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

4. Sociology Psychology Biology

5. 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?

6. Sociology Psychology Biology

12. 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

13. Sociology Psychology Biology

14. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 Are these means different?

15. 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 SS between in the one-way

16. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 SS M at Female = 3*((2.67 – 1.78) 2 + (1.00 – 1.78) 2 + (1.67 – 1.78) 2 = 4.23

17. Note

18. Sociology Psychology Biology

19. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 Are these means different?

20. Simple Effects SS Major at Male –Same formula as SS between in the one-way

21. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 SS M at Male = 3*((3.67 – 2.33) 2 + (3.00 – 2.33) 2 + (0.33 – 2.33) 2 = 18.71

23. Sociology Psychology Biology

24. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 Are these means different?

25. Simple Effects SS Gender at Socio –Same formula as SS between in the one-way

26. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 SS G at Socio = 3*((2.67 – 3.17) 2 + (3.67 – 3.17) 2 = 1.5

28. Sociology Psychology Biology

29. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 Are these means different?

30. Simple Effects SS Gender at Psych –Same formula as SS between in the one-way

31. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 SS G at Psych = 3*((1.00 – 2.00) 2 + (3.00 – 2.00) 2 = 6.00

33. Sociology Psychology Biology

34. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 Are these means different?

35. Simple Effects SS Gender at Bio –Same formula as SS between in the one-way

36. SociologyPsychologyBiologyMean Female2.001.00 3.00.002.00 3.002.00 Mean 1j 2.671.001.671.78 Males4.002.001.00 3.004.00.00 4.003.00.00 Mean 2j Mean.j 3.67 3.17 3.00 2.00 0.33 1.00 2.33 2.06 SS G at Bio = 3*((1.67 – 1.00) 2 + (0.33 – 1.00) 2 = 2.69

38. Overall ANOVA SourcedfSSMSF Gender11.36 2.47 Major214.167.0812.87* G x M28.834.428.03* Within126.59.55 Total1730.94

39. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio Major M at Female M at Male Within126.59.55

40. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio 1.50 6.00 2.69 Major M at Female M at Male 4.23 18.71 Within126.59.55

41. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio 111111 1.50 6.00 2.69 Major M at Female M at Male 2222 4.23 18.71 Within126.59.55 dfA (Gender) = a – 1 dfB (Major) = b – 1

42. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio 111111 1.50 6.00 2.69 1.50 6.00 2.69 Major M at Female M at Male 2222 4.23 18.71 2.12 9.36 Within126.59.55 Compute MS

43. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio 111111 1.50 6.00 2.69 1.50 6.00 2.69 2.72 10.91 4.89 Major M at Female M at Male 2222 4.23 18.71 2.12 9.36 3.85 17.02 Within126.59.55 Compute F

44. Simple Effects SourcedfSSMSF Gender G at Socio G at Psych G at Bio 111111 1.50 6.00 2.69 1.50 6.00 2.69 2.72 10.91* 4.89* Major M at Female M at Male 2222 4.23 18.71 2.12 9.36 3.85 17.02* Within126.59.55 F critical (1, 12) = 4.75 F critical B (2, 12) = 3.89

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46. 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

51. SourcedfSSMSF Delay D at Neutral D at Area A D at Area B 222222 1.20 254.80 304.53 0.60 127.40 152.26.02 4.34* 5.19* Area A at D 50 A at D 100 A at D 150 222222 357.74 363.33 6.93 178.87 181.67 3.47 6.10* 6.19*.12 Within361055.2029.31

52. SPSS Problem 13.1 Compute a factorial ANOVA Conduct a complete set of simple effects (you can do this by hand)