Conducting a 3-Way ANOVA Why? ANOVA can be used to handle multiple independent variables and we need to know how this works in a factorial ANOVA design with 2 or more independent variables. This includes the very valuable process of understanding interaction effects. Assignment As a reading specialist, and based on your literature review, you hypothesize that a student’s performance (score) on a reading task may be predicted by the difficulty of the reading passage (0=easy, 1=difficult), length of the passage (0=short, 1=long), and the gender of the student (0=female, 1=male). Run a 3-way factorial ANOVA in SPSS. Be sure to create your syntax file as part of the process. Interpret your results and think about what they mean. Are there any main effects of note? Are there any interaction effects of note? What are the omnibus eta-squared effect sizes? What are the specific Cohen’s d effect sizes for mean differences for main effects or any specific interaction mean differences of note? Remember to check your assumptions. It would be a good idea to practice writing up your results in a format suitable for a journal article. Subject Gender Difficulty Length Score 1 0 0 0 16 2 0 0 0 17 3 0 0 0 16 4 0 1 0 12 5 0 1 0 11 6 0 1 0 16 7 0 0 1 16 8 0 0 1 12 9 0 0 1 18 10 0 1 1 5 11 0 1 1 4 12 0 1 1 8 13 1 0 0 11 14 1 0 0 22 15 1 0 0 14 16 1 1 0 12 17 1 1 0 9 18 1 1 0 13 19 1 0 1 13 20 1 0 1 17 21 1 0 1 12 22 1 1 1 7 23 1 1 1 4 24 1 1 1 3 Conducting a Repeated Measures ANOVA Why? Repeated measures ANOVA can be used to study the same group of individuals over time or across different treatment levels. It is useful to help explore change in individuals or differences in treatments. Because we study the same individuals each time, we are able to reduce the variability due to error (SSwithin) which can make this approach more powerful at times. Assignment Assume you are researching different approaches to warm-up and stretching for high school athletes. According to your literature review (completely hypothetical here!), there seems to be evidence that dynamic plyometric warm-ups (active, movement-oriented warm-ups that often involve jumping) result in fewer lower body injuries during team sports. Also, plyometric warm-ups seem to result in greater speed and quickness levels, although the research on this area is more sporadic and less certain. As a kinesiology researcher who is working with a local high school sports program, you decide to study the issue further by testing four different approaches to warm-up and stretching and examining potential impact on the speed of 9th and 10th grade males (randomly selected from the junior varsity football roster) in the 40 yard sprint. You selected 10 athletes for your study. The four conditions included: (a) no stretch or warm-up, (b) traditional static stretching which involves non-movement stretching/elongating of the muscles, (c) plyometric warm-up, and (d) both static stretchi.

1. Conducting a 3-Way ANOVA
Why? ANOVA can be used to handle multiple independent
variables and we need to know how this works in a factorial
ANOVA design with 2 or more independent variables. This
includes the very valuable process of understanding interaction
effects.
Assignment
As a reading specialist, and based on your literature review, you
hypothesize that a student’s performance (score) on a reading
task may be predicted by the difficulty of the reading passage
(0=easy, 1=difficult), length of the passage (0=short, 1=long),
and the gender of the student (0=female, 1=male).
Run a 3-way factorial ANOVA in SPSS. Be sure to create your
syntax file as part of the process. Interpret your results and
think about what they mean. Are there any main effects of
note? Are there any interaction effects of note? What are the
omnibus eta-squared effect sizes? What are the specific
Cohen’s d effect sizes for mean differences for main effects or
any specific interaction mean differences of note? Remember to
check your assumptions. It would be a good idea to practice
writing up your results in a format suitable for a journal article.
Subject
Gender
Difficulty
Length
Score
1
0
0
0

2. 16
2
0
0
0
17
3
0
0
0
16
4
0
1
0
12
5
0
1
0
11
6
0
1
0
16
7
0
0
1
16
8
0
0
1
12

3. 9
0
0
1
18
10
0
1
1
5
11
0
1
1
4
12
0
1
1
8
13
1
0
0
11
14
1
0
0
22
15
1
0
0
14
16

