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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