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t-test
Dr. Tipsuda Janjamlha
23 Aug 08
t-test : Compute mean differences
1 one group t-test.
2 two independent groups t-test
3 two paired (dependent) groups t-test
1 one group t-test
compare ‘gr. mean’ with ‘constant’
A class of 30 students is given special training to
improve intelligence. After training, are their IQ
significantly different from 100 ?
105 112 128 98 98
106 116 124 98 97
107 125 106…..
100
2 two independent groups t-test
•To compare means of two independent samples.
•Ex. Measurements on the two difference samples
•Analysis performed on differences between group
means
105 112 128 98
112 128 98 98
106 116 124 98
•
124 98 97
107 125 106…..
•
125 …..
GROUP 1
GROUP 2
3 two paired (dependent) groups t-test
•To compare means of two non-dependent samples.
•Ex. Measurements on the same individuals before and
after a treatment
•Analysis performed on differences between individual
pairs of observations
105 112 128 98
112 128 98 98
106 116 124 98
•
124 98 97
107 106…..
•
125 …..
GROUP 1
GROUP 2
3 two paired (dependent) groups t-test
SUBJECT
Data1
Data2
Difference
1
105
112
-7
2
112
128
-16
3
128
98
-30
4
98
98
0
5
106
105
1
6
124
124
0
7
98
98
0
etc.
etc.
etc.
etc.
A Comparison of one or two group’s means
Questionnaire: 9
items
male
gender
Space
satisfaction
1..
2..
…
9..
female
natural
Window
views
building
Illness
recover
duration
ผูช้ ายเก็บความลับเก่งกว่าผูห้ ญิง
H 0 : male   female
H a : male   female
ผูใ้ ช้ครีมหน้าเด้งยีห่ อ้ A มีความพึงพอใจระดับมากในความเด้ง
H 0 :  sat. A  4
H a :  sat. A  4
คนอายุมากกับคนอายุนอ้ ยมีความขี้บ่นแตกต่างกัน H 0 : old   young
H a : old   young
ปริมาณผมบนศีรษะมีความสัมพันธ์กบั อาการใจน้อย
H0 :   0
Ha :   0
วัยรุน่ มักจะขับรถเร็วกว่าที่กฎหมายกาหนด (90 km/hr)
H 0 :   90
H a :   90
นักศึกษา APTU ใช้เวลานอนแตกต่างจากนักศึกษาคณะอื่น
H 0 :  APTU   Engineer   Medicine   Social
H a : มีค่าเฉลี่ยเวลานอนอย่างน้อย 1 คู่ที่แตกต่างกัน
Steps in t-test
Is the DV : interval/ratio and
IV : nominal level?
No
Yes
Find other
methods
Assumption of normality
To test assumption of normality:
- Explore the skewness, and kurtosis (-1 and + 1)
No
- Kolmogorov – Smirnov and Shapiro – Wilk test
Yes
Is there a pair or independent gr.?
Independent
Compute the independent t test
Pair
Compute the pair t test
Nonparametric
stat.
Assumption of Equal Variances:
See the p-value for the Levene’s test for equality of variances
p-value < alpha: not assumed
p-value > alpha: assumed
Equality not assumed
Equality assumed
Decision about Hypotheses:
Yes
Is the p-value for
the t test <= alpha?
Reject Ho,
difference between group
No
Not reject Ho,
no difference at all
Case1: 1 group t-test
The researcher wants to examine ‘the personal space bubble’ of the
TU students.
Sample: 24 TU students.
The international standard of the student space is 454 cm2 /person
465
456
438
454
447
449
442
449
446
447
468
433
454
463
450
446
447
456
452
444
447
456
456
435
Do the data provide sufficient evidence to conclude that the personal
space bubble of the TU students is different from the international
standard (454 cm2 /person).
