Royani, Rani (2026) Multivariate Analysis of Variance (MANOVA) berdimensi tinggi dengan pendekatan median geometrik dan Bootstrapping. Sarjana thesis, UIN Sunan Gunung Djati Bandung.
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Abstract
INDONESIA: Penelitian ini bertujuan mengkaji Multivariate Analysis of Variance (MANOVA) berdimensi tinggi dengan pendekatan median geometrik dan bootstrapping. MANOVA klasik memiliki keterbatasan ketika jumlah variabel lebih besar daripada jumlah observasi (large p, small n) karena matriks kovarians sampel menjadi singular sehingga statistik uji MANOVA klasik tidak dapat diterapkan. Langkah-langkah analisis MANOVA berdimensi tinggi dimulai dengan estimasi median geometrik, parameter standardisasi, perhitungan statistik uji pasangan, perhitungan statistik uji global, pembentukan distribusi empiris menggunakan wild bootstrap, dilanjutkan dengan penentuan nilai kritis dan pengambilan keputusan. Implementasi analisis MANOVA berdimensi tinggi diterapkan pada data RNA-Seq dengan bantuan bahasa pemrograman Python. Hasil penelitian menunjukkan bahwa MANOVA berdimensi tinggi berbasis median geometrik dan bootstrapping dapat diterapkan pada data berdimensi tinggi dan menghasilkan statistik uji global sebesar 31,5917, yang melebihi nilai kritis bootstrap sebesar 30,9941, dengan p-value empiris sebesar 0,0267. Karena p-value empiris lebih kecil dari taraf signifikansi 0,05, maka H0 ditolak, yang menunjukkan bahwa terdapat paling sedikit satu pasangan kelompok yang memiliki parameter lokasi multivariat berbeda secara signifikan. ENGLISH: This study aims to examine high-dimensional Multivariate Analysis of Variance (MANOVA) using a geometric median and bootstrapping approach. Classical MANOVA has limitations when the number of variables is greater than the number of observations (large p, small n) because the sample covariance matrix becomes singular, making the classical MANOVA test statistic inapplicable. The high- dimensional MANOVA analysis begins with the estimation of the geometric median, standardization parameters, calculation of pairwise test statistics, calculation of the global test statistic, construction of the empirical distribution using wild bootstrap, followed by the determination of the critical value and decision making. The high-dimensional MANOVA analysis was implemented on RNA-Seq data using the Python programming language. The results show that high-dimensional MANOVA based on the geometric median and bootstrapping can be applied to high-dimensional data and produces a global test statistic of 31.5917, which exceeds the bootstrap critical value of 30.9941, with an empirical p-value of 0.0267. Since the empirical p-value is less than the significance level of 0.05, H0 is rejected, indicating that at least one pair of groups has significantly different multivariate location parameters.
| Item Type: | Thesis (Sarjana) |
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| Uncontrolled Keywords: | MANOVA Berdimensi Tinggi; Median Geometrik; Wild Bootstrap; Bootstrapping; RNA-Seq |
| Subjects: | Mathematics > Data Processing and Analysis of Mathematics Applied mathematics > Statistical Mathematics |
| Divisions: | Fakultas Sains dan Teknologi > Program Studi Matematika |
| Depositing User: | Rani Royani |
| Date Deposited: | 31 Aug 2026 04:09 |
| Last Modified: | 31 Aug 2026 04:09 |
| URI: | https://digilib.uinsgd.ac.id/id/eprint/139931 |
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