2. Practice These are sample data from Diener et. al (1999). Participants were asked their marital status and how often they engaged in religious behavior. They also indicated how happy they were on a scale of 1 to 10. Examine the data

3. NeverOccasionallyOften Married637 278 459 Unmarried433 217 355 Frequency of religious behavior

7. Practice Participants were asked about their current romantic relationship (dating, married, or cohabitating) and the number of children they have (none, one, or two). They also indicated how many arguments they had with their romantic partner during the past year. Use the data on the next page to complete the incomplete ANOVA table.

8. SourcedfSSMSF Children188.58 Relationship356.04 AB371.96 Within Total1971.78

9. NoneOneTwo Dating253028 302531 282726 403520 2335 Married113123 182028 262235 152327 141921 Cohabitating231828 302421 18930 281630 231323 Number of children

10. SourcedfSSMSF Children2188.5894.293.22 Relationship2356.04178.026.07* AB4371.9692.993.17* Within361055.2029.31 Total441971.78 F critical A (2, 36) = 3.27 F critical B (2, 36) = 3.27 F critical AB (4, 36) = 2.64

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

15. Sociology Psychology Biology

16. 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?

17. Sociology Psychology Biology

23. 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

24. Sociology Psychology Biology

25. 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?

26. 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

27. 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

28. Note

29. Sociology Psychology Biology

30. 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?

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

32. 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

34. Sociology Psychology Biology

35. 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?

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

37. 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

39. Sociology Psychology Biology

40. 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?

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

42. 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

44. Sociology Psychology Biology

45. 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?

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

47. 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

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

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

51. 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

52. 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

53. 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

54. 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

55. 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

56. Sociology Psychology Biology

57. 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

64. 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

65. Handout

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