2. Six Easy Steps for an ANOVA
1) State the hypothesis
2) Find the F-critical value
3) Calculate the F-value
4) Decision
5) Create the summary table
6) Put answer into words

3. Example
Want to examine the effects of feedback on self-esteem. Three different conditions -- each have five subjects
1) Positive feedback
2) Negative feedback
3) Control
Afterward all complete a measure of self-esteem that can range from 0 to 10.

4. Example:
Question: Is the type of feedback a person receives significantly (.05) related their self-esteem?

5. Results

6. Step 1: State the Hypothesis
H1: The three population means are not all equal
H0: pos = neg = cont

7. Step 2: Find F-Critical Step 2.1
Need to first find dfbetween and dfwithin
dfbetween = k (k = number of groups)
dfwithin = N - k (N = total number of observations)
dftotal = N - 1
Check yourself
dftotal = dfbetween + dfwithin

8. Step 2: Find F-Critical Step 2.1
Need to first find dfbetween and dfwithin
dfbetween = (k = number of groups)
dfwithin = (N = total number of observations)
dftotal = 14
Check yourself
14 =

9. Step 2: Find F-Critical Step 2.2 Look up F-critical using table F

10. Step 2: Find F-Critical Step 2.2 Look up F-critical using table F

11. Step 3: Calculate the F-value
Has 4 Sub-Steps
3.1) Calculate the needed ingredients
3.2) Calculate the SS
3.3) Calculate the MS
3.4) Calculate the F-value

12. Step 3.1: Ingredients X
X2
Tj2 N n

13. Step 3.1: Ingredients

14. X
X = 85
Xp = 40
Xn = 25
Xc = 20

15. X2 X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90

16. T2 = (X)2 for each group X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20
T2n = 625
T2c = 400
T2p = 1600

17. Tj2 X = 85 X2 = 555 Tj2 = 2625 Xp = 40 Xn = 25 Xc = 20
T2n = 625
T2c = 400
T2p = 1600

18. N X = 85 X2 = 555 Tj2 = 2625 N = 15 Xp = 40 Xn = 25 Xc = 20
T2n = 625
T2c = 400
T2p = 1600

19. n X = 85 X2 = 555 Tj2 = 2625 N = 15 n = 5 Xp = 40 Xn = 25
Xc = 20
X2n = 135
X2c = 90
X2p = 330
T2n = 625
T2c = 400
T2p = 1600

20. Step 3.2: Calculate SS SStotal X = 85 X2 = 555 Tj2 = 2625 N = 15

21. Step 3.2: Calculate SS 85 73.33 555 15 SStotal X = 85 X2 = 555
Tj2 = 2625
N = 15
n = 5
Step 3.2: Calculate SS
SStotal 85
73.33
555 15

22. Step 3.2: Calculate SS SSWithin X = 85 X2 = 555 Tj2 = 2625 N = 15

23. Step 3.2: Calculate SS 2625 30 555 5 SSWithin X = 85 X2 = 555
Tj2 = 2625
N = 15
n = 5
Step 3.2: Calculate SS
SSWithin
2625 30
555 5

24. Step 3.2: Calculate SS SSBetween X = 85 X2 = 555 Tj2 = 2625 N = 15

25. Step 3.2: Calculate SS 43.33 2625 85 5 15 SSBetween X = 85 X2 = 555
Tj2 = 2625
N = 15
n = 5
Step 3.2: Calculate SS
SSBetween
43.33
2625 85 5 15

26. Step 3.2: Calculate SS
Check!
SStotal = SSBetween + SSWithin

27. Step 3.2: Calculate SS
Check!
73.33 =

28. Step 3.3: Calculate MS

29. Step 3.3: Calculate MS
43.33
21.67 2

30. Calculating this Variance Ratio

31. Step 3.3: Calculate MS 30
2.5 12

32. Step 3.4: Calculate the F value

33. Step 3.4: Calculate the F value
21.67
8.67
2.5

34. Step 4: Decision If F value > than F critical
Reject H0, and accept H1
If F value < or = to F critical
Fail to reject H0

35. Step 4: Decision If F value > than F critical
Reject H0, and accept H1
If F value < or = to F critical
Fail to reject H0

36. Step 5: Create the Summary Table

37. Step 6: Put answer into words
Question: Is the type of feedback a person receives significantly (.05) related their self-esteem?
H1: The three population means are not all equal
The type of feedback a person receives is related to their self-esteem

39. Practice
You are interested in comparing the performance of three models of cars. Random samples of five owners of each car were used. These owners were asked how many times their car had undergone major repairs in the last 2 years.

