2. SPSS
SPSS Problem (Part 1)

3. SPSS Problem (Part 2)
Due Wed
12.1

4. 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

5. 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

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

7. 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

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

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

11. Linear Contrasts
a = weight given to a group

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

13. 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

14. SS Contrast

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

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

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

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

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

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

21. F Test
Note: MS contrast = SS contrast

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

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

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

25. SPSS

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

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

29. 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

32. 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

34. Contrasts Some contrasts are independent Some are not
Freshman vs. Sophomore
(1, -1, 0, 0)
Junior vs. Senior
(0, 0, 1, -1)
Some are not
Freshman vs. Sophomore, Junior, Senior
(3, -1, -1, -1)
Freshman vs. Sophomore & Junior
(2, -1, -1, 0)

35. Orthogonal Contrasts
If you have a complete set of orthogonal contrasts
The sum of SScontrast = SSbetween

36. Orthogonal Contrasts 1) ∑ aj = 0 2) ∑ aj bj = 0
Already talked about
2) ∑ aj bj = 0
Ensures contrasts of independent of one another
3) Number of comparisons = K -1
Ensures enough comparisons are used

37. Orthogonal Contrasts ∑ aj bj = 0 Fresh, Sophomore, Junior, Senior
(3, -1, -1, -1) and (2, -1, -1, 0)
(3*2)+(-1*-1)+(-1*-1) = 8

38. Orthogonal Contrasts ∑ aj bj = 0 Fresh, Sophomore, Junior, Senior
(-1, 1, 0, 0) & (0, 0, -1, 1)
(-1*0)+(1*0)+(-1*0)+(1*0) = 0
*Note: this is not a complete set of contrasts (rule 3)

39. Orthogonal Contrasts Lets go to five groups
What would the complete set contrasts be that would satisfy the earlier rules?

40. Orthogonal Contrasts
General rule
There is more than one right answer

41. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen

42. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen
2 limbs are created
The elements on different limbs can not be combined with each other
Elements on the same limbs can be combined with each other (making new limbs)

43. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen

44. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen

45. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen

46. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen
3, 3, -2, -2, -2

47. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen
3, 3, -2, -2, -2
1, -1, 0, 0, 0

48. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen
3, 3, -2, -2, -2
1, -1, 0, 0, 0
0, 0, 1, 1, -2

49. Orthogonal Contrasts Fresh, Soph, Jun, Sen, Grad
Fresh & Soph vs. Jun, Sen, & Grad
Fresh vs. Soph Jun & Sen vs. Grad
Jun vs. Sen
3, 3, -2, -2, -2
1, -1, 0, 0, 0
0, 0, 1, 1, -2
0, 0, 1, -1, 0

50. Orthogonal Contrasts 1) ∑ aj = 0 2) ∑ aj bj = 0
3) Number of comparisons = K -1
3, 3, -2, -2, -2
1, -1, 0, 0, 0
0, 0, 1, 1, -2
0, 0, 1, -1, 0

51. Orthogonal Contrasts 1) ∑ aj = 0 2) ∑ aj bj = 0
3) Number of comparisons = K -1
3, 3, -2, -2, -2 = 0
1, -1, 0, 0, 0 = 0
0, 0, 1, 1, -2 = 0
0, 0, 1, -1, 0 = 0

52. Orthogonal Contrasts A) 3, 3, -2, -2, -2 B) 1, -1, 0, 0, 0
D) 0, 0, 1, -1, 0
A, B = 0; A, C = 0; A, D = 0
B, C = 0; B, D = 0
C, D = 0

53. Orthogonal Contrasts
If you have a complete set of orthogonal contrasts
The sum of SScontrast = SSbetween

54. Compute a complete set of orthogonal contrasts for the following data.
Test each of the contrasts you create for significance

55. Orthogonal Contrasts Fresh, Soph, Jun, Sen Fresh & Soph vs. Jun & Sen
Fresh vs. Soph Jun vs Sen
1, 1, -1, -1
1, -1, 0, 0
0, 0, 1, -1

56. 1, 1, -1, -1
L = 1
SScontrast = 1.5; F = .014
1, -1, 0, 0
L = 4
SScontrast = 48; F = .48
0, 0, 1, -1
L = -23
SScontrast = 1587; F = 15.72*
F crit (1, 20) = 4.35

57. SScontrast = 1.5
SScontrast = 48
SScontrast = 1587 =
F crit (1, 20) = 4.35

58. Orthogonal Contrasts Why use them? People like that they sum together
People like that they are independent
History
I would rather have contrasts based on reason then simply because they are orthogonal!

