the researcher manipulates two independent variables to create two or more treatment conditions, with different group of individuals tested in all of the conditions III. A nonexperimental study in which the same group of individuals is simply observed at two or more different times a. I only b. I and II only c. III only d. I, II, and III

b. I and II only

For an independent-measures ANOVA, what happens to the individual differences in the numerator and denominator of the F-ratio? a. They are measured and subtracted out during the analysis in both the numerator and the denominator. b. They contribute to the variance in the numerator and in the denominator of the F-ratio. c. The individual differences in the numerator do not exist because the same individuals participate in all of the treatments. d. They do not exist in the denominator and are measured and subtracted out from the numerator.

b. They contribute to the variance in the numerator and in the denominator of the F-ratio.

Four individuals are given an experimental treatment for cancer. White blood count will be used as one measure of the effectiveness of the treatment. The white blood count of the four individuals is measured before the treatment, 1 week after the treatment, 6 months after the treatment, and 1 year after the treatment. Which of the following are stages in the analysis? a. The total variability is separated into two components: between-treatments variability and within-treatments variability. b. The analysis partitions the between-treatments variability into three components. c. Both a and b d. Neither a nor b

c. Both a and b

For a two-factor ANOVA, if SSwithin treatments = 86, SSbetween treatments = 80, SSbetween subjects = 62, dfwithin treatments = 12, dfbetween treatments = 1, and dfbetween subjects = 4, find the F-ratio. a. F = 2.389 b. F = 11.16 c. F = 26.667 d. F = 72.833

c. F = 26.667

The following matrix represents the outcome of a two-factor experiment. (look up) Which of the following occurs?I. A main effect for factor AII. A main effect for factor BIII. An interaction between factor A and factor B a. I only b. II only c. I and II only d. I, II, and III

c. I and II only

In an experiment, an independent variable is a manipulated variable. Which of the following describes a quasi-independent variable?I. It is not a manipulated variable.II. It is a manipulated variable.III. It defines the groups of scores in a nonexperimental study. a. I only b. II only c. I and III only d. II and III only

c. I and III only

In a two-factor analysis of variance, there are six subjects who each underwent three treatments. What are dfbetween subjects? a. dfbetween subjects = 15 b. dfbetween subjects = 20 c. dfbetween subjects = 5 d. dfbetween subjects = 10

c. dfbetween subjects = 5

Which of the following is a correct interpretation of the F-ratio in an analysis of variance? (look up) a. I only b. III only c. II and III only d. I, II, and III

d. I, II, and III

Which of the following is not one of the hypothesis tests used in two-factor ANOVA? a. The main effect of factor A (often called the A-effect). Assuming that factor A is used to define the rows of the matrix, the main effect of factor A evaluates the mean differences between rows. b. The main effect of factor B (called the B-effect). Assuming that factor B is used to define the columns of the matrix, the main effect of factor B evaluates the mean differences between columns. c. The interaction (called the A × B interaction). The interaction evaluates mean differences between treatment conditions that are not predicted from the overall main effects from factor A or factor B. d. The interaction (called the A + B interaction). The interaction evaluates mean differences between treatment conditions that are not predicted from the overall main effects from factor A or factor B.

d. The interaction (called the A + B interaction). The interaction evaluates mean differences between treatment conditions that are not predicted from the overall main effects from factor A or factor B.

Which of the following is not an assumption for using a two-factor ANOVA? a. The observations within each treatment condition must be independent. b. The population distribution within each treatment must be normal. c. The variances of the population distributions for each treatment should be equivalent. d. The number of treatments must be fewer than three.

d. The number of treatments must be fewer than three.