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

3. 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

4. Conceptual Understanding
Distinguish between: Between-group variability and within-group variability

5. 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

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

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

8. 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?

9. 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

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

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

14. Example
Freshman, Sophomore, Junior, Senior
Measure Happiness (1-100)

16. ANOVA Traditional F test just tells you not all the means are equal
Does not tell you which means are different from other means

17. Why not Do t-tests for all pairs Fresh vs. Sophomore Fresh vs. Junior
Fresh vs. Senior
Sophomore vs. Junior
Sophomore vs. Senior
Junior vs. Senior

18. Problem What if there were more than four groups?
Probability of a Type 1 error increases.
Maximum value = comparisons (.05)
6 (.05) = .30

19. Chapter 12 A Priori and Post Hoc Comparisons Multiple t-tests
Linear Contrasts
Orthogonal Contrasts
Trend Analysis
Bonferroni t
Fisher Least Significance Difference
Studentized Range Statistic
Dunnett’s Test

20. Multiple t-tests Good if you have just a couple of planned comparisons
Do a normal t-test, but use the other groups to help estimate your error term
Helps increase you df

21. Remember

22. Note

23. Proof
Candy Gender

25. t = / .641 = 4.16

26. t = / .641 = 4.16

27. t = / .641 = 4.16

28. t = / .641 = 4.16

29. Also, when F has 1 df between

30. Within Variability
Within variability of all the groups represents “error”
You can therefore get a better estimate of error by using all of the groups in your ANOVA when computing a t-value

31. Note: This formula is for equal n

32. Hyp 1: Juniors and Seniors will have different levels of happiness
Hyp 2: Seniors and Freshman will have different levels of happiness

33. Hyp 1: Juniors and Seniors will have different levels of happiness

34. Hyp 1: Juniors and Seniors will have different levels of happiness

35. Hyp 1: Juniors and Seniors will have different levels of happiness

36. Hyp 1: Juniors and Seniors will have different levels of happiness
t crit (20 df) = 2.086

37. Hyp 1: Juniors and Seniors will have different levels of happiness
t crit (20 df) = 2.086
Juniors and seniors do have significantly different levels of happiness

38. Hyp 2: Seniors and Freshman will have different levels of happiness

39. Hyp 2: Seniors and Freshman will have different levels of happiness

40. Hyp 2: Seniors and Freshman will have different levels of happiness

41. Hyp 2: Seniors and Freshman will have different levels of happiness
t crit (20 df) = 2.086

42. Hyp 2: Seniors and Freshman will have different levels of happiness
t crit (20 df) = 2.086
Freshman and seniors do not have significantly different levels of happiness

43. Hyp 1: Juniors and Sophomores will have different levels of happiness
Hyp 2: Seniors and Sophomores will have different levels of happiness
PRACTICE!

46. Chapter 12 A Priori and Post Hoc Comparisons Multiple t-tests
Linear Contrasts
Orthogonal Contrasts
Trend Analysis
Bonferroni t
Fisher Least Significance Difference
Studentized Range Statistic
Dunnett’s Test

48. Linear Contrasts
You think that Freshman and Seniors will have different levels of happiness than Sophomores and Juniors

49. Linear Contrasts
Allows for the comparison of one group or set of groups with another group or set of groups

50. Linear Contrasts
a = weight given to a group

51. Linear Contrasts a1 = 0, a2 = 0, a3 = 1, a4 = -1 L = -23

52. SS Contrast You can use the linear contrast to compute a SS contrast
SS contrast is like SS between
SS contrast has 1 df
SS contrast is like MS between

53. SS Contrast

54. SS Contrasts
a1 = .5, a2 = -.5, a3 = -.5, a4 = .5
L = 80.5 – 67 = 13.5

55. SS Contrasts a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5
Sum a2 = = 1

56. SS Contrasts a1 = .5, a2 = -.5, a3 = -.5, a4 = .5 L = 80.5 – 67 = 13.5
Sum a2 = = 1

57. SS Contrasts
a1 = 1, a2 = -1, a3 = -1, a4 = 1
L = 161 – 134 = 27

58. SS Contrasts a1 = 1, a2 = -1, a3 = -1, a4 = 1 L = 161 – 134 = 27 n = 6
Sum a2 = = 4

59. SS Contrasts a1 = 1, a2 = -1, a3 = -1, a4 = 1 L = 161 – 134 = 27 n = 6
Sum a2 = = 4

60. F Test
Note: MS contrast = SS contrast

61. F Test
Fresh & Senior vs. Sophomore & Junior

62. F Test
Fresh & Senior vs. Sophomore & Junior

63. F Test
Fresh & Senior vs. Sophomore & Junior
F crit (1, 20) = 4.35

64. SPSS

65. Make contrasts to determine
If seniors are happier than everyone else?
2) If juniors and sophomores have different levels of happiness?

66. If seniors are happier than everyone else?
a1 = -1, a2 = -1, a3 = -1, a4 = 3
L = 45
F crit (1, 20) = 4.35

68. 2) If juniors and sophomores have different levels of happiness?
a1 = 0, a2 = -1, a3 = 1, a4 = 0
L = -10
F crit (1, 20) = 4.35

71. Practice
To investigate the maternal behavior of lab rats, we move the rat pup a fixed distance from the mother and record the time required for the mother to retrieve the pup. We run the study with 5, 20, and 35 day old pups.
Figure out if 5 days is different than 35 days.
SPSS Homework (Do the ANOVA analysis in SPSS – use output to answer question above)
5 days 15 10 25 20 18
20 days 30 23
35 days 40 35 50 43 45