SPSS QUESTIONS launching 3-way ANOVA

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 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	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	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 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	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	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	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.

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	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. (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.)

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	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

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?