Chapter 13

1. An experimenter is interested in the effects of two independent variables on self esteem. What is better about conducting a factorial experiment than conducting two separate experiements, one for each independent variable?

2. An experiment is conducted on the effect of age and treatment condition (experimental versus control) on reading speed. Which statistical term (main effect, simple effect, interaction, specific comparison) applies to each of the descriptions of effects.

a. The effect of the treatmentwas larger for 15-year olds than it was for 5- or 10-year olds.
b. Overall, subjects in the treatment condition performed faster than subjects in the control condition.
c. The difference between the 10- and 15-year olds was significant under the treatment condition.
d. The difference between the 15- year olds and the average of the 5- and 10-year olds was significant.
e. As they grow older, children read faster.

3. An A(2) x B(4) factorial design with 8 subjects in each group is analyzed. Give the source and degrees of freedom columns of the analysis of variance summary table.

4. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table and test simple effects.

  12-year olds 16-year olds
30 minutes 65
68
59
72
46
74
71
66
82
76
60 minutes 69
61
69
73
61
95
92
95
98
94

5. Define "Three-way interaction"

6. Define interaction in terms of simple effects.

7. Plot an interaction for an A(2) x B(2) design in which the effect of B is greater at A1 than it is at A2. The dependent variable is "Number correct." Make sure to label both axes.

8. Following are two graphs of population means for 2 x 3 designs. For each graph, indicate which effect(s) (A, B, or A x B) are nonzero.

 

9. The following data are from an A(2) x B(4) factorial design.

  B1 B2 B3 B4
A1 1
3
4
5
2
2
4
5
3
3
2
6

4
5
6
8

A2 1
1
2
2
2
3
2
4
4
6
7
8
8
9
9
8

a. Compute an analysis of variance.
b. Test differences among the four levels of B using the Tukey hsd test at the .05 level.
c. Test the linear component of trend for the effect of B.
d. Plot the interaction.
e. Describe the interaction in words.

Selected Answers