By Hui Bian Office for Faculty Excellence 1
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By Hui Bian
Office for Faculty Excellence
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One-way ANOVA with SPSS
Two-way Factorial ANOVA with SPSS
How to interpret SPSS outputs
How to report results
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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.
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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
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The partitioning of the total
sum of squares of deviations
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Total sum of Squares of
deviations of DV
Independent variable 1
Independent variable 2
Independent variable 3
Error
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.
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Data considerations 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.
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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.
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Running a one-way between-subjects ANOVA with SPSS. Select Analyze General Linear Model
Univariate
Move Q81
Move Q3r
Click Post Hoc
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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
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Options
In the Display box: check •Descriptive statistics •Estimate of effect size •Homogeneity test
Click Continue Then click OK
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SPSS output
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SPSS output
The Leven’s test is about equal variance. p = .48, means homogeneous variances across four groups.
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SPSS output
There was a significant difference across four grades in Q81, Q3r accounting for 1% of the total variance in Q81.
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SPSS output
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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).
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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.
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Example: Research design: between-subjects design
Research question: Is there a different relationship between grade levels and sedentary behavior across the gender? Two independent variable: 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)
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SPSS output
It is significant, which means violation of
homogeneity of variance.
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Select Analyze General Linear Model Univariate
Click Plots
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SPSS output
The interaction effect is significant
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SPSS output
You might need to report this table for your paper
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SPSS output
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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).
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Post hoc test for significant interaction effect
Males Females 25
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, 15687) = 2.73, p < .05, partial η2 = .001, was analyzed using one-way ANOVA and Tukey HSD comparison test.
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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.
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Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc.
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