Rumus Skor Standar Z
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Rumus Skor Standar Z

Rabu, 17 Juni 2020

Transformasi linear z atau skor standar z adalah salah satu bentuk transformasi linear yang sering digunakan dalam statistik pendidikan. Skor standar Z seringkali digunakan untuk mengolah data hasil belajar siswa sekaigus memudahan perbandingan hasil belajar antar siswa dan antar kelas.

 

Bentuk rumus skor standar z sebenarnya diperoleh dari basis rumus transformasi linear. Perkembangannya rumus dasarnya hingga menjadi rumus skor standar Z sebagai berikut:

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Kedua konstanta a dan b di atas kemudian diinput kedalam rumus transformasi linear Y = aX + b

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Sehingga dapat disederhanakan menjadi bentuk ini:

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Oleh karena itu, jika mencermati rumus transformasi linear Y = aX + b maka rumus skor standar Z juga bisa dituliskan menjadi:

MathML (base64):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

Perubahan dari z kecil menjadi Z kapital dimaksudkan untuk menghindari agar tidak dijumpai skor z negatif, sehingga Zi=Xi. Ada beberapa pemahaman baru yang bisa didapat dari rumus di atas, diantaranya:

  • Mean baru = nol
  • Varian baru = satu
  • Simpangan baku baru = satu
  • Skor hasil transformasi linear merupakan distribusi z dengan mean=0 dan simpangan baru=1
  • Distribusi skor z masih serupa dengan distribusi skor lama, jadi kalau dari awal distribusinya tidak normal lalu diubah menjadi skor Z maka tetap tidak normal

Rumus skor standar z tidak berhenti berkembang sampai disitu, sebab para peneliti terus berupaya untuk mengembangkan skor standar terbaru yang lebih mudah diterima, khususnya untuk menghidndari nilai skor negatif.

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