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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Sinaga, Steven Jansen
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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HIERARCHICAL CLUSTER ANALYSIS OF DISTRICTS/CITIES IN NORTH SUMATRA PROVINCE BASED ON HUMAN DEVELOPMENT INDEX INDICATORS USING PSEUDO-F Satyahadewi, Neva; Sinaga, Steven Jansen; Perdana, Hendra
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1429-1438

Abstract

Human development is needed to create prosperity and assist development in a country. In realising this, it is necessary to first look at the quality of human resources in the country, so that its use is more targeted. The measure used as a standard for the success of human development in a country is the Human Development Index (HDI). HDI figure are calculated from the aggregation of three dimensions, namely longevity and healthy living, knowledge, and decent standard of living. The longevity and healthy living dimension is represented by the Life Expectancy. Average Years of Schooling (AYS) and Expected Years of Schooling (EYS) are indicators representing the knowledge dimension. Meanwhile, the decent standard of living dimension is represented by the Expenditure per Capita indicator. The purpose of this study is to explain the characteristics of each cluster obtained from Hierarchical Cluster Analysis of districts/cities in North Sumatra Province based on HDI indicators in 2022 using Pseudo-F. The methods used are Hierarchical Cluster Analysis and Calinski-Harabasz Pseudo-F Statistic. The main concept of this method is to determine the optimum number of groups. This research uses secondary data obtained from BPS. The sample size in this study are 33 districts/cities and the number of variables are 4 variables. The results of the analysis of this study are the formation of 4 clusters with the best method is Ward. Cluster 1 consists of four members, namely Medan City, Pematang Siantar City, Binjai City, and Padang Sidempuan City, where this cluster has a very high HDI level. Meanwhile, Cluster 4 is a cluster that has a very low HDI level with four cluster members, namely Nias District, South Nias District, North Nias District, and West Nias District. Thus, it can be seen that there is a gap between regions in North Sumatra Province.
Determining the Optimum Number of Clusters in Hierarchical Clustering Using Pseudo-F Sinaga, Steven Jansen; Satyahadewi, Neva; Perdana, Hendra
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23113

Abstract

Poverty refers to the condition where a person cannot meet the basic necessities based on the minimum living standards. Statistics Indonesia proxied an increase in the poverty rate in North Sumatra Province in 2021 from 8.75% to 9.01%. However, this increase is exclusive to North Sumatra Province, which has Indonesia's 3rd largest number of districts/cities. This study discussed mapping the North Sumatra Province region based on 10 poverty factor variables. The 10 variables are life expectancy, health complaints, poverty line, Gross Regional Domestic Product (GRDP), population growth rate, Expected Years of Schooling (EYS), Human Development Index (HDI), labor force participation rate, open unemployment rate, and district/city minimum wage. The Hierarchical Clustering analysis was employed to compare single, complete, and average linkage methods. The best method was determined based on the pseudo-F statistic value. 4 clusters had complete linkage methods, each of which possessed varied characteristics. Cluster 1 contains cities with the lowest poverty rate, including Medan City and  Pematang Siantar City. Cluster 2 consists of cities with low poverty rates, while Cluster 3 consists of cities with high poverty rates. Cities that are included in Cluster 4 have very high poverty rates, including South Nias District and Pakpak Bharat District. The clusters present significant poverty rate gaps among North Sumatra Province regions.
Co-Authors Hendra Perdana Neva Satyahadewi