1.
A researcher randomly assigns members of a statistics class to two groups. In one group, each participant is assigned a tutor. The tutor is available to meet with the student 20 minutes
before each class. The other group is a control group
not assigned a tutor. Suppose the researcher finds
that the tutored group scores significantly better on exams.
a.
Can the researcher conclude that the experimental group students learned
statistical information in tutoring sessions that enabled them to perform
better on the exam? Why or why not?
Hint: Is the tutoring the only difference between the groups? See pages 426-427.
b.
What changes would you recommend in the study?
Hints: Your control group is an empty control group? What are the problems with such groups? How can you replace the empty control group with a placebo control group? If you can't find one really great control group, could you use still have decent construct validity by using two good control groups? See pages 430-432.
2.
Suppose people living in homes for the elderly were randomly assigned to two
groups: a no treatment group and a
transcendental mediation (TM) group. Transcendental mediation
involves more than sitting with eyes closed.
The technique involves both a "mantra, or
meaningless sound selected for its value in facilitating or settling down
process and a specific procedure for using it mentally without effort again to
facilitate transcending" (Alexander, Langer, Newman, Chandler, &
Davies, 1989). Thus, the TM group was
given instruction in how to perform the technique, then "they met with
their instructors 1/2 hour each week to verify that they were mediating
correctly and regularly. They were to
practice their program 20 minutes twice daily (morning and afternoon) sitting
comfortably in their own room with eyes closed and using a timepiece to ensure
correct length of practice."
(Alexander, Langer, Newman,
a.
Could the researcher conclude that it was the transcendental meditation that
caused the effect?
No,
because the control group was an empty control group.
b.
What besides the specific aspects of TM could cause the difference between the
two groups?
The
extra attention the TM group received, the structure of a routine that was
imposed on the TM group, as well as the fact that those who weren't able to
learn the TM technique or who didn't continue to apply the technique would be
dropped from the study. Thus, people may be dropping
out of the experimental group, but not out of the control group.
c.
What control groups would you add?
A group that had to undergo some
training (e.g., critical thinking) and would have to practice what they had
learned twice a day and meet with their instructors once a week.
d.
Suppose you added these control groups and then got a significant F for the treatment variable? What could you conclude? Why?
Conclusion:
That at least one of the groups differ from the others. In
other words, at least one of the treatments had an effect. However,
we would not be able to say which groups differed from each other until we did
a post hoc test.
3.
Assume you want to test the effectiveness of a new kind of therapy. This
therapy involves screaming and hugging people in group sessions followed by
individual meetings with a therapist. What control
group(s) would you use? Why?
Hints:
What type of control group would allow you to see whether therapy was more harmful than no therapy?
What control group would allow
you to see whether hugging was an essential part of the therapy
What control group would allow you
to see whether screaming was an essential part of the therapy
What control group would allow you to see whether the group meetings were a useful part of the therapy?
4.
Assume a researcher is looking at the relationship between caffeine consumption
and sense of humor.
a.
How many levels of caffeine should the researcher use? Why?
At
least three because the relationship might be nonlinear. For
example, people might have little sense of humor with no caffeine (they're not
awake) and little with an extreme amount of caffeine (they are too hyped up and
irritable), but a good sense of humor under moderate levels of caffeine. Using three or more levels of caffeine would allow us to detect some
nonlinear trends and help us make predictions about the effects of levels of
caffeine that we had not directly tested.
b.
What levels would you choose? Why?
Three
to four levels. A no caffeine group, a low caffeine
group, a moderate caffeine group, and a high caffeine group. Make
sure that the amounts of caffeine are evenly spaced (e.g., 0 mg.,
20, 40, 60, 80) so that trend analyses can be performed.
c.
If a graph of the data suggests a curvilinear relationship, can the researcher
assume that the functional relationship between the independent and dependent
variable is curvilinear? Why or why not?
No—the
researcher do a post hoc trend analysis to make sure the observed pattern is
reliable.
d. Suppose the researcher used
the following four levels of caffeine: 0 mg., 20 mg., 25 mg., 26 mg. Can the researcher do a trend analysis? Why
or why not?
No—the levels are not evenly or proportionately
spaced.
e.
Suppose the researcher ranked participants
based on their sense of humor. That is, the person
that laughed least got a score of "1", the person who laughed second
least got a "2", etc. Can the
researcher use this data to do a trend analysis? Why
or why not?
