Matakuliah
Tahun
Versi
: I0284 - Statistika
: 2005
: Revisi
Pertemuan 26
Uji-uji Nonparametrik Lanjutan
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menghasilkan
simpulan hasil uji Krushal Wallis, Friedman
dan Koefisien Korelasi.
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Outline Materi
• Uji kruskal Wallis
• Uji Friedman
• Koefisien korelasi peringkat Spearman
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Rank Correlation
• The Pearson correlation coefficient, r, is a
measure of the linear association between two
variables for which interval or ratio data are
available.
• The Spearman rank-correlation coefficient, rs , is
a measure of association between two variables
when only ordinal data are available.
• Values of rs can range from –1.0 to +1.0, where
– values near 1.0 indicate a strong positive
association between the rankings, and
– values near -1.0 indicate a strong negative
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association between the rankings.
Rank Correlation
• Spearman Rank-Correlation Coefficient, rs
rs  1 
6 di2
n(n2  1)
where: n = number of items being ranked
xi = rank of item i with respect to one variable
yi = rank of item i with respect to a second
variable
di = xi - yi
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Test for Significant Rank
Correlation
• We may want to use sample results to
make an inference about the population
rank correlation ps.
• To do so, we must test the hypotheses:
H0: ps = 0
Ha: ps ≠ 0
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Rank Correlation
• Sampling Distribution of rs when ps = 0
– Mean
r  0
s
– Standard Deviation
1
 rs 
n1
– Distribution Form
Approximately normal, provided n > 10
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Contoh Soal: Connor Investors
• Rank Correlation
Connor Investors provides a portfolio
management service for its clients. Two of
Connor’s analysts rated ten investments from
high (6) to low (1) risk as shown below. Use
rank correlation, with a = .10, to comment on
the agreement of the two analysts’ ratings.
Investment A B C D E F G H I J
Analyst #1 1 4 9 8 6 3 5 7 2 10
Analyst #2 1 5 6 2 9 7 3 10 4 8
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Contoh Soal: Connor Investors
Analyst #1 Analyst #2
Investment
A
B
C
D
E
F
G
H
I
J
Rating
1
4
9
8
6
3
5
7
2
10
Rating
1
5
6
2
9
7
3
10
4
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Differ. (Differ.)2
0
0
-1
1
3
9
6
36
-3
9
-4
16
2
4
-3
9
-2
4
2
4
Sum =92
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Contoh Soal: Connor
Investors
• Hypotheses
H0: ps = 0 (No rank correlation exists.)
Ha: ps = 0 (Rank correlation exists.)
• Sampling Distribution
Sampling distribution of
rs under the assumption
of no rank correlation
1
 rs 
 .333
10  1
r = 0
rs
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Contoh Soal: Connor Investors
• Rejection Rule
Using .10 level of significance,
Reject H0 if z < -1.645 or z > 1.645
• Test Statistic
6 di2
6(92)
rs  1 
1
 0.4424
2
n(n  1)
10(100  1)
z = (rs - r )/r = (.4424 - 0)/.3333 = 1.33
• Conclusion
Do no reject H0. There is not a significant
rank correlation. The two analysts are not
showing agreement in their rating of the risk
associated with the different investments.
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• Selamat Belajar Semoga Sukses.
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