Configuration of Classical Biplot and Canonical Biplot with Various Sample Sizes
Konfigurasi Biplot Biasa dan Biplot Kanonik dengan Berbagai Ukuran Contoh
Abstract
This study provides a configuration of 18 provinces in Indonesia based on the performance of Islamic High School graduates. The data used in this study are scores of subjects and GPA from the IPB first year students who receive provincial representing scholarship from the Ministry of Religious Affairs (BUD DEPAG) in 2009/2010 academic year. Configurations obtained through classical biplot with original data, aggregate data, and canonical biplot. The dissimilarity of inter-configurations is obtained via Procrustes analysis. Configuration obtained from classical biplot with aggregate data is more in line with configuration obtained by the original data as compared to configuration obtained from canonical biplot. The canonical biplot result reveals that the provinces of DKI Jakarta, Bali, and Lampung are relatively good, while the provinces of NAD, Banten, NTB, and Gorontalo have relatively low performance of Islamic High School graduates. The provinces of Jakarta and Bali in general have relatively good scores on subjects related to the natural sciences, while the province of Lampung has relatively good scores of subjects related to the socials sciences. To explore possibility of configuration changes obtained by the canonical biplot, a simulation with various sample sizes is then conducted. The results obtained provide configuration changes due to the differences in the sample size used. Studi ini memberikan konfigurasi 18 provinsi di Indonesia berdasarkan kinerja lulusan Madrasah Aliyahnya. Data yang digunakan ialah nilai mutu mata kuliah dan IPK mahasiswa Beasiswa Utusan Daerah Departemen Agama Tingkat Persiapan Bersama Institut Pertanian Bogor (BUD DEPAG TPB IPB) tahun akademik 2009/2010 lulusan Madrasah Aliyah dari 18 provinsi di Indonesia. Konfigurasi diperoleh melalui biplot biasa dengan menggunakan data asal maupun agregat dan biplot kanonik. Ketaksesuaian antarkonfigurasi diperoleh melalui analisis Procrustes. Konfigurasi yang diperoleh dari biplot biasa dengan data agregat lebih sesuai dengan konfigurasi biplot biasa dengan data asal dibandingkan dengan konfigurasi yang diperoleh dari biplot kanonik. Dari biplot kanonik diperoleh hasil bahwa provinsi Jakarta, Bali dan Lampung merupakan provinsi yang relatif baik, sedangkan provinsi NAD, Banten, NTB dan Gorontalo relatif rendah kinerja lulusan Madrasah Aliyahnya. Provinsi Jakarta dan Bali secara umum memiliki nilai yang relatif baik pada mata kuliah yang berhubungan dengan pengetahuan alam, sedangkan provinsi Lampung memiliki nilai yang relatif baik dalam pengetahuan sosial. Untuk menelusuri kemungkinan perubahan konfigurasi yang dihasilkan biplot kanonik, dilakukan simulasi dengan berbagai ukuran contoh. Hasil yang diperoleh memberikan gambaran adanya perubahan konfigurasi akibat perbedaan ukuran contoh yang digunakan.
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- UT - Mathematics [1431]
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