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
Total sum of
Squares of
deviations of DV
Independent
variable 1
Independent
variable 2
Independent
variable 3
Error
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 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 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)
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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
Females
Males
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 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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