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  1. Remember • You were asked to determine the effects of both college major (psychology, sociology, and biology) and gender (male and female) on class attendance

  2. Sociology Psychology Biology

  3. Simple Effects • The effect of one factor at one level on the other factor. • Use to “tease apart” a significant interaction • You wonder if college major has an effect on class attendance for just females? • You wonder if male and female psychology students differ in their class attendance?

  4. Sociology Psychology Biology

  5. Sociology Psychology Biology

  6. Sociology Psychology Biology

  7. Sociology Psychology Biology

  8. Sociology Psychology Biology

  9. Sociology Psychology Biology

  10. Simple Effects • Why not just do 5 new analyses • 2 ANOVAs • 3 Independent Samples t-tests • You will lose df! • Type I error problem still exists

  11. Sociology Psychology Biology

  12. Are these means different?

  13. Simple Effects • SS Major at Female • Represents the SS deviations of the treatment means around the Female mean • Its multiplied by n to give an estimate of the population variance (Central limit theorem) • Same formula as SSbetween in the one-way

  14. SS M at Female = 3*((2.67 – 1.78)2 + (1.00 – 1.78)2 + (1.67 – 1.78)2 = 4.23

  15. Note

  16. Sociology Psychology Biology

  17. Are these means different?

  18. Simple Effects • SS Major at Male • Same formula as SSbetween in the one-way

  19. SS M at Male = 3*((3.67 – 2.33)2 + (3.00 – 2.33)2 + (0.33 – 2.33)2 = 18.71

  20. Sociology Psychology Biology

  21. Are these means different?

  22. Simple Effects • SS Gender at Socio • Same formula as SSbetween in the one-way

  23. SS G at Socio = 3*((2.67 – 3.17)2 + (3.67 – 3.17)2 = 1.5

  24. Sociology Psychology Biology

  25. Are these means different?

  26. Simple Effects • SS Gender at Psych • Same formula as SSbetween in the one-way

  27. SS G at Psych = 3*((1.00 – 2.00)2 + (3.00 – 2.00)2 = 6.00

  28. Sociology Psychology Biology

  29. Are these means different?

  30. Simple Effects • SS Gender at Bio • Same formula as SSbetween in the one-way

  31. SS G at Bio = 3*((1.67 – 1.00)2 + (0.33 – 1.00)2 = 2.69

  32. Overall ANOVA

  33. Simple Effects

  34. Simple Effects

  35. Simple Effects dfA (Gender) = a – 1 dfB (Major) = b – 1

  36. Simple Effects Compute MS

  37. Simple Effects Compute F

  38. F critical (1, 12) = 4.75 F critical B (2, 12) = 3.89 Simple Effects

  39. Sociology Psychology Biology

  40. Practice • ANOVA is from exercise 13.5 • 1) Interpret the ANOVA results • 2) Plot the cell means • 3) Compute an entire set of simple effects