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, r s
, is a measure of association between two variables when only ordinal data are available.
• Values of r s 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, r s r s
6
 d i
2 n n 2  1) where: n = number of items being ranked x i
= rank of item i with respect to one variable y i
= rank of item i with respect to a second variable d i
= x i
y i
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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 p s
.
• To do so, we must test the hypotheses:
H
0
: p s
= 0
H a
: p s
≠ 0
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Rank Correlation
• Sampling Distribution of r s
– Mean
 r s
 0 when p s
= 0
– Standard Deviation
 r s
 n
1
 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 Rating
A 1
B
C
4
9
G
H
I
J
D
E
F
8
6
3
5
7
2
10
Rating Differ. (Differ.) 2
1 0 0
5
6
-1
3
1
9
2
9
7
6
-3
-4
36
9
16
3
10
4
8
2
-3
-2
2 4
Sum = 92
4
9
4
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Contoh Soal: Connor Investors
• Hypotheses
H
0
: p s
= 0 (No rank correlation exists.)
H a
: p s
= 0 (Rank correlation exists.)
• Sampling Distribution
Sampling distribution of r s under the assumption of no rank correlation
 r s

1
 .333
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= 0 r s
11

Contoh Soal: Connor Investors
• Rejection Rule
Using .10 level of significance,
Reject H
0
• Test Statistic r s if z < -1.645 or z > 1.645
6
 d i
2 n n 2  1)
6(92)
 0.4424
z = ( r s
• Conclusion
-
 r
)/
 r
= (.4424 - 0)/.3333 = 1.33
Do no reject H
0
. 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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