niversity of North Texas Dr. J. Kyle Roberts © 2004 Unit 9: Planned Contrast ANOVA Lesson 1: Merging Regression and ANOVA EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Planned Contrast Next Slide
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 9: Planned Contrast ANOVA
Lesson 1: Merging Regression and ANOVA
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
Planned Contrast
Next Slide
University of North Texas Dr. J. Kyle Roberts © 2004
Being a “Not-Smart” Researcher
One-Way 3 Level ANOVA•Mean IQ
•Blondes = 105•Brunettes = 107•Redheads = 111.5
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453.2
University of North Texas Dr. J. Kyle Roberts © 2004
Being a “Smart” Researcher
H0: MeanBlonde=MeanBrunette=MeanRedhead
•Blondes = 105
•Brunettes = 107
•Redheads = 111.5
H0:MBlonde & MBrunette=MRed
Probably is statistically significantly different
H0:MBlonde=MBrunette
Probably not statistically significantly different
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University of North Texas Dr. J. Kyle Roberts © 2004
Creating Contrast Variables
Mean Contrast 1 Contrast 2
Blondes 105 1 1
Brunettes 107 -1 1
Redheads 111.5 0 -2
Contrasts reflect the associations that we want to test
Contrast 1 tests H0: Mblondes=Mbrunettes
Contrast 2 tests H0: Mblondes & brunettes=Mredheads
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Maximum number of contrasts = K –1
University of North Texas Dr. J. Kyle Roberts © 2004
Practice Contrast VariablesC1 C2 C3 C4
White 1 0 1 1
Black -1 0 1 -3
Asian 0 1 -4 1
Hispanic 0 1 1 0
Native American
0 -2 1 1
C1 – H0: Mwhite=Mblack
C2 – H0: Masian and hisp.=Mnat.amer. C4 – H0: Mw,a,na.=Mb
C3 – H0: Mw,b,h,na=Ma
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University of North Texas Dr. J. Kyle Roberts © 2004
Back to “IQ” – “Hair” Example
3210
210
:2
:1
XXHc
XXHc
and
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University of North Texas Dr. J. Kyle Roberts © 2004
Regression as ANOVAAnalyze Regression Linear
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University of North Texas Dr. J. Kyle Roberts © 2004
Planned Contrast ANOVA Output
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University of North Texas Dr. J. Kyle Roberts © 2004
Planned Contrast ANOVA Output (cont.)
SSc2= 88.667 – 8.0 = 80.667
F-crit on 1 and 9 df = 5.12
Y
N
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SSc2=SS2 regression – SS1 regression
University of North Texas Dr. J. Kyle Roberts © 2004
Smart vs. Not-Smart Researchers
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University of North Texas Dr. J. Kyle Roberts © 2004
A New Example
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You will have 5 “Blocks.” C1 in Block 1; C2 in Block 2; etc.
University of North Texas Dr. J. Kyle Roberts © 2004
SPSS Output for “New Example”
SSc2=.333 - .250
SSc3=.375 - .333
SSc4=.400 - .375
SSc5=370.417 - .400
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University of North Texas Dr. J. Kyle Roberts © 2004
Results for “New Example”
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F-crit on 1 and 6 df = 5.99
University of North Texas Dr. J. Kyle Roberts © 2004
“Other” Examples
C1 C2 C3 C4
Group 1 1 0 1 -1
Group 2 -1 0 1 -1
Group 3 0 0 0 4
Group 4 0 1 -1 -1
Group 5 0 -1 -1 -1
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 9: Planned Contrast ANOVA
Lesson 1: Merging Regression and ANOVA
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
Planned Contrast
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