unit 6 lesson 1
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 6: Analysis of Variance (ANOVA)
Lesson 1: Comparing 2 or More Sample Means
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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University of North Texas Dr. J. Kyle Roberts © 2004
ANOVATwo or more different groups measured on the same
construct, typically on the same occasion
Males ↔ Females
Hispanic ↔ Asian ↔ Black ↔ White ↔ Others
School1 ↔ School2 ↔ School3 ↔ School4
“Ways” and “Levels”
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GenderMalesFemales
University of North Texas Dr. J. Kyle Roberts © 2004
Null Hypothesis
43210 : SchoolSchoolSchoolSchool XXXXH
For Ethnicity, the null hypothesis states that there is no difference between the means of the ??? ethnicities on
the dependent variable ???.
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University of North Texas Dr. J. Kyle Roberts © 2004
ANOVA Summary Table
B
B
df
SS
W
B
MS
MS
T
B
SS
SS
W
W
df
SS
n-1
dfT-dfBSST – SSB
K-1SST - SSW
Total
Within
Between
eta2SigFMSdfSSSource
2XX i
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University of North Texas Dr. J. Kyle Roberts © 2004
Source SS df MS F Sig eta2
Between
Within
Total
Practice ANOVA’s
20
80
100
4
10
14
5
8
.625 .20
Page 639 in 4th ed, page 640 in 5th ed
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University of North Texas Dr. J. Kyle Roberts © 2004
Determining F-critical
df Numerator = df Betweendf Denominator = df Within
df Between = 4df Within = 10
F-crit = 3.48at the p = .05 level
If F-calc > F-crit, reject the null hypothesis
Since F-calc was 0.625 in our study, we fail to reject the H0
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University of North Texas Dr. J. Kyle Roberts © 2004
Source SS df MS F Sig eta2
Between
Within
Total
Practice ANOVA’s
300 43
30
5.25
.30
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University of North Texas Dr. J. Kyle Roberts © 2004
Practice ANOVA’s
90
210
300
3
40
5.71
Total
Within
Between
eta2SigFMSdfSSSource
43
30
5.25
.30
F-crit = 2.84
Y
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University of North Texas Dr. J. Kyle Roberts © 2004
Source SS df MS F Sig eta2
Between
Within
Total
Practice ANOVA’s
6.25
125
10
18
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University of North Texas Dr. J. Kyle Roberts © 2004
Source SS df MS F Sig eta2
Between
Within
Total
Practice ANOVA’s
6.25
118.75
125
8
10
18
.78
11.88
.066 .05
F-crit = 3.07
N
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University of North Texas Dr. J. Kyle Roberts © 2004
Assumptions in ANOVA
1. Balanced Design
2. Homogeneity of Variance
- At least 2 people in each “cell”
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XH ...: 3210
University of North Texas Dr. J. Kyle Roberts © 2004
Running an ANOVA in SPSS
Asian Black Hispanic White
9 7 6 8
7 9 5 8
8 3 2 7
7 5 1 7
7 8 3 5
2 Variables:Grouping VariableScore Variable
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University of North Texas Dr. J. Kyle Roberts © 2004
Running an ANOVA in SPSSAnalyzeCompare MeansOne-Way ANOVA
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University of North Texas Dr. J. Kyle Roberts © 2004
SPSS Output for One-Way ANOVADescriptives
SCORE
5 7.6000 .89443 .40000 6.4894 8.7106 7.00 9.00
5 6.4000 2.40832 1.07703 3.4097 9.3903 3.00 9.00
5 3.4000 2.07364 .92736 .8252 5.9748 1.00 6.00
5 7.0000 1.22474 .54772 5.4793 8.5207 5.00 8.00
20 6.1000 2.31471 .51759 5.0167 7.1833 1.00 9.00
Asian
Black
Hispanic
White
Total
N Mean Std. Deviation Std. Error Lower Bound Upper Bound
95% Confidence Interval forMean
Minimum Maximum
Test of Homogeneity of Variances
SCORE
2.636 3 16 .085
LeveneStatistic df1 df2 Sig.
ANOVA
SCORE
52.200 3 17.400 5.613 .008
49.600 16 3.100
101.800 19
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
We do not want to reject this H0
We reject the null hypothesis that the mean of the Asian students = the mean of the Black students = the mean of the Hispanic students = the mean of the White students
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 6: Analysis of Variance (ANOVA)
Lesson 1: Comparing 2 or More Sample Means
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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