2. Practice
I think it is colder in Philadelphia than in Anaheim ( = .10).
To test this, I got temperatures from these two places on the Internet.

3. Results
Philadelphia 52 53 54 61 55
Anaheim 77 75 67

4. Hypotheses Alternative hypothesis Null hypothesis
H1: Philadelphia < Anaheim
Null hypothesis
H0:  Philadelphia = or >  Anaheim

5. Step 2: Calculate the Critical t
df = N1 + N2 - 2
df = = 6
 = .10
One-tailed
t critical =

6. Step 3: Draw Critical Region
tcrit = -1.44

7. Now Step 4: Calculate t observed
tobs = (X1 - X2) / Sx1 - x2

8. X1= 275
X12= 15175
N1 = 5
X1 = 55
X2= 219
X22= 16043
N2 = 3
X2 = 73
219
275
16043
15175 3 5 5 3

9. = 3.05 X1= 275 X12= 15175 N1 = 5 X1 = 55 X2= 219 X22= 16043
15987
15175
15125 3 5 5 3 6
= 3.05

10. Step 4: Calculate t observed
-5.90 = ( ) / 3.05
Sx1 - x2 = 3.05
X1 = 55
X2 = 73

11. Step 5: See if tobs falls in the critical region
tcrit = -1.44
tobs = -5.90

12. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

13. Step 7: Put answer into words
We Reject H0, and accept H1
Philadelphia is significantly ( = .10) colder than Anaheim.

14. So far. . . . We have been doing independent samples designs
The observations in one group were not linked to the observations in the other group

15. Example
Philadelphia 52 53 54 61 55
Anaheim 77 75 67

16. Matched Samples Design
This can happen with:
Natural pairs
Matched pairs
Repeated measures

17. Natural Pairs
The pairing of two subjects occurs naturally (e.g., twins)

18. Matched Pairs
When people are matched on some variable (e.g., age)

19. Repeated Measures
The same participant is in both conditions

20. Matched Samples Design
In this type of design you label one level of the variable X and the other Y
There is a logical reason for paring the X value and the Y value

21. Matched Samples Design
The logic and testing of this type of design is VERY similar to what you have already done!

22. Example
You just invented a “magic math pill” that will increase test scores.
On the day of the first test you give the pill to 4 subjects. When these same subjects take the second test they do not get a pill
Did the pill increase their test scores?

23. Hypothesis One-tailed
Alternative hypothesis
H1: pill > nopill
In other words, when the subjects got the pill they had higher math scores than when they did not get the pill
Null hypothesis
H0: pill < or = nopill
In other words, when the subjects got the pill their math scores were lower or equal to the scores they got when they did not take the pill

24. Results Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2

25. Step 2: Calculate the Critical t
N = Number of pairs
df = N - 1
4 - 1 = 3
 = .05
t critical = 2.353

26. Step 3: Draw Critical Region
tcrit = 2.353

27. Step 4: Calculate t observed
tobs = (X - Y) / SD

28. Step 4: Calculate t observed
tobs = (X - Y) / SD

29. Step 4: Calculate t observed
tobs = (X - Y) / SD
X = 3.75
Y = 2.00

30. Step 4: Calculate t observed
tobs = (X - Y) / SD
Standard error of a difference

31. Step 4: Calculate t observed
tobs = (X - Y) / SD
SD = SD / N
N = number of pairs

32. S =

33. S = Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3 Test 2 w/o Pill (Y)

34. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
S =

35. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4
S =

36. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4 7
S =

37. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4 7
S = 13

38. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4 7
S = 13 4
4 - 1

39. S = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4 7
S = 13
12.25 4 3

40. .5 = Difference (D) 2 1 Test 1 w/ Pill (X) Mel 3 Alice 5 Vera 4 Flo 3
Test 2 w/o Pill (Y) 1 3 2
D = 7
D2 =13
N = 4 7
.5 =
.75 4 3

41. Step 4: Calculate t observed
tobs = (X - Y) / SD
SD = SD / N
N = number of pairs

42. Step 4: Calculate t observed
tobs = (X - Y) / SD
.25=.5 / 4
N = number of pairs

43. Step 4: Calculate t observed
7.0 = ( ) / .25

44. Step 5: See if tobs falls in the critical region
tcrit = 2.353

45. Step 5: See if tobs falls in the critical region
tcrit = 2.353
tobs = 7.0

46. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

47. Step 7: Put answer into words
Reject H0, and accept H1
When the subjects took the “magic pill” they received statistically ( = .05) higher math scores than when they did not get the pill

48. SPSS

50. New Step Should add a new page Determine if One-sample t-test
Two-sample t-test
If it is a matched samples design
If it is a independent samples

51. Thus, there are 3 different kinds of designs
Each design uses slightly different formulas
You should probably make up ONE cook book page (with all 7 steps) for each type of design
Will help keep you from getting confused on a test

53. Practice Does drinking milkshakes affect (alpha = .05) your weight?
To see if milkshakes affect a persons weight you collected data from 5 sets of twins. You randomly had one twin drink water and the other twin drank milkshakes. After 3 months you weighed them.

54. Results Water Twin A 186 Twin B 200 Twin C 190 Twin D 162 Twin E 175
Milkshakes
195
202
196
165
183

55. Hypothesis Two-tailed
Alternative hypothesis
H1: water = milkshake
Null hypothesis
H0: water = milkshake

56. Step 2: Calculate the Critical t
N = Number of pairs
df = N - 1
5 - 1 = 4
 = .05
t critical = 2.776

57. Step 3: Draw Critical Region
tcrit =
tcrit = 2.776

58. Step 4: Calculate t observed
tobs = (X - Y) / SD

59. (D) -9 -2 -6 -3 -8
D = -28
D2 =194
N = 6
-28
3.04 =
194 5
5 - 1

60. Step 4: Calculate t observed
tobs = (X - Y) / SD
1.36=3.04 / 5
N = number of pairs

61. Step 4: Calculate t observed
-4.11 = (182.6 – 188.2) / 1.36
X = 182.6
Y = 188.2
SD = 1.36

62. Step 5: See if tobs falls in the critical region
tcrit =
tcrit = 2.776
tobs = -4.11

63. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

64. Step 7: Put answer into words
Reject H0, and accept H1
Milkshakes significantly ( = .05) affect a persons weight.

66. Practice
You wonder if psychology majors have higher IQs than sociology majors ( = .05)
You give an IQ test to 4 psychology majors and 4 sociology majors

67. Results
Psychology
110
150
140
135
Sociology 90 95 80 98

68. Step 1: Hypotheses Alternative hypothesis Null hypothesis
H1: psychology > sociology
Null hypothesis
H0: psychology = or < sociology

69. Step 2: Calculate the Critical t
df = N1 + N2 - 2
df = = 6
 = .05
One-tailed
t critical = 1.943

70. Step 3: Draw Critical Region
tcrit = 1.943

71. Now Step 4: Calculate t observed
tobs = (X1 - X2) / Sx1 - x2

72. X1= 535
X12= 72425
N1 = 4
X1 =
X2= 363
X22= 33129
N2 = 4
X2 = 90.75
9.38 =
363
535
72425
33129 4 4
4 (4 - 1)

73. Step 4: Calculate t observed
4.58 = ( ) / 9.38
Sx1 - x2 = 9.38
X1 =
X2 = 90.75

74. Step 5: See if tobs falls in the critical region
tcrit = 1.943
tobs = 4.58

75. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

76. Step 7: Put answer into words
We Reject H0, and accept H1
Psychology majors have significantly ( = .05) higher IQs than sociology majors.

77. Practice
I think it is colder in Philadelphia than in Anaheim ( = .10).
To test this, I got temperatures from these two places on the Internet.

78. Results
Philadelphia 52 53 54 61 55
Anaheim 77 75 67

79. Hypotheses Alternative hypothesis Null hypothesis
H1: Philadelphia < Anaheim
Null hypothesis
H0:  Philadelphia = or >  Anaheim

80. Step 2: Calculate the Critical t
df = N1 + N2 - 2
df = = 6
 = .10
One-tailed
t critical =

81. Step 3: Draw Critical Region
tcrit = -1.44

82. Now Step 4: Calculate t observed
tobs = (X1 - X2) / Sx1 - x2

83. = 3.05 X1= 275 X12= 15175 N1 = 5 X1 = 55 X2= 219 X22= 16043
15987
15175
15125 3 5 5 3 6
= 3.05

84. Step 4: Calculate t observed
-5.90 = ( ) / 3.05
Sx1 - x2 = 3.05
X1 = 55
X2 = 73

85. Step 5: See if tobs falls in the critical region
tcrit = -1.44
tobs = -5.90

86. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

87. Step 7: Put answer into words
We Reject H0, and accept H1
Philadelphia is significantly ( = .10) colder than Anaheim.

