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Pertemuan 26 Uji-uji Nonparametrik Lanjutan

Pertemuan 26 Uji-uji Nonparametrik Lanjutan. Matakuliah : I0284 - Statistika Tahun : 2005 Versi : Revisi. 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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Pertemuan 26 Uji-uji Nonparametrik Lanjutan

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  1. Pertemuan 26Uji-uji Nonparametrik Lanjutan Matakuliah : I0284 - Statistika Tahun : 2005 Versi : Revisi

  2. Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : • Mahasiswa akan dapat menghasilkan simpulan hasil uji Krushal Wallis, Friedman dan Koefisien Korelasi.

  3. Outline Materi • Uji kruskal Wallis • Uji Friedman • Koefisien korelasi peringkat Spearman

  4. 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, rs , is a measure of association between two variables when only ordinal data are available. • Values of rs 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.

  5. Rank Correlation • Spearman Rank-Correlation Coefficient, rs where: n = number of items being ranked xi = rank of item i with respect to one variable yi = rank of item i with respect to a second variable di = xi - yi

  6. Test for Significant Rank Correlation • We may want to use sample results to make an inference about the population rank correlation ps. • To do so, we must test the hypotheses: H0: ps = 0 Ha: ps≠ 0

  7. Rank Correlation • Sampling Distribution of rswhen ps = 0 • Mean • Standard Deviation • Distribution Form Approximately normal, provided n> 10

  8. 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 ABCDEFGHIJ Analyst #1 1 4 9 8 6 3 5 7 2 10 Analyst #2 1 5 6 2 9 7 3 10 4 8

  9. Contoh Soal: Connor Investors Analyst #1 Analyst #2 InvestmentRatingRatingDiffer. (Differ.)2 A 1 1 0 0 B 4 5 -1 1 C 9 6 3 9 D 8 2 6 36 E 6 9 -3 9 F 3 7 -4 16 G 5 3 2 4 H 7 10 -3 9 I 2 4 -2 4 J 10 8 2 4 Sum = 92

  10. Contoh Soal: Connor Investors • Hypotheses H0: ps = 0 (No rank correlation exists.) Ha: ps = 0 (Rank correlation exists.) • Sampling Distribution Sampling distribution of rs under the assumption of no rank correlation rs r = 0

  11. Contoh Soal: Connor Investors • Rejection Rule Using .10 level of significance, Reject H0 if z < -1.645 or z > 1.645 • Test Statistic z = (rs - r )/r = (.4424 - 0)/.3333 = 1.33 • Conclusion Do no reject H0. 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.

  12. Selamat Belajar Semoga Sukses.

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