60. 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

61. Trend Analysis
The logic of trend analysis is exactly the same logic we just talked about with contrasts!

62. Example
You collect axon firing rate scores from rats in one of four conditions.
Condition 1 = 10 mm of Zeta inhibitor
Condition 2 = 20 mm of Zeta inhibitor
Condition 3 = 30 mm of Zeta inhibitor
Condition 4 = 40 mm of Zeta inhibitor
Condition 5 = 50 mm of Zeta inhibitor
You think Zeta inhibitor reduces the number of times an axon fires – are you right?

63. What does this tell you ?

65. Trend Analysis
Contrast Codes!

66. Trend Analysis

67. a1 = -2, a2 = -1, a3 = 0, a4 = 1, a5 = 2
L = 7.2
F crit (1, 20) = 4.35

69. Note

70. Example
You place subjects into one of five different conditions of anxiety.
1) Low anxiety
2) Low-Moderate anxiety
3) Moderate anxiety
4) High-Moderate anxiety
5) High anxiety
You think subjects will perform best on a test at level 3 (and will do worse at both lower and higher levels of anxiety)

71. What does this tell you ?

73.
Contrast Codes!

74. Trend Analysis
Create contrast codes that will examine a quadratic trend.
-2, 1, 2, 1, -2

75. a1 = -2, a2 = 1, a3 = 2, a4 = 1, a5 = -2
L = 10
F crit (1, 20) = 4.35

77. Trend Analysis
How do you know which numbers to use?
Page 742

78. Linear
(NO BENDS)

79. Quadratic
(ONE BEND)

80. Cubic
(TWO BENDS)

82. Practice
You believe a balance between school and one’s social life is the key to happiness. Therefore you hypothesize that people who focus too much on school (i.e., people who get good grades) and people who focus too much on their social life (i.e., people who get bad grades) will be more depressed.
You collect data from 25 subjects
5 subjects = F
5 subjects = D
5 subjects = C
5 subjects = B
5 subjects = A
You measured their depression

83. Practice
Below are your findings – interpret!

84. Trend Analysis
Create contrast codes that will examine a quadratic trend.
-2, 1, 2, 1, -2

85. a1 = -2, a2 = 1, a3 = 2, a4 = 1, a5 = -2
L = -12.8
F crit (1, 20) = 4.35

89. Remember
Freshman, Sophomore, Junior, Senior
Measure Happiness (1-100)

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

92. 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

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

94. 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

95. Bonferoni t
Controls for Type I error by using a more conservative alpha

96. Do t-tests for all pairs
Fresh vs. Sophomore
Fresh vs. Junior
Fresh vs. Senior
Sophomore vs. Junior
Sophomore vs. Senior
Junior vs. Senior

97. Maximum probability of a Type I error
6 (.05) = .30
But what if we use
Alpha = .05/C
= .05 / 6
6 (.00855) = .05

98. t-table Compute the t-value the exact same way
Problem: normal t table does not have these p values
Test for significance using the Bonferroni t table (page 751)

99. Practice

101. Practice Fresh vs. Sophomore t = .69 Fresh vs. Junior t = 2.41
Fresh vs. Senior
t = -1.55
Sophomore vs. Junior
t = 1.72
Sophomore vs. Senior
t = -2.24
Junior vs. Senior
t = -3.97*
Critical t = 6 comp/ df = 20 = 2.93

102. Bonferoni t Problem Silly What should you use as the value in C?
Increases the chances of the Type II error!

103. Fisher Least Significance Difference
Simple
1) Do a normal omnibus ANOVA
2) If there it is significant you know that there is a difference somewhere!
3) Do individual t-test to determine where significance is located

104. Fisher Least Significance Difference
Problem
You may have an ANOVA that is not significant and still have results that occur in a manner that you predict!
If you used this method you would not have “permission” to look for these effects.

