📋 Daftar Isi
Berikut adalah cara manual Korelasi Kendall Tau.
Hipotesis
H0 : Tidak ada kesesuaian rangking skor hasil belajar statistik teori dan praktik mahasiswa pada tingkat populasi
H1 : Ada kesesuaian rangking skor hasil belajar statistik teori dan praktik mahasiswa pada tingkat populasi
Perankingan
Rangking berdasarkan urutan mahasiswa
.tg-wrap {padding-bottom:20px;} .tg {border-collapse:collapse;border-spacing:0;margin:0px auto;} .tg td{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-wa1i{font-weight:bold;text-align:center;vertical-align:middle} .tg .tg-6k50{text-align:center;vertical-align:middle} .tg .tg-sx1p{font-weight:bold;position:-webkit-sticky;position:sticky;text-align:center;top:-1px;vertical-align:middle; will-change:transform} .tg .tg-awal{width:20%;font-weight:bold;position:-webkit-sticky;position:sticky;text-align:center;top:-1px;vertical-align:middle; will-change:transform} .tg .tg-vkbb{font-weight:bold;text-align:center;vertical-align:middle} .tg .tg-nrix{text-align:center;vertical-align:middle} @media screen and (max-width: 767px) {.tg {width: auto !important;}.tg col {width: auto !important;}.tg-wrap {overflow-x: auto;-webkit-overflow-scrolling: touch;margin: auto 0px;}}| Mahasiswa | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ranking Nilai Statistik (T) | 3 | 4 | 2 | 1 | 8 | 11 | 10 | 6 | 7 | 12 | 5 | 9 |
| Ranking Nilai Statistik (P) | 2 | 6 | 5 | 1 | 10 | 9 | 8 | 3 | 4 | 12 | 7 | 11 |
Urutkan berdasarkan peringkat nilai statistik (T)
.tg-wrap {padding-bottom:20px;} .tg {border-collapse:collapse;border-spacing:0;margin:0px auto;} .tg td{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-wa1i{font-weight:bold;text-align:center;vertical-align:middle} .tg .tg-6k50{text-align:center;vertical-align:middle} .tg .tg-sx1p{font-weight:bold;position:-webkit-sticky;position:sticky;text-align:center;top:-1px;vertical-align:middle; will-change:transform} .tg .tg-awal{width:20%;font-weight:bold;position:-webkit-sticky;position:sticky;text-align:center;top:-1px;vertical-align:middle; will-change:transform} .tg .tg-vkbb{font-weight:bold;text-align:center;vertical-align:middle} .tg .tg-nrix{text-align:center;vertical-align:middle} @media screen and (max-width: 767px) {.tg {width: auto !important;}.tg col {width: auto !important;}.tg-wrap {overflow-x: auto;-webkit-overflow-scrolling: touch;margin: auto 0px;}}| Mahasiswa | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ranking Nilai Statistik (T) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Ranking Nilai Statistik (P) | 1 | 5 | 3 | 6 | 7 | 3 | 4 | 10 | 11 | 8 | 9 | 12 |
Sesudah mengatur rangking-rangking variabel X dalam urutan yang wajar, kita tetapkan S untuk rangking yang saling berhubungan dengan variabel Y.
.tg-wrap {overflow:auto;width:100%;padding-bottom:10px; margin-bottom:20px} #post-2259 > div.text-holder > div > div:nth-child(16) > table {width:140%;} .tgr {border-collapse:collapse;border-spacing:0;margin:0px auto;} .tgr td{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;word-break:normal;} .tgr th{border-bottom-width:1px;border-color:black;border-style:solid;border-top-width:1px;border-width:0px; font-family:Arial, sans-serif;font-size:14px;font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tgr .tg-6k50{text-align:center;vertical-align:middle} .tgr .tg-sx1p{font-weight:bold;position:-webkit-sticky;position:sticky;text-align:center;top:-1px;vertical-align:middle; will-change:transform} .tgr .tg-nrix{text-align:center;vertical-align:middle} .tgr .tg-vkbb{font-weight:bold;text-align:center;vertical-align:middle} @media screen and (max-width: 767px) {.tg {width: auto !important;}.tg col {width: auto !important;}.tg-wrap {overflow-x: auto;-webkit-overflow-scrolling: touch;margin: auto 0px;}}| Mahasiswa | 4 | 3 | 1 | 2 | 11 | 8 | 9 | 5 | 12 | 7 | 6 | 10 | ∑ C | ∑ D |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rxi | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
| Ryi | 1 | 5 | 2 | 6 | 7 | 3 | 4 | 10 | 11 | 8 | 9 | 12 | ||
| 1 | C | C | C | C | C | C | C | C | C | C | C | 11 | 0 | |
| 5 | D | C | C | D | D | C | C | C | C | C | 7 | 3 | ||
| 2 | C | C | C | C | C | C | C | C | C | 9 | 0 | |||
| 6 | C | D | D | C | C | C | C | C | 6 | 2 | ||||
| 7 | D | D | C | C | C | C | C | 5 | 2 | |||||
| 3 | C | C | C | C | C | C | 6 | 0 | ||||||
| 4 | C | C | C | C | C | 5 | 0 | |||||||
| 10 | C | D | D | C | 2 | 2 | ||||||||
| 11 | D | D | C | 1 | 2 | |||||||||
| 8 | C | C | 2 | 0 | ||||||||||
| 9 | C | 1 | 0 | |||||||||||
| 12 | 0 | 0 | ||||||||||||
| ∑∑ C = 55 | ∑∑ D = 11 |
\[
S = \sum \sum C – \sum \sum D
\]
\[
S = 55 – 11
\]
\[
S = 44
\]
Statistik Uji
Karena n > 10 dan tidak ada data kembar maka:
\[
\tau = \frac{2S}{n(n-1)}
\]
\[
\tau = \frac{2 \cdot 44}{12(21-1)}
\]
\[
\tau = 0,6667
\]
\[
z = \frac{\tau – \mu}{\sigma}
\]
\[
z = \frac{\tau – \mu}{\sqrt{ \frac{2(2n+5)}{9n(n-1)} }}
\]
\[
z = \frac{0,6667 – 0}{ \sqrt{ \frac{ 2( 2 \cdot 12 + 5 ) }{ 9(12)(12-1) } } }
\]
\[
z = \frac{0,6667}{0,221}
\]
\[
z = 3,0167
\]
\[
z_{tabel} = 2,58
\]
Keputusan
Karena (Zhit = 3,0167) > (Ztabel = 2,58); maka Tolak H0
Kesimpulan
Dengan tingkat signifikansi sebesar 1%, maka terdapat cukup bukti untuk mengatakan bahwa ada hubungan nilai mata kuliah statistik teori dan nilai mata kuliah statistik praktik.
Materi Lengkap
Untuk lebih memperdalam materi Korelasi Kendall Tau, maka Anda bisa baca juga bagian berikut:
