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