105. Remember

106. Remember

108. 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

109. Studentized Range Statistic
Which groups would you likely select to determine if they are different?

110. Studentized Range Statistic
Which groups would you likely select to determine if they are different?
This statistics controls for Type I error if (after looking at the data) you select the two means that are most different.

111. Studentized Range Statistic
Easy!
1) Do a normal t-test

112. Studentized Range Statistic
Easy!
2) Convert the t to a q

113. Studentized Range Statistic
3) Critical value of q (note: this is a two-tailed test)
Figure out df (same as t)
Example = 20
Figure out r
r = the number of groups

114. Studentized Range Statistic
3) Critical value of q (note: this is a two-tailed test)
Figure out df (same as t)
Example = 20
Figure out r
r = the number of groups
Example = 4

115. Studentized Range Statistic
3) Critical value of q
Page 744
Example
q critical = +/- 3.96

116. Studentized Range Statistic
4) Compare q obs and q critical same way as t values
q = -5.61
q critical = +/– 3.96

117. Practice
You collect axon firing rate scores from rates in one of four conditions.
Condition 1 = 10 mm of Zeta inhibitor
Condition 2 = 20 mm of Zeta inhibitor
Condition 3 = 30 mm of Zeta inhibitor
Condition 4 = 40 mm of Zeta inhibitor
Condition 5 = 50 mm of Zeta inhibitor
You are simply interested in determining if any two groups are different from each other – use the Studentized Range Statistic

118. Studentized Range Statistic
Easy!
1) Do a normal t-test

119. Studentized Range Statistic
Easy!
2) Convert the t to a q

120. Studentized Range Statistic
3) Critical value of qnote: this is a two-tailed test)
Figure out df (same as t)
Example = 20
Figure out r
r = the number of groups
Example = 5

121. Studentized Range Statistic
3) Critical value of q
Page 744
Example
q critical = +/- 4.23

122. Studentized Range Statistic
4) Compare q obs and q critical same way as t values
q = -4.34
q critical = +/– 4.23

123. Dunnett’s Test
Used when there are several experimental groups and one control group (or one reference group)
Example:
Effect of psychotherapy on happiness
Group 1) Psychoanalytic
Group 2) Humanistic
Group 3) Behaviorism
Group 4) Control (no therapy)

125. Psyana vs. Control
Human vs. Control
Behavior vs. Control

126. Psyana vs. Control = 47.8 – 51.4 = -3.6
Human vs. Control = 50.8 – = -0.6
Behavior vs. Control = 59 – 51.4 = 7.6

127. Psyana vs. Control = 47.8 – 51.4 = -3.6
Human vs. Control = 50.8 – = -0.6
Behavior vs. Control = 59 – 51.4 = 7.6
How different do these means need to be in order to reach significance?

131. Dunnett’s t is on page 753
df = Within groups df / k = number of groups

132. Dunnett’s t is on page 753
df = 16 / k = 4

133. Dunnett’s t is on page 753
df = 16 / k = 4

134. Psyana vs. Control = 47.8 – 51.4 = -3.6
Human vs. Control = 50.8 – = -0.6
Behavior vs. Control = 59 – 51.4 = 7.6*
How different do these means need to be in order to reach significance?

135. Practice
As a graduate student you wonder what undergraduate students (freshman, sophomore, etc.) have different levels of happiness then you.

137. Dunnett’s t is on page 753
df = 25 / k = 5

138. Fresh vs. Grad = -17.5*
Soph vs. Grad = -21.5*
Jun vs. Grad = -31.5*
Senior vs. Grad = -8.5