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

Next Slide

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

Next Slide

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

Next Slide

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

Next Slide

University of North Texas Dr. J. Kyle Roberts © 2004

Back to “IQ” – “Hair” Example

3210

210

:2

:1

XXHc

XXHc

and

Next Slide

University of North Texas Dr. J. Kyle Roberts © 2004

Regression as ANOVAAnalyze Regression Linear

Next Slide

University of North Texas Dr. J. Kyle Roberts © 2004

Planned Contrast ANOVA Output

Next Slide

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

Next Slide

SSc2=SS2 regression – SS1 regression

University of North Texas Dr. J. Kyle Roberts © 2004

Smart vs. Not-Smart Researchers

Next Slide

University of North Texas Dr. J. Kyle Roberts © 2004

A New Example

Next Slide

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

Next Slide

University of North Texas Dr. J. Kyle Roberts © 2004

Results for “New Example”

Next Slide

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

Next Slide

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