88. Practice
You just created a new program that is suppose to lower the number of aggressive behaviors a child performs.
You watched 6 children on a playground and recorded their aggressive behaviors. You gave your program to them. You then watched the same children and recorded this aggressive behaviors again.

89. Practice
Did your program significantly lower ( = .05) the number of aggressive behaviors a child performed?

90. Results Time 1 (X) Child1 18 Child2 11 Child3 19 Child4 6 Child5 10
Time 2 (Y) 16 10 17 4 11 12

91. Hypothesis One-tailed
Alternative hypothesis
H1: time1 > time2
Null hypothesis
H0: time1 < or = time2

92. Step 2: Calculate the Critical t
N = Number of pairs
df = N - 1
6 - 1 = 5
 = .05
t critical = 2.015

93. Step 4: Calculate t observed
tobs = (X - Y) / SD

94. 1.21 = (D) 2 1 -1 Time 1 (X) Child1 18 Child2 11 Child3 19 Child4 6
Test 2 (Y) 16 10 17 4 11 12
D = 8
D2 =18
N = 6 8
1.21 = 18 6
6 - 1

95. Step 4: Calculate t observed
tobs = (X - Y) / SD
.49=1.21 / 6
N = number of pairs

96. Step 4: Calculate t observed
2.73 = ( ) / .49
X = 13
Y = 11.66
SD = .49

97. Step 5: See if tobs falls in the critical region
tcrit = 2.015
tobs = 2.73

98. Step 6: Decision If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

99. Step 7: Put answer into words
Reject H0, and accept H1
The program significantly ( = .05) lowered the number of aggressive behaviors a child performed.

100. SPSS

102. Practice
An early hypothesis of schizophrenia was that it has a simple genetic cause. In accordance with the theory 25% of the offspring of a selected group of parents would be expected to be diagnosed as schizophrenic. Suppose that of 140 offspring, 19.3% were schizophrenic. Test this theory.

103. Goodness of fit chi-square
Make sure you compute the Chi square with the frequencies.
Chi square observed = 2.439
Critical = 3.84
These data are consistent with the theory!

105. Practice
In the 1930’s 650 boys participated in the Cambridge-Somerville Youth Study. Half of the participants were randomly assigned to a delinquency-prevention pogrom and the other half to a control group. At the end of the study, police records were examined for evidence of delinquency. In the prevention program 114 boys had a police record and in the control group 101 boys had a police record. Analyze the data and write a conclusion.

106. Chi Square observed = 1.17 Chi Square critical = 3.84 Phi = .04
Note the results go in the opposite direction that was expected!

107. Practice
A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. Determine if age is related to life satisfaction.

108. Older Adults
Younger Adults 45 34 38 22 52 15 48 27 25 37 39 41 51 24 46 19 55 26 36

109. Age is related to life satisfaction.
Older
Younger
Mean = 44.5
Mean = 28.1
S =
S =
S2 =
S2 =
tobs = 4.257; t crit = 2.101
Age is related to life satisfaction.

110. Practice
Sleep researchers decide to test the impact of REM sleep deprivation on a computerized assembly line task. Subjects are required to participate in two nights of testing. On each night of testing the subject is allowed a total of four hours of sleep. However, on one of the nights, the subject is awakened immediately upon achieving REM sleep. Subjects then took a cognitive test which assessed errors in judgment. Did sleep deprivation lower the subjects cognitive ability?

111. REM Deprived
Control Condition 26 20 15 4 8 9 44 36 13 3 38 25 24 10 17 6 29 14

112. tobs = 6.175
 tcrit = 1.83
Sleep deprivation lowered their cognitive abilities.

113. SPSS Problem #2
7.37
7.11