Deck 14: Using Designs With More Than One Independent Variable and Two-Way Between-Subjects Anova

Question 1

In a two-way factorial ANOVA, the formula for calculating SS_Total is:

A) $\quad \sum\left(X-\bar{X}_{G}\right)^{2}$ .

B) $\quad \Sigma\left(X-\bar{X}_{g}\right)^{2}$ .

C) $\quad \Sigma\left[\left(\bar{X}_{g}-\bar{X}_{\mathrm{G}}\right)^{2} n\right]$ .

D) $\quad \Sigma\left[\left(\bar{X}_{g}-\bar{X}_{\mathrm{G}}\right)^{2}\right]$ .

Answer 1

$\quad \sum\left(X-\bar{X}_{G}\right)^{2}$ .

Question 2

In a two-way factorial ANOVA, the formula for calculating SS_{Factor A} is:

A) $\quad \Sigma\left(X-\bar{X}_{G}\right)^{2}$ .

B) $\quad \Sigma\left(X-\bar{X}_{g}\right)^{2}$ .

C) $\quad \Sigma\left[\left(\bar{X}_{\mathrm{A}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{A}}\right]$ .

D) $\quad \Sigma\left[\left(\bar{X}_{A}-\bar{X}_{\mathrm{g}}\right)^{2}\right]$ .

Answer 2

$\quad \Sigma\left[\left(\bar{X}_{\mathrm{A}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{A}}\right]$ .

Question 3

In a two-way factorial ANOVA, the formula for calculating SS_{Factor B} is:

A) $\quad \sum\left(X-\bar{X}_{G}\right)^{2}$ .

B) $\quad \Sigma\left(X-\bar{X}_{g}\right)^{2}$ .

C) $\quad \Sigma\left[\left(\bar{X}_{\mathrm{B}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{B}}\right]$ .

D) $\quad \Sigma\left[\left(\bar{X}_{B}-\bar{X}_{\mathrm{g}}\right)^{2}\right]$ .

Answer 3

$\quad \Sigma\left[\left(\bar{X}_{\mathrm{B}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{B}}\right]$ .

Question 4

In a two-way factorial ANOVA, the formula for calculating SS_A×B is:

A) $\quad \sum\left(X-\bar{X}_{G}\right)^{2}$ .

B) $\quad\left[\Sigma\left(\bar{X}_{\mathrm{C}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{C}}\right]-S S_{\mathrm{A}}-S S_{\mathrm{B}}$

C) $\quad \Sigma\left[\left(\bar{X}_{\mathrm{A}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{B}}\right]$ .

D) $\quad\left[\Sigma\left(\bar{X}_{\mathrm{C}}-\bar{X}_{\mathrm{G}}\right)^{2} n_{\mathrm{C}}\right]$ .

Question 5

In a two-way factorial ANOVA, the formula for calculating SS_Error is:

A) $\quad \Sigma\left(X-\bar{X}_{\mathrm{C}}\right)^{2}$ .

B) $\quad \Sigma\left(X-\bar{X}_{\mathrm{C}}\right)^{2}-S S_{S}$ .

C) $\Sigma\left[\left(\bar{X}_{\mathrm{C}}-\bar{X}_{\mathrm{G}}\right)^{2} n\right]-S S_{S}$ .

D) $\quad \Sigma\left[\left(\bar{X}_{\mathrm{C}}-\bar{X}_{\mathrm{G}}\right)^{2}\right]$ .

Question 6

In a study with three levels of factor A, three levels of factor B, and 6 subjects in each condition, df_A and df_B would be _____ and _____, respectively.

A) 3; 3
B) 2; 3
C) 3; 2
D) 2; 2

Question 7

In a study with three levels of factor A, three levels of factor B, and 6 subjects in each condition, the df_AxB would be:

A) 9.
B) 6.
C) 4.
D) 3.

Question 8

A two-way ANOVA has _____, and a three-way ANOVA has _____.

A) two independent variables; three dependent variables
B) two dependent variables; three dependent variables
C) two independent variables; three independent variables
D) two dependent variables; three independent variables

Question 9

The following ANOVA table corresponds to an experiment with two IV's; 1) Time of Day (Morning or Afternoon) and 2) Room Temperature (Cool, Normal, or Warm). The productivity level (on a 0-100 scale) of employees during the morning or afternoon is measured in either cool, normal, or warm working conditions. This is a completely between-subjects design. The corresponding means for each group are as follows:
Cool Temp/Afternoon - 55
Cool Temp/Morning - 100
Normal Temp/Afternoon - 60
Normal Temp/Morning - 60
Warm Temp/Afternoon - 50
Warm Temp/Morning - 10
Construct the matrix showing the means in each cell, give the factorial notation, fill in the ANOVA table, draw a graph showing the results, calculate Tukey's HSD if appropriate, and draw conclusions concerning this study. There are 10 subjects in each cell (condition).

Question 10

An experiment with two variables each with three levels is a _____ factorial design.

A) 3 × 3
B) 2 × 2
C) 2 × 2 × 2
D) 3 × 3 × 3

Question 11

An experiment with four variables each with two levels is a _____ factorial design.

A) 2 × 4
B) 2 × 2
C) 2 × 2 × 2 × 2
D) 2 × 3 × 4

Question 12

When graphed, a significant interaction will definitely have _____.

A) parallel lines
B) nonparallel lines
C) a crossover interaction
D) none of the above

Question 13

According to the experiment discussed in the text [i.e., 2 IV's: Word Type (Concrete vs. Abstract) and Rehearsal Type (Elaborative vs. Rote) and one DV: % of words recalled correctly], show the graph for the experimental results of NO main effect of rehearsal, NO interaction effect, and NO main effect of Word Type. Hint: First, construct a matrix of what you think the cell means should be. It might help you.