part
2. The repeated-measures ANOVA can be viewed as a two-stage process. What is the purpose of the second stage?
4. A researcher conducts a repeated-measures experiment using a sample of n = 8 subjects to evaluate the differences among four treatment conditions. If the results are examined with an ANOVA, what are the df values for the F-ratio?
6. A published report of a repeated-measures research study includes the following description
of the statistical analysis. “The results show significant differences among the treatment conditions, F(2, 20) = 6.10, p
a. How many treatment conditions were compared in the study?
b. How many individuals participated in the study?
8. The following data were obtained from a repeated measures study comparing two treatment
conditions.
use a repeated-measures ANOVA with sd .05 to determine whether there are significant mean differences between the two treatments.
Treatments
Person I
II Totals
A 3
5 P = 8
B 5 9
P = 14
N = 16
C 1 5
P =6
G =80
D 1 7 P
=8 = X2 = 500
E 5
9 P
= 14
F 3
7 P
= 10
G 2 6
P = 8
H 4 8
P = 12
M
=3 M = 7
T
= 24 T = 56
SS=18 SS = 18
10. For the data in problem 9,
a. Compute SStotal and SSbetween treatments.
b. Eliminate the
mean differences between treatments by adding 2 points to each score in
treatment I,
adding 1 point to each score in
treatment II, and subtracting 3 points from each score in treatment
III. (All three treatments should
end up with M = 3and T = 15.)
c. Calculate SStotal for the modified
scores. (Caution: You first must find the new value for EX2.)
d. Because the treatment effects were eliminated in part b, you should find that SS total for the modifiedscores is smaller than SS total for the original scores. The difference between the two SS values should be exactly equal to the value of SS between treatments for the original scores.
12. In Problem 11 the data show large and consistent differences between subjects. For example,
subject A has the largest score in every treatment and subject D always has the
smallest score. In the second stage of the ANOVA, the large individual
differences are subtracted out of the denominator of the F-ratio, which results
in a larger value for F.
The following data were created by using the same numbers that appeared in Problem 11. However, we eliminated the consistent individual differences by scrambling the scores within each treatment.
Treatment
Subject
I II III P
A 6 2 3 11 G = 48
B 5 1 5 11 =X2 = 294
C 0 5 10 15
D 1 8 2 11
T _ 12
T _ 16 T _ 20
SS _ 26
SS _ 30 SS _ 38
a. Use a repeated-measures ANOVA with sd .05 to determine whether these data are sufficient to
demonstrate significant differences between the treatments.
b. Explain how the results of this analysis compare with the results from Problem 11.
14. The following data are from an experiment comparing three different treatment conditions:
A B C
0 1 2 N = 15
2 5 5 =EX2 =354
1 2 6
5 4 9
2 8 8
T =10
T = 20 T = 30
SS =14
SS =30 SS =30
a. If the experiment
uses an independent-measures design, can the researcher conclude that
the treatments are significantly different? Test at the .05 level of
significance.
b. If the experiment
is done with a repeated-measures design, should the researcher conclude
that the treatments are significantly different? Set alpha at .05 again.
c. Explain why the
analyses in parts a and b lead to different conclusions.
16. The following summary
table presents the results from a repeated-measures ANOVA comparing three
treatment
conditions with a sample of n = 11
subjects. Fill in the missing values in the table. (Hint: Start with the
df values.)
Source
SS df MS
Between treatments F = 5.00
Within treatments 80
Between subjects
Error 60
Total
18. A recent study
indicates that simply giving college students a pedometer can result in
increased walking
(Jackson & Howton, 2008).
Students were given pedometers for a 12-week period, and asked to record the average number of steps per day during weeks 1,6, and 12. The following data are similar to the results obtained in the study.
Number of steps (x1000)
Week
Participant
1 6 12 P
A 6 8 10 24
B 4 5 6 15
C 5 5 5 15 G = 72
D 1 2 3 6 EX2 = 400
E 0 1 2 3
F 2 3 4 9
T =18
T = 24 T =30
SS =28
SS =32 SS _ 40
a. Use a
repeated-measures ANOVA with sd .05 to determine
whether the mean number of steps changes significantly from one week to
another.
b. Compute 2 to measure the
size of the treatment effect.
c. Write a sentence
demonstrating how a research report would present the results of the hypothesis
test and the measure of effect size.
20. For either independent-measures or repeated-measures designs comparing two treatments, the
mean difference can be evaluated with either a t test or an ANOVA. The two tests are related by the equation F= t2. For the following data,
a. Use a repeated-measures t test with sd .05 to determine whether the mean difference between treatments is statistically significant.
b. Use a repeated-measures ANOVA with sd.05 to determine whether the mean difference between treatments is statistically significant. (You should find that F _ t2.)
Person
Treatment 1 Treatment 2 Difference
A 4 7 3
B 2 11 9
C 3 6 3
D 7 10 3
M _=4
M =8.5 MD = 4.5
T =16
T = 34
SS =14
SS = 17 SS =27
22. The endorphins released by the brain act as natural painkillers. For example, Gintzler (1970)
monitored endorphin activity and pain thresholds in pregnant rats during the days before they gave birth. The data showed an increase in pain threshold as the pregnancy progressed. The change was gradual until 1 or 2 days before birth, at which point there was an abrupt increase in pain threshold. Apparently a natural painkilling mechanism was preparing the animals for the stress of giving birth. The following data represent pain-threshold scores similar to the results obtained by Gintzler. Do these data indicate a significant change in pain threshold? Use a repeated-measures ANOVA with sd.01.
Days
Before Giving Birth
Subject
7 5 3 1
A 39 40 49 52
B 38 39 44 55
C 44 46 50 60
D 40 42 46 56
E 34 33 41 52