1. SPSS Series 1: ANOVA and Factorial ANOVA
By Hui Bian
Office for Faculty Excellence

2. List of topics One-way ANOVA with SPSS
Two-way Factorial ANOVA with SPSS
How to interpret SPSS outputs
How to report results

3. Data used in this workshop
We use 2009 Youth Risk Behavior Surveillance System (YRBSS, CDC) as an example.
YRBSS monitors priority health-risk behaviors and the prevalence of obesity and asthma among youth and young adults.
The target population is high school students
Multiple health behaviors include drinking, smoking, exercise, eating habits, etc.

4. One-way ANOVA ANOVA means Analysis of Variance
ANOVA: compare means of two or more levels of the independent variable
One independent variable
One dependent variable
The basic test uses F distribution
Comparing means is a special case of a regression analysis

5. Total sum of Squares of deviations of DV
Reasoning of ANOVA
The partitioning of the total
sum of squares of deviations
Independent variable 1
Independent variable 2
Total sum of Squares of deviations of DV
Independent variable 3
Error

6. One-way ANOVA Research design
Between-subjects design*: different individuals are assigned to different groups (level of independent variable).
Within-subjects design: all the participants are exposed to several conditions.
* This presentation only focuses on between-subject design.

7. One-way ANOVA Data considerations Assumptions
Independent variable (factor variable) is categorical.
Dependent variable should be quantitative (interval level of measurement).
Assumptions
Independent: each group is an independent random sample from a normal population.
Normality: analysis of variance is robust to departures from normality, although the data should be symmetric.
Homogeneity: the groups should come from populations with equal variances.

8. One-way ANOVA Example: Research design: between-subjects design
Research question: Is there a difference in sedentary behavior across four grade levels?
One independent variable: Grade with 4 levels: 9th, 10th, 11th, and 12th grade (Q3r).
One dependent variable: sedentary behavior (Q81: How many hours watch TV)
Higher score of Q81 = More hours on watching TV.

9. One-way ANOVA Running a one-way between-subjects ANOVA with SPSS.
Select Analyze General Linear Model Univariate
Move Q81
Move Q3r
Click Post Hoc

10. One-way ANOVA Post Hoc Comparisons
This analyses assess mean differences between all combinations of pairs of groups (6 comparions)
If the F ratios for the independent variable is significant
To determine which groups differ from which
It is a follow-up analysis
Check Tukey checkbox
Click Continue

11. One-way ANOVA Options In the Display box: check Descriptive statistics
Estimate of effect size
Homogeneity test
Click Continue
Then click OK

12. One-way ANOVA
SPSS output

13. One-way ANOVA SPSS output
The Leven’s test is about equal variance. p = .48, means homogeneous variances across four groups.

14. One-way ANOVA SPSS output
There was a significant difference across four grades in Q81, Q3r accounting for 1% of the total variance in Q81.

15. One-way ANOVA
SPSS output

16. One-way ANOVA
Results
The one-way ANOVA test showed there was a statistically significant difference across grade levels in sedentary behavior, F (3, 15709) = 26.86, p <.01, partial η2 = .01. A Tukey HSD test indicated that 9th (M = 3.91, SD = 1.76) and 10th (M = 3.83, SD= 1.76) graders spent more time on watching TV on average school day than 11th (M = 3.65, SD = 1.71)and 12th (M = 3.61, SD = 1.71) graders did (p < .01).

17. Factorial ANOVA Two-way between-subjects ANOVA
A factorial combination of two independent variables
Two main effects: comparing the means of the various levels of an independent variable. Each independent variable has its own main effect.
One interaction effect: reflects the effect associated with the various combinations of two independent variables.

18. Two-way ANOVA Example: Research design: between-subjects design
Research question: Is there a different relationship between grade levels and sedentary behavior across the gender?
Two independent variables: Grade with 4 levels: 9th, 10th, 11th, and 12th grade (Q3r); Gender (Q2) with two levels: female and male.
One dependent variable: sedentary behavior (Q81)

19. It is significant, which means violation of homogeneity of variance.
Two-way ANOVA
SPSS output
It is significant, which means violation of homogeneity of variance.

20. Two-way ANOVA Select Analyze General Linear Model Univariate
Click Plots

21. Two-way ANOVA
SPSS output
The interaction effect is significant

22. You might need to report this table for your paper
Two-way ANOVA
SPSS output
You might need to report this table for your paper

23. Two-way ANOVA
SPSS output

24. Two-way ANOVA Post hoc comparison
Selecting Female (use select cases), then running one- way ANOVA (Tukey as Post hoc test).
Selecting Male (use select cases), then running one-way ANOVA (Tukey as Post hoc test).

25. Two-way ANOVA Post hoc test for significant interaction effect Females

26. Two-way ANOVA
Results
The sedentary behavior was analyzed by means of a two-way between-subjects ANOVA test with four levels of grade and two levels of gender. All effects were statistically significant. The interaction effect, F (3, ) = 2.73, p < .05, partial η2 = .001, was analyzed using one-way ANOVA and Tukey HSD comparison test.

27. Two-way ANOVA
Results
For males, 9th and 10th graders spent more time on watching TV on average school day than 11th and 12th graders did.
For females, the pattern was different. There was no difference found in sedentary behavior between 10th and 12th graders.
Those results, collectively, produced the significant interaction effect.

28. Reference
Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc.

29. THANK YOU