Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 26
Uji Kebebasan
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menghasilkan
uji khi-kuadrat untuk uji kebebasan dan
faktor.
2
Outline Materi
•
•
•
•
Hasil pengamatan
Statistik uji khi-kuadrat
Nilai harapan pengamatan
Pengambilan keputusan
3
Uji Kebebasan
• Goodness of Fit Test: A Multinomial
Population
• Tests of Independence: Contingency
Tables
• Goodness of Fit Test: Poisson and
Normal Distributions
4
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
5
A Multinomial Population
4. Compute the value of the test statistic.
22
(
f

e
)
 22   ii ii
eii
ii11
kk
 2   2
5. Reject H0 if
(where  is the significance level and
there are k - 1 degrees of freedom).
6
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.
(Row i Total)(Column j Total)
eij 
Sample Size
7
Test of Independence:
Contingency Tables
4. Compute the test statistic.
2   
i
j
( f ij  eij ) 2
eij
2
2



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).
8
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
9
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
Total
55
45
100
10
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
With  = .05 and (2 - 1)(4 - 1) = 3 d.f.,
.205  7.81
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.
11
• Selamat Belajar Semoga Sukses.
12