40. Results

41. Practice
Is there a significant (.05) relationship between the model of car and repair records?

42. Step 1: State the Hypothesis
H1: The three population means are not all equal
H0: V = F = G

43. Step 2: Find F-Critical Step 2.1
Need to first find dfbetween and dfwithin
Dfbetween = (k = number of groups)
dfwithin = (N = total number of observations)
dftotal = 14
Check yourself
14 =

44. Step 2: Find F-Critical Step 2.2
Look up F-critical using table F on pages
F (2,12) = 3.88

45. Step 3.1: Ingredients
X = 60
X2 = 304
Tj2 = 1400
N = 15
n = 5

46. Step 3.2: Calculate SS SStotal X = 60 X2 = 304 Tj2 = 1400 N = 15

47. Step 3.2: Calculate SS 60 64 304 15 SStotal X = 60 X2 = 304
Tj2 = 1400
N = 15
n = 5
Step 3.2: Calculate SS
SStotal 60 64
304 15

48. Step 3.2: Calculate SS SSWithin X = 60 X2 = 304 Tj2 = 1400 N = 15

49. Step 3.2: Calculate SS 1400 24 304 5 SSWithin X = 60 X2 = 304
Tj2 = 1400
N = 15
n = 5
Step 3.2: Calculate SS
SSWithin
1400 24
304 5

50. Step 3.2: Calculate SS SSBetween X = 60 X2 = 304 Tj2 = 1400 N = 15

51. Step 3.2: Calculate SS 40 1400 60 5 15 SSBetween X = 60 X2 = 304
Tj2 = 1400
N = 15
n = 5
Step 3.2: Calculate SS
SSBetween 40
1400 60 5 15

52. Step 3.2: Calculate SS
Check!
SStotal = SSBetween + SSWithin

53. Step 3.2: Calculate SS
Check!
64 =

54. Step 3.3: Calculate MS

55. Step 3.3: Calculate MS 40 20 2

56. Calculating this Variance Ratio

57. Step 3.3: Calculate MS 24 2 12

58. Step 3.4: Calculate the F value

59. Step 3.4: Calculate the F value20 10 2

60. Step 4: Decision If F value > than F critical
Reject H0, and accept H1
If F value < or = to F critical
Fail to reject H0

61. Step 4: Decision If F value > than F critical
Reject H0, and accept H1
If F value < or = to F critical
Fail to reject H0

62. Step 5: Create the Summary Table

63. Step 6: Put answer into words
Question: Is there a significant (.05) relationship between the model of car and repair records?
H1: The three population means are not all equal
There is a significant relationship between the type of car a person drives and how often the car is repaired

64. Conceptual Understanding
Complete the above table for an ANOVA having 3 levels of the independent variable and n = 20. Test for significant at .05.

65. Conceptual Understanding
Fcrit = 3.18
Complete the above table for an ANOVA having 3 levels of the independent variable and n = 20. Test for significant at .05.
Fcrit (2, 57) = 3.15

66. Conceptual Understanding
Distinguish between: Between-group variability and within-group variability
What do they measure? How do they work together?

67. Conceptual Understanding
Distinguish between: Between-group variability and within-group variability
Between concerns the differences between the mean scores in various groups
Within concerns the variability of scores within each group

68. Between and Within Group Variability
Between-group variability
Within-group variability

69. Between and Within Group Variability
sampling error + effect of variable
sampling error

70. Conceptual Understanding
Under what circumstance will the F ratio, over the long run, approach 1.00? Under what circumstances will the F ratio be greater than 1.00?

71. Conceptual Understanding
Under what circumstance will the F ratio, over the long run, approach 1.00? Under what circumstances will the F ratio be greater than 1.00?
F ratio will approach 1.00 when the null hypothesis is true
F ratio will be greater than 1.00 when the null hypothesis is not true

72. Conceptual Understanding
Without computing the SS within, what must its value be? Why?

73. Conceptual Understanding
The SS within is 0. All the scores within a group are the same (i.e., there is NO variability within groups)