No—you
need at least interval scale measurement to do a trend analysis. Ranked data is only ordinal.
f.
If a researcher used 4 levels of caffeine, how many trends can the researcher
look for?
3 (one less than the number of
levels)
What is the treatment's degrees of freedom?
3 (one less than the number of
levels)
g.
If the researcher used 3 levels of caffeine and 30 participants, what are the
degrees of freedom for the treatment?
2
(3-1)
the
degrees of freedom for the error term?
27
(30-3)
h.
Suppose the F is 3.34 Referring to the degrees of freedom
you obtained in your answer to "g" (above) and to the table F-3, are the results
statistically significant?
No—if
the significance rule is that p <
.05
Can the
researcher look for linear and quadratic trends?
No—if
the results are not statistically significant, then the researcher cannot look
for trends.
5.
A computer analysis reports that F (6,23)=
2.54. The analysis is telling you that the F ratio was 2.54, and the degrees of freedom for the top part of the F ratio is 6 and the degrees of freedom for the bottom part
is 23.
a.
How many groups did the researcher use?
Hint: See the "Treatment (between groups") row of Table 11.1 on page 443.
b.
How many participants were in the experiment?
Hint: See the last row of Table 11.1 on page 443.
c.
Is this result statistically significant at the .05 level (refer to table F-3)?
Hint: If 2.54 is larger than
the critical F
for (6,23) in Table F-3, the result is significant.
6.
A friend gives you the following Fs
and significance levels. On what basis, would you want
these Fs (or significance levels)
re-checked?
a.
F (2, 63)=.10,
not significant
Even
when the treatment has no effect, F's
rarely tend to be zero. Instead, they are usually
closer to 1.00. After all, if there is no treatment effect,
then, at a conceptual level, you are dividing an estimate of error variance by
another, estimate of the same error variance. Dividing
anything by itself should result in a number close to 1.
b.
F (3, 85) = -1.70, not significant
Fs can’t be
negative. You are dividing a square term by another
squared term.
c.
F (1, 120)=
52.8, not significant
Such
a large F with so many degrees of freedom would have to be significant. Indeed, according to the F table in Appendix F, the critical value of F(1,120) is 3.92.
d.
F (5, 70) = 1.00, significant
Fs close to one are rarely
significant. An F
of one is expected even when there is absolutely no effect. Indeed,
the lowest critical value of F on the
entire F table in Appendix F is
1.46—and that's for an F(30,
and an infinite number of degrees of freedom).
7. Complete the following table.
Hints: See the table accompanying summary point 13 on page 451
|
Source of Variance (SV) |
Sum of Squares (SS) |
degrees of freedom (df) |
Mean Square (MS) |
F |
|
Treatment (T) 3 levels of
treatment |
SST= 180 |
Hint: There are 3 levels of the treatment factor, so, according to summary point 10 on p. 450, df is |
Hint: MS is SST/dfT |
Hint: F is MST/MSE |
|
Error (E) |
SSE= 80 |
8 |
Hint: A mean square is always the sum of squares divided by its df. |
|
8.
Complete the following table.
|
(SV) |
(SS) |
(df) |
(MS) |
F |
|
|
Treatment (T) |
50 |
5 |
10 |
2.5 |
|
|
Error
(E) |
100 |
25 |
4 |
|
|
|
Total |
SS
Total= 150 |
30 |
|
|
|
9.
A study compares the effect of having a snack, taking a 10 minute walk, or
getting no treatment on energy levels. Sixty participants
are randomly assigned to condition and then asked to rate their energy level of
a 0 (not at all energetic) to 10 (very energetic) scale. The
mean for the "do nothing" group is 6.0, for
having a snack 7.0, and for walking 7.8.
The F-ratio is 6.27.
a. Graph the means
Hints: You can use either a line graph or a bar chart. Remember to put your
three conditions on the horizontal axis (the x-axis) and put energy level on the
vertical axis (the y-axis).
b.
Are the results statistically significant?
c.
If so, what conclusions can you draw?
Why?
Hints: Can you conclude that at least one of the groups differs from the others? From an ANOVA alone, can you say which groups differ from each other?
d. What additional analyses would you do? Why? Hint: What analyses would allow you to know which groups differed from each other? If you are still not sure, re-read pages 446-447.
e.
How would you extend this study?
Hints: How could you change the study so that you could
map
the functional relationship between length of walk and energy level,
compare different types of exercise?
comparing different types of snacks?
comparing other activities besides
exercise?