Matakuliah
Tahun
: Statistika Psikologi
: 2008
Uji Kesamaan Proporsi dan Uji Kebebasan
Pertemuan 24
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menghasilkan simpulan dari uji
kebebasan dan kesamaan proporsi.
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Outline Materi
• Uji kebebasan
• Uji kesamaan proporsi
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Uji Kebebasan
• Goodness of Fit Test: A Multinomial Population
• Tests of Independence: Contingency Tables
• Goodness of Fit Test: Poisson and Normal Distributions
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A Multinomial Population
1. Set up the null and alternative hypotheses.
2. Select a random sample and record the observed
frequency, fi , for each of the k categories.
3. Assuming H0 is true, compute the expected
frequency, ei , in each category by multiplying the
category probability by the sample size.
continued
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A Multinomial Population
4. Compute the value of the test statistic.
( f ii  eii ) 22
 
eii
ii11
22
kk
2
2



5. Reject H0 if

(where  is the significance level and there are k - 1
degrees of freedom).
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Test of Independence: Contingency
Tables
1. Set up the null and alternative hypotheses.
2. Select a random sample and record the
observed
frequency, fij , for each cell of the contingency
table.
3. Compute the expected frequency, eij , for
each cell.
eij 
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(Row i Total)(Column j Total)
Sample Size
8
Test of Independence: Contingency
Tables
4. Compute the test statistic.
2   
i
( f ij  eij ) 2
j
eij
5. Reject H0 if     (where  is the significance level
and with n rows and m columns there are
(n - 1)(m - 1) degrees of freedom).
2
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Contoh Soal : Finger Lakes Homes
(B)
• Contingency Table (Independence) Test
Price
Colonial Ranch Split-Level A-Frame
< $65,000
18
6
19
12
> $65,000
12
14
16
3
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Contoh Soal : Finger Lakes Homes

Contingency Table (Independence) Test
• Hypotheses
H0: Price of the home is independent of the style
of the home that is purchased
Ha: Price of the home is not independent of the
style of the home that is purchased
• Expected Frequencies
Price Colonial Ranch Split-Level A-Frame
< $99K
18
6
19
12
> $99K
12
14
16
3
Total
30
20
35
15
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Total
55
45
100
11
Contoh Soal : Finger Lakes Homes
• Contingency Table (Independence) Test
– Test Statistic
2
2
2
(
18

16
.
5
)
(
6

11
)
(
3

6
.
75
)
2 

 ... 
16. 5
11
6. 75
= .1364 + 2.2727 + . . . + 2.0833 = 9.1486
– Rejection Rule
.205  7.81
With  = .05 and (2 - 1)(4 - 1) = 3 d.f.,
Reject H0 if 2 > 7.81
– Conclusion
We reject H0, the assumption that the price of the
home is independent of the style of the home
that is purchased.
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• Selamat Belajar Semoga Sukses.
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