Pada pemilihan ketua Osis di SMAN 18 Kota Batam, didapatkan hasil pemungutan suara seba berikut: multirow(2)(*)( Pemungutan suara ) & multicolumn(2)(|c|)( Nama Calon Ketua Osis ) cline ( 2 - 3 ) & Robby (R) & Adhit (A) Kelas X & 15 & 80 Kelas XI & 42 & 56 Kelas XII & 44 & 72 Berdasarkan data di atas, tentukan nilai U yang akan digunakan dalam Uji Mann-Whitney!

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Pertanyaan

Pada pemilihan ketua Osis di SMAN 18 Kota Batam, didapatkan hasil pemungutan suara seba berikut: multirow(2)(*)( Pemungutan suara ) & multicolumn(2)(|c|)( Nama Calon Ketua Osis ) cline ( 2 - 3 ) & Robby (R) & Adhit (A) Kelas X & 15 & 80 Kelas XI & 42 & 56 Kelas XII & 44 & 72 Berdasarkan data di atas, tentukan nilai U yang akan digunakan dalam Uji Mann-Whitney!

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Answer 1

Nilai U yang akan digunakan dalam Uji Mann-Whitney adalah nilai U terkecil dari perhitungan di atas setelah menghitung dan merangking semua suara.

Answer 2

Step 1:

Understanding the Mann-Whitney U Test

The Mann-Whitney U test is a non-parametric test used to determine whether there is a difference between two independent groups. In this context, we are comparing the votes received by Robby and Adhit across different classes.

Step 2:

Organizing the Data

We have two groups:

votes for Robby (R) and votes for Adhit (A). The data from the table is as follows:
- Kelas X: R = 15, A = 80
- Kelas XI: R = 42, A = 56
- Kelas XII: R = 44, A = 72

Step 3:

Calculating the Total Votes

Calculate the total number of votes for each candidate:

- Total votes for Robby (R): \(15 + 42 + 44 = 101\)
- Total votes for Adhit (A): \(80 + 56 + 72 = 208\)

Step 4:

Ranking the Data

Combine all the votes into a single list and rank them. Assign ranks starting from 1 for the smallest value. If there are ties, assign the average rank to the tied values.

Step 5:

Calculating the U Value

The formula for calculating the U statistic for each group is:

\[ U_1 = n_1 \cdot n_2 + \frac{n_1(n_1+1)}{2} - R_1 \]
\[ U_2 = n_1 \cdot n_2 + \frac{n_2(n_2+1)}{2} - R_2 \]
Where:
- \( n_1 \) and \( n_2 \) are the sample sizes for groups 1 and 2.
- \( R_1 \) and \( R_2 \) are the sum of ranks for groups 1 and 2.

For Robby (R):

- \( n_1 = 3 \) (number of classes)
- \( R_1 \) is the sum of ranks for Robby's votes.

For Adhit (A):

- \( n_2 = 3 \) (number of classes)
- \( R_2 \) is the sum of ranks for Adhit's votes.

Calculate \( U_1 \) and \( U_2 \), then take the smaller value as the Mann-Whitney U statistic.

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