ANSWERS TO CHAPTER 12 EXERCISES
1. Match the terms to their
definition
|
Hints:
See the answers to 2 (below). If you need more help,
see summary points 5 and 7 on page 514.
2. What is the difference between
a.
a simple main effect and an overall main effect?
The treatment’s overall main effect
is the average of its simple main effects.
b.
an overall main effect and an interaction?
A main effect is estimated by
looking at the average of a treatment’s simple main effects. An
interaction, on the other hand, is estimated by looking at the differences
between a treatment’s main effects. Put another way,
the overall main effect emphasizes the general, average effect of a treatment,
whereas the interaction emphasizes how the effect of the treatment depends on
the level of another variable.
3. Can you have an interaction
without a main effect? Why or why not
Hints:
1.
For the question “Can you have an
interaction without a main effect?,” see summary point #12 on page 514. (For an example, see page 496-498).
2.
For the question “Why or why not?”, see p. 484, especially paragraph 3.
4. Suppose an experimenter looked
at the status of speaker and rate of speech on attitude change. Describe the pattern of results in the following table in
terms of main effects and interactions. Assume that
all differences are statistically significant.
|
|
Status of Speaker |
|
|
Rate
of Speech |
Low
Status |
High
Status |
|
Slow |
10 |
15 |
|
Fast |
20 |
30 |
|
|
Attitude Change |
|
Main effect for status, main effect for rate of speech, and an interaction.
(The best estimate for the average main effect for speech is 12.5, the best estimate for average main effect for status is 7.5, and the effect of status seems to vary depending on whether there is a slow rate of speech (15-10=5) or a fast rate of speech 30-20=10.)
5. Describe the pattern of
results in the following table in terms of main effects and interactions. Assume that all differences are statistically significant.
|
|
Status of Speaker |
|
|
Rate
of Speech |
Low
Status |
High
Status |
|
Slow |
10 |
15 |
|
Fast |
20 |
25 |
|
|
Attitude Change |
|
Hints:
1. Compare the low status column with the high status column. Is there a difference between the average score of the participants who hear the low status speaker and the average score of the participants who hear the high status speaker? If so, there is a main effect for status of the speaker.
2. Compare the slow speech row with the fast speech row. Is there a difference between the average score of the participants who hear the slow speaker and the average score of the participants who hear the fast speaker? If so, there is a main effect for rate of speech.
3. Look at the difference between the averages of the low and high status speakers in the slow rate of speech row. Compare that to the difference between the averages of the low and high status speakers in the fast rate of speech row. If the two differences are the same, there is no interaction.
6.
Forty participants receive a placebo.
The other forty receive a drug that blocks the
effect of endorphins (a pain-receiving substance, similar to morphine, that is
produced by the brain). Half the placebo
group and half the drug group get acupuncture.
Then, all participants are asked to rate the pain of various shocks on a
1 (not at all painful) to 10 (very painful) scale. The results are as follows: placebo, no acupuncture group, 7.2; placebo,
acupuncture group, 3.3; drug, no acupuncture group, 7.2; drug and acupuncture
group, 3.3.
a.
Graph the results.
b.
Describe the results in terms of main effects and interactions (making a table
of the date may help).
Main effect for acupuncture; no main effect for drug; no interaction
c.
What conclusions would you draw?
These
results suggest that the effect of acupuncture is not mediated by endorphins.
7.
The following table is an ANOVA summary table of a study looking at the effects
of similarity and attractiveness on liking. Complete
the table. Then, answer these three questions.
a.
How many participants were used in the study?
Hint: The total degrees of freedom (df) is 59. According to the bottom entry of the degrees of freedom column for the table on page 515, how many participants would you need to have 59 total df?
b.
How many levels of similarity were used?
Hint: The degrees of freedom (df) for similarity is 1. According to the first row of the degrees of freedom column for the table on page 515, how many levels of similarity would you need to for df for similarity to be 1? That is, if we labeled similarity as "A," how many levels of "A" would we need for A's df to be 1?
c.
How many levels of attractiveness were used?
