2. 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.

3. Source df SS MS F
Children
188.58
Relationship
356.04 AB
371.96
Within
Total

4. None One Two Dating 25 30 28 31 27 26 40 35 20 23 Married 11 18 22 15
Number of children
None
One
Two
Dating 25 30 28 31 27 26 40 35 20 23
Married 11 18 22 15 14 19 21
Cohabitating 24 9 16 13

5. Source df SS MS F Children 2 188.58 94.29 3.22 Relationship 356.04
178.02
6.07* AB 4
371.96
92.99
3.17*
Within 36
29.31
Total 44
F critical A (2, 36) = 3.27
F critical B (2, 36) = 3.27
F critical AB (4, 36) = 2.64

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

10. Sociology Psychology Biology

11. 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?

12. Sociology Psychology Biology

13. Sociology Psychology Biology

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17. Sociology Psychology Biology

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

19. Sociology Psychology Biology

20. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
Are these means different?

21. 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

22. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
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

23. Note

24. Sociology Psychology Biology

25. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
Are these means different?

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

27. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
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

29. Sociology Psychology Biology

30. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
Are these means different?

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

32. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
SS G at Socio = 3*((2.67 – 3.17)2 + (3.67 – 3.17)2 = 1.5

34. Sociology Psychology Biology

35. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
Are these means different?

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

37. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
SS G at Psych = 3*((1.00 – 2.00)2 + (3.00 – 2.00)2 = 6.00

39. Sociology Psychology Biology

40. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
Are these means different?

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

42. Sociology Psychology Biology Mean Female 2.00 1.00 3.00 .00 Mean1j
2.67
1.67
1.78
Males
4.00
Mean2j
Mean.j
3.67
3.17
0.33
2.33
2.06
SS G at Bio = 3*((1.67 – 1.00)2 + (0.33 – 1.00)2 = 2.69

44. Overall ANOVA Source df SS MS F Gender 1 1.36 2.47 Major 2 14.16 7.08
12.87*
G x M
8.83
4.42
8.03*
Within 12
6.59
.55
Total 17
30.94

45. Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio
Major
M at Female
M at Male
Within 12
6.59
.55

46. Simple Effects Source df SS MS F 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
Within 12
6.59
.55

47. Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio
dfA (Gender) = a – 1
dfB (Major) = b – 1
Simple Effects
Source df SS MS F
Gender
G at Socio
G at Psych
G at Bio 1
1.50
6.00
2.69
Major
M at Female
M at Male 2
4.23
18.71
Within 12
6.59
.55

48. Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio
Compute MS
Simple Effects
Source df SS MS F
Gender
G at Socio
G at Psych
G at Bio 1
1.50
6.00
2.69
Major
M at Female
M at Male 2
4.23
18.71
2.12
9.36
Within 12
6.59
.55

49. Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio
Compute F
Simple Effects
Source df SS MS F
Gender
G at Socio
G at Psych
G at Bio 1
1.50
6.00
2.69
2.72
10.91
4.89
Major
M at Female
M at Male 2
4.23
18.71
2.12
9.36
3.85
17.02
Within 12
6.59
.55

50. Simple Effects Source df SS MS F Gender G at Socio G at Psych G at Bio
F critical (1, 12) = 4.75
F critical B (2, 12) = 3.89
Simple Effects
Source df SS MS F
Gender
G at Socio
G at Psych
G at Bio 1
1.50
6.00
2.69
2.72
10.91*
4.89*
Major
M at Female
M at Male 2
4.23
18.71
2.12
9.36
3.85
17.02*
Within 12
6.59
.55

51. Sociology Psychology Biology

52. 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

59. Source df SS MS F
Delay
D at Neutral
D at Area A
D at Area B 2
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
357.74
363.33
6.93
178.87
181.67
3.47
6.10*
6.19*
.12
Within 36
29.31

60. Handout

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

63. Bring computers to class!