., Dapiah (2018) Pemodelan Rata-Rata Nilai Ujian Nasional SMAN Di Jawa Barat Dengan Menggunakan Pendekatan Bayesian Mixture Normal Hirarki. Masters thesis, Institut Teknologi Surabaya.
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Abstract
Ujian Nasional (UN) merupakan salah satu sistem evaluasi standar pendidikan di Indonesia. Hasil UN dapat digunakan sebagai salah satu bahan pertimbangan untuk pembinaan dan pemberian bantuan kepada satuan pendidikan dalam upaya peningkatan mutu pendidikan. Penelitian ini dilakukan untuk mendapatkan model yang terbaik serta melihat faktor apa saja yang mempengaruhi rata-rata nilai UN. Data yang digunakan pada penelitian ini adalah rata-rata nilai UN SMAN di Jawa Barat tahun 2015. Data rata-rata nilai UN merupakan data berstruktur hirarki. Analisis statistik yang sesuai untuk memodelkan tipe data ini adalah model linier hirarki. Pemodelan dilakukan menggunakan model linear hirarki dua level dengan sembilan karakteristik sekolah di level pertama dan empat karakteristik wilayah kabupaten/kota di level kedua. Selain struktur data, pada penelitian ini mempertimbangkan pola distribusi data rata-rata nilai UN, yang terbukti mempunyai pola distribusi mixture normal dan univariate multi-modal. Oleh Karena itu dimodelkan dengan menggunakan pendekatan Bayesian Mixture normal hirarki. Estimasi distribusi mixture normal hirarki menggunakan metode Bayesian dilakukan dengan menemukan distribusi posterior dari perkalian distribusi prior dan likelihood data. Model mixture normal hirarki merupakan model yang kompleks karena mempunyai banyak parameter, maka untuk mendapatkan distribusi posterior parameter nya digunakan pendekatan numerik Markov Chain Monte Carlo (MCMC). Hasil menunjukkan bahwa Model mixture normal hirarki yang terbentuk terbukti dapat menjelaskan variasi data, variasi koefisien mixture regresi model mikro antar kabupaten/kota terbukti secara signifikan dipengaruhi oleh karakteristik sekolah dan karakteristik kabupaten/kota. Dengan demikian, model mixture normal hirarki dua level dengan pendekatan Bayesian terbukti dapat menggambarkan pengaruh prediktor pada tingkatan berbeda terhadap rata-rata nilai UN SMAN di Jawa Barat. ============================================================================================================= National Examination (UN) is one of the standard evaluation system of education in Indonesia. The results of the UN can be used as one of the considerations for guidance and provision of assistance to educational units in an effort to improve the quality of education. This study was conducted to obtain the best model and see what factors affect the average value of the UN. The data used in this study is the average value of High School UN in West Java in 2015. Average data value of the UN is a hierarchical data structure. The appropriate statistical analysis for modeling this data type is the hierarchical linear model. The modeling was done using a two-level linear hierarchy model with nine characteristics of the school in the first level and four characteristics of the district /city in the second level. In addition to the data structure, this study considers the average data distribution pattern of UN value, which has proved to have mixture pattern of normal and multi-modal univariate. Therefore it is modeled by using a normal Bayesian Mixture hierarchy approach. Estimation of normal hierarchical mixture distribution using Bayesian method is done by finding posterior distribution of multiplication of prior and likelihood distribution data. Normal mixed hierarchy model is a complex model because it has many parameters, so to obtain the posterior distribution of its parameters used numerical approach Markov Chain Monte Carlo (MCMC). The results show that the normal hierarchy mixed model of mixture is proven to explain the variation of data, the variation of micro regression model mixture between district/city proved significantly influenced by the characteristics of the school and the characteristics of the district/city. Thus, a normal two-level hierarchy mixture model with a Bayesian approach is shown to illustrate the influence of predictors on different levels of the average value of High School UN in West Java.
| Item Type: | Thesis (Masters) |
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| Additional Information: | RTSt 519.542 Dap p-1 3100018074964 |
| Uncontrolled Keywords: | Bayesian, Hirarki, MCMC, Mixture, Nilai UN; Hierarchy; National Exam |
| Subjects: | H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory. |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | dapiah dapiah |
| Date Deposited: | 04 Apr 2018 04:55 |
| Last Modified: | 15 Sep 2020 05:11 |
| URI: | https://repository.its.ac.id/id/eprint/50557 |
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