Ketidaksesuaian Distribusi Poisson dalam Pemodelan Jumlah Kehadiran Siswa Sekolah Menengah Kejuruan

Aditya Pranata; Mitra Pranata; Marsini Sibuea; Sumiran Sumiran; Joni Joni; Rian Farta Wijaya

doi:10.60076/indotech.v4i2.2083

Authors

Aditya Pranata Universitas Pembangunan Panca Budi
Mitra Pranata Universitas Pembangunan Panca Budi
Marsini Sibuea Universitas Pembangunan Panca Budi
Sumiran Sumiran Universitas Pembangunan Panca Budi
Joni Joni Universitas Pembangunan Panca Budi
Rian Farta Wijaya Universitas Pembangunan Panca Budi Medan

DOI:

https://doi.org/10.60076/indotech.v4i2.2083

Keywords:

Distribusi Poisson, Underdispersion, Data Cacahan Berbatas, Uji Kesesuaian, Kehadiran Siswa

Abstract

Kehadiran siswa merupakan indikator penting dalam kontinuitas proses pembelajaran, tetapi jumlah siswa hadir per hari pada kelas berukuran tetap merupakan data cacahan dengan batas atas yang dapat membatasi kesesuaian model Poisson. Penelitian ini bertujuan mengevaluasi kelayakan distribusi Poisson dalam memodelkan jumlah kehadiran harian 30 siswa kelas XI TKJ SMK Putra Anda Binjai selama 224 hari efektif pada periode Juli 2025-April 2026. Parameter rata-rata diestimasi dengan Maximum Likelihood Estimation (MLE), sedangkan kesesuaian model dievaluasi melalui rasio variansi terhadap mean, probabilitas model pada nilai yang melampaui batas kelas, serta statistik Kolmogorov-Smirnov (K-S) yang dikalibrasi dengan bootstrap parametrik 20.000 replikasi. Hasil menunjukkan λ = 28,5134 siswa/hari atau tingkat kehadiran agregat 95,04%, dengan variansi 0,4220 dan rasio variansi/mean 0,0148 yang menunjukkan underdispersion sangat kuat. Model Poisson juga menempatkan sekitar 34,50% probabilitas pada X > 30, yaitu kejadian yang tidak mungkin untuk kelas berukuran 30 siswa. Statistik K-S sebesar D = 0,4367 dengan p-value bootstrap < 0,0001 menunjukkan bahwa data tidak konsisten dengan distribusi Poisson. Dengan demikian, distribusi Poisson tidak tepat digunakan secara langsung untuk pemodelan probabilitas kehadiran pada data cacahan berbatas ini; model dengan batas atas eksplisit dan/atau kemampuan mengakomodasi underdispersion perlu dibandingkan pada penelitian lanjutan. Temuan ini terbatas pada satu kelas dan satu sekolah

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