This document discusses planned contrast ANOVA, which allows researchers to test specific hypotheses about group mean differences rather than an overall hypothesis. It provides an example comparing IQ scores of blondes, brunettes and redheads. Researchers can create contrast variables to test the hypotheses that blonde and brunette means equal each other and that blonde and brunette means together equal the redhead mean. Planned contrast ANOVA merges regression and ANOVA techniques to test these focused hypotheses rather than an overall difference in means.

1. 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

2. Being a “Not-Smart” Researcher One-Way 3 Level ANOVA Mean IQ Blondes = 105 Brunettes = 107 Redheads = 111.5 Next Slide

3. Being a “Smart” Researcher H 0 : Mean Blonde =Mean Brunette =Mean Redhead Blondes = 105 Brunettes = 107 Redheads = 111.5 Next Slide H 0 :M Blonde & M Brunette =M Red Probably is statistically significantly different H 0 :M Blonde =M Brunette Probably not statistically significantly different

4. Creating Contrast Variables Contrasts reflect the associations that we want to test Contrast 1 tests H 0 : M blondes =M brunettes Contrast 2 tests H 0 : M blondes & brunettes =M redheads Next Slide Maximum number of contrasts = K –1 -2 0 111.5 Redheads 1 -1 107 Brunettes 1 1 105 Blondes Contrast 2 Contrast 1 Mean

5. Practice Contrast Variables C1 – H 0 : M white =M black C2 – H 0 : M asian and hisp. =M nat.amer. C4 – H 0 : M w,a,na. =M b C3 – H 0 : M w,b,h,na =M a Next Slide 1 1 -2 0 Native American 0 1 1 0 Hispanic 1 -4 1 0 Asian -3 1 0 -1 Black 1 1 0 1 White C4 C3 C2 C1

6. Back to “IQ” – “Hair” Example Next Slide

7. Regression as ANOVA Analyze  Regression  Linear Next Slide

8. Planned Contrast ANOVA Output Next Slide

9. Planned Contrast ANOVA Output (cont.) SS c2 = 88.667 – 8.0 = 80.667 F-crit on 1 and 9 df = 5.12 Next Slide SS c2 =SS 2 regression – SS 1 regression Y N

10. Smart vs. Not-Smart Researchers Next Slide

11. A New Example Next Slide You will have 5 “Blocks.” C1 in Block 1; C2 in Block 2; etc.

12. SPSS Output for “New Example” Next Slide SS c2 =.333 - .250 SS c3 =.375 - .333 SS c4 =.400 - .375 SS c5 =370.417 - .400

13. Results for “New Example” Next Slide F-crit on 1 and 6 df = 5.99

14. “Other” Examples Next Slide -1 -1 -1 0 Group 5 -1 -1 1 0 Group 4 4 0 0 0 Group 3 -1 1 0 -1 Group 2 -1 1 0 1 Group 1 C4 C3 C2 C1

15. 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