Test of normality: analysis > descriptive statistics > explore…
Descriptives
SPA CE
Mean
95% Confidence
Interval for Mean
Low er Bound
Upper Bound
5% T rimmed Mean
Median
V ariance
Std. Deviation
Minimum
Maximum
Range
Interquart ile Range
Skew ness
Kurtosis
Statistic
450.0000
446.3420
Std. Error
1.76828
453.6580
449.9537
449.0000
75.043
8.66276
433.00
468.00
35.00
10.0000
.104
.084
.472
.918
Histogram
480
8
470
6
460
4
450
Frequency
2
440
Mean = 450.0
N = 24.00
0
435.0
430
N=
Std. Dev = 8.66
24
SPA C E
SPACE
440.0
445.0
450.0
455.0
460.0
465.0
470.0
1
2
3
Interpretation
1.
The TU student personal space is 450 cm2, SD =8.663
2.
t = -2.262 ,df=23,p=.033 ,so the TU space mean is not equal to
454 cm2 (standard)
‘TU space is less than the standard space’
Case2 : independent groups t-test
Crowding perception of 30 apartment residents and house
residents in Bangkok.
apartment residents
house residents
34.5 37.5 54.3 52.4 40.0 54.3 35.7 57.1 38.3 86.2 48.5 46.4 35.0
32.8 76.4 41.2 31.2 24.2 52.8 59.0 46.7 58.9 59.3 37.8 44.3 76.7
30.7 38.1 50.8 33.0 51.7 70.9 31.7 38.3 43.7 35.6 43.8 34.5 26.5
42.7 62.7 31.4 38.3 63.5 23.9 50.2 50.5 34.6 42.9 24.2 22.8 28.8
37.8 41.8 37.6 56.3 47.4 39.8 42.7 75.8 47.6 47.6 50.7 55.9 71.2
apartment
house
Resident
types
Crowing
perception
(Quantitative data)
Test of normality: analysis > descriptive statistics > explore…
Descriptives
CROWDING
RESIDENT
apartment
house
100
46
80
60
40
20
0
N =
RESIDENT
30
35
apartment
house
Mean
95% Confidence
Interval for Mean
5% T rimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquart ile Range
Skew ness
Kurtosis
Mean
95% Confidence
Interval for Mean
5% T rimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquart ile Range
Skew ness
Kurtosis
Low er Bound
Upper Bound
Low er Bound
Upper Bound
Statistic
44.33
39.43
Std. Error
2.397
49.24
43.78
40.60
172.335
13.128
24
76
53
19.05
.674
.009
46.56
41.43
.427
.833
2.525
51.69
45.87
44.30
223.151
14.938
23
86
63
20.30
.811
.572
.398
.778
1
1.1 การทดสอบ Levene test for Equality Ho :
F= 0.052, p=.820
Ha :
p> α (.05), so equal variances assumed
 12   22
 
2
1
2
2
2
interpretation
2
mean difference testing: Ho :
12   22
Ha :
12   22
t = -.635 , p = .529
p > α(.05), so not reject Ho.
There is no significant difference in crowding
perception mean between apartment and house
residents.
คนที่อาศัยในอพาร์ทเมนท์มีการรับรู้ความหนาแน่ นเฉลี่ยไม่แตกต่างจากคนที่
อาศัยในบ้าน
Case3 : pair (dependent) groups t-test
Car mileages , before and after added a new gasoline.
CAR
1
2
3
4
5
6
7
8
9
10
before
25.7
20.0
28.4
13.7
18.8
12.5
28.4
8.1
23.1
10.4
after
24.9
18.8
27.7
13.0
17.8
11.3
27.8
8.2
23.1
9.9
t = 4.714 , p= .001
p < α (.05), so reject Ho.
There is a .05 significant difference in car mileage mean
between before and after added a new gasoline. After adding
the gas, the car has a shorter mileage.
ค่าเฉลี่ยระยะทางก่อนและหลังเติมgasoline แตกต่างกันอย่างมีนัยสาคัญทางสถิติ
ที่ระดับ .05 โดยหลังเติม gasoline รถมีระยะทางการวิ่งลดลง