Hint: The degrees of freedom (df) for attractiveness is 2. According to the first row of the degrees of freedom column for the table on page 515, how many levels of attractiveness would you need to for df for similarity to be 2? That is, if we labeled attractiveness as "A," how many levels of "A" would we need for A's df to be 2?
|
SV
|
SS |
df |
MS |
F |
|
Similarity
(S) |
10 |
1 |
SS/df= |
MS(S)/
MSE |
|
Attractiveness
(A) |
This divided by 2 will equal 20. |
2 |
20 |
MS(A)/ MSE |
|
S X A
interaction |
400 |
2 |
200 |
MS (SXA)/ MSE |
|
Error |
540 |
54 |
MSE=
SSE/dfE
|
|
|
Total |
990 |
59 |
|
|
8. A professor
does a simple experiment. In that experiment,
the professor finds that students who are given lecture notes do better than
those who are not given lecture notes.
Replicate this study as a 2 X 2 factorial. What is your second variable? What predictions do you make? Do you predict an interaction? Why or why not? No set answers for this question.
9 A lab experiment on motivation yielded the following results:
|
Group |
Productivity |
|
No financial
bonus, no encouragement |
25% |
|
No financial
bonus, encouragement |
90% |
|
Financial bonus,
no encouragement |
90% |
|
Financial
bonus, encouragement |
90% |
a.
Make a 2 X 2 table of these data.
|
|
No
encouragement |
Encouragement |
|
No financial
bonus |
|
|
|
Bonus |
|
|
b.
Graph these data.
c.
Describe the results in terms of main
effects and interactions.
Hints:
1. Compare the no encouragement column with the encouragement column. Is there a difference between the average score of the no encouragement participants and the average score of the encouraged participants? If so, there is a main effect for encouragement.
2. Compare the no bonus row with the bonus row. Is there a difference between the average score of the participants who do not get a bonus and the average score of the participants who get a bonus? If so, there is a main effect for bonuses.
3. Look at the difference between the averages of the low and high status speakers in the slow rate of speech row. Compare that to the difference between the averages of the low and high status speakers in the fast rate of speech row. If the two differences are the same, there is no interaction.
d.
What is your interpretation of
the findings?
1. What does an interaction usually mean? What does the fact that one line slopes upward much more than the other suggest?
2. See pages 495-496 to review important facts about ordinal interactions.
10.
A memory researcher looks at the effects of processing time and rehearsal
strategy on memory.
|
Group |
Percent correct |
|
Short
exposure, simple strategy |
20% |
|
Short
exposure, complex strategy |
15% |
|
Long
exposure, simple strategy |
25% |
|
Long exposure,
complex strategy |
80% |
a.
Graph these data.
b.
Describe the results in terms of main effects and interactions.
Main
effect for length of exposure (long > short); Main effect for strategy
(complex > simple); Interaction between strategy and exposure time
c.
What is your interpretation of the findings?
Longer
exposure times aid memory more than shorter exposure times. Complex
strategies are better than simple ones. However, the
advantage of the complex strategies only occurs when participants have more
time to study. Or, to look at it another way, having
more time to study material is more helpful when you are using a complex
rehearsal strategy than when you are using a simple rehearsal strategy.
11. Suppose a researcher wanted to know whether lecturing was more effective than
group discussion for teaching basic facts.
Therefore, the researcher did a study and obtained the following
results:
|
Source of
Variance |
SS |
df |
MS |
F |
|
Teaching (T) |
10 |
1 |
10 |
5 |
|
Introversion/
Extroversion (I) |
20 |
1 |
20 |
10 |
|
T X I
interaction |
50 |
1 |
50 |
25 |
|
Error |
100 |
50 |
2 |
|
a.
What does the interaction seem to indicate?
Hint: The general formula for interactions is that the effect of a treatment is different depending on the level of a second variable. In this case, the treatment is teaching style and the second variable is introversion/extroversion.
b.
Even if there had been no interaction between teaching and extroversion, would
there be any value in including the introversion-extroversion variable? Explain.
Hints: See the discussion of the blocked design on pages 512 and 513. In addition, would it be useful to find that treatment's effect on introverts was not that different to its effect on extroverts? Finally, would you be interested in seeing whether introverts or extroverts learned more?
c.
What, if anything, can you conclude about the effects of introversion on
learning?
Hint: See main point 18 on page 515. If you need more details, see "Hybrid designs' key limitation: They do not allow cause-effect statement regarding the nonexperimental factor" on pages 508-509.