4. 1
1
0
12
17
1
1
0
9
18
1
1
0
13
19
1
0
1
13
20
1
0
1
17
21
1
0
1
12
22
1
1
1
7
23
1

5. 1
1
4
24
1
1
1
3
Conducting a Repeated Measures ANOVA
Why? Repeated measures ANOVA can be used to study the
same group of individuals over time or across different
treatment levels. It is useful to help explore change in
individuals or differences in treatments. Because we study the
same individuals each time, we are able to reduce the variability
due to error (SSwithin) which can make this approach more
powerful at times.
Assignment
Assume you are researching different approaches to warm-up
and stretching for high school athletes. According to your
literature review (completely hypothetical here!), there seems to
be evidence that dynamic plyometric warm-ups (active,
movement-oriented warm-ups that often involve jumping) result
in fewer lower body injuries during team sports. Also,
plyometric warm-ups seem to result in greater speed and
quickness levels, although the research on this area is more
sporadic and less certain.
As a kinesiology researcher who is working with a local high
school sports program, you decide to study the issue further by
testing four different approaches to warm-up and stretching and
examining potential impact on the speed of 9th and 10th grade

6. males (randomly selected from the junior varsity football roster)
in the 40 yard sprint. You selected 10 athletes for your study.
The four conditions included: (a) no stretch or warm-up, (b)
traditional static stretching which involves non-movement
stretching/elongating of the muscles, (c) plyometric warm-up,
and (d) both static stretching followed by plyometric warm-up.
On four consecutive days, each athlete participated in one of the
four conditions for warm-up and then was electronically timed
in a 40 yard sprint (seconds). To help control for practice
effects, the conditions were counterbalanced across all athletes.
The resulting data are below. Run an appropriate repeated
measures ANOVA to see if there are differences across the
varied conditions for warm-up. Based on your (hypothetical)
literature review, you expect to see better performance for both
static stretching and plyometrics over no warm-up and better
performance for plyometrics over static stretching. You do not
have a specific hypothesis for the combined static
stretch/plyometric condition compared to the others.
participant
no warm-up
static
plyometric
combined
1
5.28
5.31
5.21
5.29
2
4.98
4.95
4.82
4.71
3

7. 4.85
4.95
4.75
4.78
4
5.02
5.12
4.95
4.89
5
5.21
5.11
5.05
4.99
6
4.75
4.71
4.68
4.81
7
5.43
5.25
5.26
5.29
8
5.25
5.21
5.08
5.01
9
5.05
4.97
4.93
4.89
10
4.95

8. 4.93
4.77
4.85
Conducting a Multiple Regression Analysis
Why? Multiple regression is a very flexible way to evaluate
whether a set of predictor variables can explain variance in a
criterion variable. In applied research we often ask research
questions that are concerned with predicting outcomes with
other variables. Because multiple regression is the highest level
of the general linear model for univariate analyses,
understanding it well will help us understand other analyses and
how they fit together.
Assignment
Based on your literature review, you hypothesize that one’s
level of aggression is related to their levels of anger, patience,
and self-confidence. Specifically, you think that higher levels
of anger and lower levels of patience and self-confidence
correspond to higher aggression. Assume each of these
variables was measured (n=20) on an interval scale with scores
ranging from 1 (lowest level) to 50 (highest level). Be sure to
think about the direction of each variable and what that means
(e.g., high levels of aggression would be much different that
high levels of patience).
Run the appropriate multiple regression analysis. Be sure to
include descriptive statistics for the variables as well as getting
any relevant statistics you need for the interpretation (hint:
don’t forget to get and analyze your structure coefficients).
Interpret your results and think about what they mean relative to

9. your expectations. How much variance in the aggression scores
was explainable by the predictors? Which predictor(s) played
the largest role in predicting the dependent variable? Perhaps
practice writing up your findings in a format suitable for a
journal article. Below are the data for your study:
Subject
Aggression
Anger
Patience
Self-confidence
1
35
25
15
22
2
48
35
10
11
3
32
22
12
45
4
12
12
15
12
5
44
12
48
22
6

10. 33
7
12
26
7
44
45
12
15
8
12
45
18
46
9
45
46
10
15
10
37
14
15
6
11
21
49
48
33
12
44
43
12
10
13
37

