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Fundamental Statistics for the Behavioral Sciences

David C. Howell

Chapter 18

Repeated Measures Analysis of Variance - all with Video Answers

Educators

Chapter Questions

01:54

Problem 1

Migraine headaches are a problem for many people, and one way of treating them involves relaxation therapy. A study of the effectiveness of relaxation techniques in the treatment of migraines was conducted by Blanchard, Theobald, Williamson, Silver, and Brown (1978). The data that follow are in agreement with those found by Blanchard et al. (Their study was more complex than the one examined here.) I have calculated $\Sigma X^2$ to save you work.
$$
\begin{array}{lcccccr} & & \text { Baseline } & & \text { Training } \\
\text { Subject } & \text { Week 1 } & \text { Week 2 } & \text { Week 3 } & \text { Week 4 } & \text { Week 5 } & \begin{array}{c}
\text { Subject } \\
\text { Mean }
\end{array} \\
\hline 1 & 21 & 22 & 8 & 6 & 6 & 12.6 \\
2 & 20 & 19 & 10 & 4 & 9 & 12.4 \\
3 & 7 & 5 & 5 & 4 & 5 & 5.2 \\
4 & 25 & 30 & 13 & 12 & 4 & 16.8 \\
5 & 30 & 33 & 10 & 8 & 6 & 17.4 \\
6 & 19 & 27 & 8 & 7 & 4 & 13.0 \\
7 & 26 & 16 & 5 & 2 & 5 & 10.8 \\
8 & 13 & 4 & 8 & 1 & 5 & 6.2 \\
9 & 26 & 24 & 14 & 8 & 17 & 17.8 \\
\hline \text { Weekly } & 20.78 & 20.00 & 9.00 & 5.78 & 6.78 & 12.47 \\
\text { Means } & & & & & &
\end{array}
$$
$$
\text { Grand Mean }=12.47 \quad \Sigma X=561 \quad \Sigma X^2=10.483
$$

Calculate and plot the appropriate column means.

Maxime Rossetti
Maxime Rossetti
Numerade Educator

Problem 2

Run a repeated measures analysis of variance on the data in Exercise 18.1 and explain your results.

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Problem 3

If you were designing the study referred to in Exercise 18.1, what else would you like to have collected to clarify the meaning of your results?

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03:00

Problem 4

Using the data from Week 2 and Week 3 of Exercise 18.1, run a matched-sample $t$ test to test the hypothesis that migraines decreased from before to after relaxation therapy.

Saeeda Aman
Saeeda Aman
Numerade Educator

Problem 5

Run a repeated measures analysis of variance on the same data that you used in Exercise 18.4 and draw the appropriate conclusions.

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Problem 6

For Exercise 18.5 compare the results you had in the two analyses.

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Problem 7

Calculate $\hat{d}$ as an effect size estimate to elaborate on the results in Exercise 18.4.

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03:45

Problem 8

Use the protected $t$ tests with the data in Exercise 18.1 to help you interpret the results. However this time compare the mean of the two baseline measures with the mean of the three training measures. (Hint: As I pointed out, you can calculate the $t$ test as if these were independent samples because $\mathrm{MS}_{\text {error }}$ has been adjusted accordingly by removing subject differences.)

Rashmi Sinha
Rashmi Sinha
Numerade Educator

Problem 9

Calculate an estimate of $d$ for the comparison you made in Exercise 18.8 .

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Problem 10

St. Lawrence, Brasfield, Shirley, Jefferson, Alleyne, and O'Brannon (1995) investigated the effects of an 8 week Behavioral Skills Training (BST) program aimed at reducing the risk of HIV infection among African-American adolescents. The study followed males and females from a pretest to a 12 month follow-up, recording the frequency of condomprotected sex. (They also had a control condition, but I am going to look only at the males in the BST condition for this exercise.) The actual dependent variable is one thousand times the natural logarithm of the frequency of protected sex. (I multiplied the $\log$ by 1,000 to eliminate decimal values.) The data for males follow.
$$
\begin{array}{lccc}
\text { Pretest } & \text { Posttest } & \begin{array}{c}
\text { Follow-up } \\
\text { 6 Months }
\end{array} & \begin{array}{c}
\text { Follow-up } \\
\text { 12 Months }
\end{array} \\
\hline 07 & 22 & 13 & 14 \\
25 & 10 & 17 & 24 \\
50 & 36 & 49 & 23 \\
16 & 38 & 34 & 24 \\
33 & 25 & 24 & 25 \\
10 & 07 & 23 & 26 \\
13 & 33 & 27 & 24 \\
22 & 20 & 21 & 11 \\
04 & 00 & 12 & 00 \\
17 & 16 & 20 & 10
\end{array}
$$
(a) Calculate and plot the means.
(b) Use the analysis of variance to draw the appropriate conclusions.

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02:06

Problem 11

What null hypothesis did you test in Exercise 18.10?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator

Problem 12

In the study discussed in Exercise 18.10, the authors also ran a control group under the same conditions, but without the BST intervention. Those data (for males) follow.
$$
\begin{array}{lccc}
\text { Pretest } & \text { Posttest } & \begin{array}{c}
\text { Follow-up } \\
\text { 6 Months }
\end{array} & \begin{array}{c}
\text { Follow-up } \\
\text { 12 Months }
\end{array} \\
\hline \infty & 00 & 00 & 00 \\
69 & 56 & 14 & 36 \\
05 & 00 & 00 & 05 \\
04 & 24 & 00 & 00 \\
35 & 08 & 00 & 00 \\
07 & 00 & 09 & 37 \\
51 & 53 & 08 & 26 \\
25 & 00 & 00 & 15 \\
59 & 45 & 11 & 16 \\
40 & 02 & 33 & 16
\end{array}
$$
(a) Calculate the means for these data and plot them on the same graph used in Exercise 18.9.
(b) Run the analysis of variance on these data.

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Problem 13

What would you conclude from the comparison of the answers to Exercises 18.10 and 18.12? (You do not know how to run the appropriate analysis of variance, though you might be able to figure it out if you have the appropriate software, but the analysis itself is not the issue.)

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04:21

Problem 14

In Exercise 18.10 why did we treat Time as a repeated measure rather than as a between-subjects measure?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
06:39

Problem 15

Use Bonferroni tests with the data in Table 18.1 to compare performance at the following points:
(a) Week 0 and Week 6
(b) Week 0 and Week 12
(c) Week 3 and Week 12

Sheryl Ezze
Sheryl Ezze
Numerade Educator

Problem 16

Write a short paragraph describing the results of the analysis of the data in Exercise 18.1.

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