Matakuliah
Tahun
: Statistika Psikologi
: 2008
Uji-uji Nonparametrik Lanjutan
Pertemuan 26
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
association between the rankings.
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Rank Correlation
• Spearman Rank-Correlation Coefficient, rs
rs  1 
6 d
2
i
n(n  1)
2
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
Analyst #1
Analyst #2
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A B C D E
1 4 9 8 6
1 5 6 2 9
F G H I J
3 5 7 2 10
7 3 10 4 8
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Contoh Soal: Connor Investors
Investment
A
B
C
D
E
F
G
H
I
J
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Analyst #1 Analyst #2
Rating
Rating
Differ. (Differ.)2
1
1
0
0
4
5
-1
1
9
6
3
9
8
2
6
36
6
9
-3
9
3
7
-4
16
5
3
2
4
7
10
-3
9
2
4
-2
4
10
8
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
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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
2
6 di
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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