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- 1. 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 Next Slide
- 2. ANOVA Two 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” Next Slide Gender Males Females
- 3. Null Hypothesis For Ethnicity, the null hypothesis states that there is no difference between the means of the ??? ethnicities on the dependent variable ???. Next Slide
- 4. ANOVA Summary Table n-1 df T -df B SS T – SS B K-1 SS T - SS W Next Slide Total Within Between eta 2 Sig F MS df SS Source
- 5. Practice ANOVA’s 20 80 100 4 10 14 5 8 .625 .20 Next Slide Total Within Between eta 2 Sig F MS df SS Source Page 639 in 4 th ed, page 640 in 5 th ed
- 6. Determining F-critical df Numerator = df Between df Denominator = df Within df Between = 4 df Within = 10 F-crit = 3.48 at 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 H 0 Next Slide
- 7. Practice ANOVA’s 300 43 30 5.25 .30 Next Slide Total Within Between eta 2 Sig F MS df SS Source
- 8. Practice ANOVA’s 90 210 300 3 40 5.71 F-crit = 2.84 Y Next Slide Total Within Between eta 2 Sig F MS df SS Source 43 30 5.25 .30
- 9. Practice ANOVA’s 6.25 125 10 18 Next Slide Total Within Between eta 2 Sig F MS df SS Source
- 10. Practice ANOVA’s 6.25 118.75 125 8 10 18 .78 11.88 .066 .05 F-crit = 3.07 N Next Slide Total Within Between eta 2 Sig F MS df SS Source
- 11. Assumptions in ANOVA 1. Balanced Design 2. Homogeneity of Variance - At least 2 people in each “cell” Next Slide
- 12. Running an ANOVA in SPSS 2 Variables: Grouping Variable Score Variable Next Slide 5 3 8 7 7 1 5 7 7 2 3 8 8 5 9 7 8 6 7 9 White Hispanic Black Asian
- 13. Running an ANOVA in SPSS Analyze Compare Means One-Way ANOVA Next Slide
- 14. SPSS Output for One-Way ANOVA Next Slide We do not want to reject this H 0 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
- 15. 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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