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