explaining η2 单因素方差分析

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?
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.
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.
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
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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Data considerations
Independent variable (factor variable) is categorical.
Dependent variable should be quantitative (interval
level of measurement).
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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
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
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
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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SPSS output
It is significant, which means violation of homogeneity of variance. 19
Select Analyze
General Linear Model
Univariate Click Plots
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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,
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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.
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.
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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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.