11. 12
15
17
14
11
21
45
14
15
45
37
22
22
16
41
34
32
12
17
10
18
28
37
18
32
35
42
14
19
23
45
17
40
20
14
49

12. 18
34
Conducting (and Comparing) Omnibus ANOVA and Planned
Contrasts
Why? The post hoc tests following an omnibus ANOVA all
inherently correct for inflation of familywise Type I error rates
because of the multiple group mean comparisons that are
necessary. Planned contrasts ask specific (theoretically
motivated) questions about group means, thereby limiting the
number of comparisons made and avoiding the need to correct
for comparisons that are not of theoretical interest.
Assignment
As a higher education researcher interested in the political
views of undergraduates across the US, you conduct a study to
evaluate whether the level of conservativism among college
students differs depending on whether they attend college in the
south (1), southwest (2), northeast (3), or western (4) regions of
the nation. Your outcome measure yields scores that reflect a
continuum of liberalism (low scores) to conservativism (high
scores), with a possible range of 0 to 20. Your data for n=32
students is below.
Drawing on your experience and several related studies, you
specifically hypothesize that there is no difference between the
south and southwestern students, nor any difference between
these two and the students from the northeast. You do,
however, expect to find differences between these three groups
and the students who attend college in the west.

13. region
conserv
1
8
1
10
1
15
1
13
1
12
1
11
1
10
1
11
2
8
2
9
2
15
2
12
2
12
2
11
2
10
2
11
3

14. 8
3
9
3
15
3
13
3
12
3
11
3
9
3
10
4
7
4
11
4
11
4
9
4
10
4
6
4
10
4
9
PART 1: Conduct an omnibus ANOVA for this example and
check any appropriate assumptions. As part of the analysis,
conduct Tukey, Scheffe, LSD, and Bonferonni post hoc tests.

15. (NOTE: Using multiple post hoc tests is for the purposes of this
assignment only to help prove a point. You would never do this
in the real world because you would select the post hoc test that
best fits your situation, although the Tukey test is the most
common.) Interpret and make sense of the results.
PART 2: Conduct a planned (orthogonal) contrast analysis that
reflects your theoretical expectations described above. Create
your coded contrast variables and use the regression procedure
in SPSS to run the analysis, as described in the lectures.
Interpret and make sense of the results. Be sure to compare the
results obtained in this approach with what you found in the
omnibus ANOVA. (NOTE: Running both the omnibus ANOVA
and planned contrasts on the same data is done here for the
purposes of this assignment only so we can compare their
outcomes. Normally you would not follow an omnibus ANOVA
with planned contrasts but rather decide which you wished to
conduct based on theoretical reasons.)

16. Understanding General Linear Model Relationships (one-way
ANOVA, t-test, r, simple regression)
Why? Understanding how general linear model analyses are
related as part of the same analytical family helps us develop
greater conceptual awareness of what our methods are doing for
us and how they can be used. Regression, ANOVA, t-tests, etc.
are all ultimately correlational-type analyses. It is important to
realize how the correlation coefficient is connected to each of
these.
Assignment
The data set below represents a grouping variable with 2 levels
and a dependent variable. Use this data set to conduct the
following analyses:
a. One-way ANOVA to examine mean differences between the
two groups.
b. Independent samples t-test to examine mean differences
between the two groups.
c. Pearson’s r between the group and dependent variables to
examine their relationship.
d. Simple (one predictor) regression where the group
membership variable predicts the
dependent variable.
group
dv
1
30
1
32
1

17. 25
1
29
1
19
1
35
1
26
1
15
1
16
1
28
2
25
2
19
2
20
2
56
2
43
2
33
2
23
2
43
2
44
2
45

18. After conducting the analyses, be sure to examine (and compute
them if necessary) the effect sizes for each analysis. Look for
similarities in the results across each of the analyses. Are there
similarities between the p-values across approaches? Are there
similarities between the effect sizes? Are there similarities in
the degrees of freedom or anything else? What is the
connection/relationship between the F statistic obtained in the
ANOVA and the t statistic obtained in the t-test? What are your
broad conclusions, if any, about the general linear model and
relationships among come of our common statistical analyses?