By Hui Bian Office for Faculty Excellence 1. One-way ANOVA with SPSS Two-way Factorial ANOVA with SPSS How to interpret SPSS outputs How to report results.

By Hui BianOffice for Faculty Excellence

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One-way ANOVA with SPSSTwo-way Factorial ANOVA with SPSSHow to interpret SPSS outputsHow 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 studentsMultiple health behaviors include drinking,

smoking, exercise, eating habits, etc.

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ANOVA means Analysis of VarianceANOVA: compare means of two or more

levels of the independent variable One independent variableOne dependent variableThe basic test uses F distributionComparing means is a special case of a

regression analysis

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The partitioning of the totalsum 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 designBetween-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 considerationsIndependent 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 designResearch 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

UnivariateMove Q81 Move Q3rClick Post Hoc

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Post Hoc ComparisonsThis 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 whichIt is a follow-up analysisCheck Tukey checkbox Click Continue

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Options

In the Display box: check•Descriptive statistics•Estimate of effect size•Homogeneity test

Click ContinueThen 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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ResultsThe 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 ANOVAA factorial combination of two independent

variablesTwo 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 designResearch 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 comparisonSelecting 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

MalesFemale

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ResultsThe 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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ResultsFor 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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