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Jawaban Soal Korelasi Kendall Parsial

๐Ÿ“‹ Daftar Isi

Berikut adalah jawaban soal Korelasi Kendall Parsial.

Hipotesis

H0 : Tidak terdapat hubungan antara nilai statistik dengan nilai fisika bila nilai matematika dianggap konstan
H1 : Terdapat hubungan antara nilai statistik dengan nilai fisika bila nilai matematika dianggap konstan

Perangkingan

Misalkan :
X โ†’ Statistik
Y โ†’ Fisika
Z โ†’ Matematika

N = 5, sampel kecil, dan tidak ada observasi bernilai sama

Untuk nilai ฯ„xy

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Subjek Statistik Rank Statistik Fisika Rank Fisika Konkordan Diskordan
S 7 4 3 1 1 3
Q 8 5 4 2 0 3
R 5 2 6 3 1 1
T 4 1 7 4 1 0
P 6 3 8 5 0 0
Total P = 3 Q = 7
\[ S = P – Q \] \[ S = 3 – 7 \] \[ S = -4 \] \[ \tau_{xy} = \frac{S}{\frac{1}{2} N(N-1)} \] \[ \tau_{xy} = \frac{-4}{\frac{1}{2} (5)(5-1)} \] \[ \tau_{xy} = -0,4 \]

Untuk nilai ฯ„xz

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Subjek Statistik Rank Statistik Matematika Rank Matematika Konkordan Diskordan
P 6 3 9 5 0 0
Q 8 5 8 4 0 1
R 5 2 7 3 2 0
S 7 4 5 2 1 2
T 4 1 3 1 4 0
Total P = 7 P = 3
\[ S = P – Q \] \[ S = 7 – 3 \] \[ S = 4 \] \[ \tau_{xz} = \frac{S}{\frac{1}{2} N(N-1)} \] \[ \tau_{xz} = \frac{4}{\frac{1}{2} (5)(5-1)} \] \[ \tau_{xz} = 0,4 \]

Untuk nilai ฯ„yz

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Subjek Fisika Rank Fisika Matematika Rank Matematika Konkordan Diskordan
P 8 5 9 5 0 0
Q 4 2 8 4 1 0
R 6 3 7 3 1 1
S 3 1 5 2 4 0
T 7 4 3 1 1 3
Total P = 7 P = 4
\[ S = P – Q \] \[ S = 7 – 4 \] \[ S = 3 \] \[ \tau_{yz} = \frac{S}{\frac{1}{2} N(N-1)} \] \[ \tau_{yz} = \frac{3}{\frac{1}{2} (5)(5-1)} \] \[ \tau_{yz} = 0,3 \]

Statistik Uji

\[ \tau_{xy,z} = \frac{\tau_{xy} – \tau_{xz} \tau_{yz}}{\sqrt{(1-\tau_{xz}^2)(1-\tau_{yz}^2)}} \] \[ \tau_{xy,z} = \frac{-0,4 – (0,4)(0,3)}{\sqrt{(1-0,4^2)(1-0,3^2)}} \] \[ \tau_{xy,z} = 0,5163 \]

Keputusan

Untuk N = 5 dan merupakan uji dua arah

Sehingga akan Tolak H0 jika
– ฯ„hitung > ฯ„(1-ฮฑ/2;n) atau
– ฯ„hitung < -ฯ„(1-ฮฑ/2;n)

Nilai ฯ„(0,975;5) = 0.8 (Tabel S dibuku Castellan)

Maka Tolak H0

Kesimpulan

Dengan tingkat signifikansi sebesar 5%, maka terdapat cukup bukti untuk mengatakan bahwa terdapat hubungan antara nilai statistik dengan fisika jika nilai matematika dianggap konstan.


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