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CLUSTER SAMPLING

PERTEMUAN 5-MPC 2 TEORI. CLUSTER SAMPLING. Oleh : J. Purwanto Ruslam. SEKOLAH TINGGI ILMU STATISTIK. Unequal Cluster Sampling. ILUSTRASI. Populasi. Cluster 4. Cluster 3. Cluster 1. Cluster 2. Sampel. Cluster 3. Cluster 1. Unequal Cluster Sampling.

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CLUSTER SAMPLING

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  1. PERTEMUAN 5-MPC 2 TEORI CLUSTER SAMPLING Oleh: J. PurwantoRuslam SEKOLAH TINGGI ILMU STATISTIK

  2. Unequal Cluster Sampling ILUSTRASI Populasi Cluster 4 Cluster 3 Cluster 1 Cluster 2 Sampel Cluster 3 Cluster 1

  3. Unequal Cluster Sampling • Misalkan terdapatpopulasisebanyak cluster. Setiap cluster memuatelemensebanyak unit sehingga: • Rata-rata per elemen cluster ke-idirumuskan: • Rata-rata per elemenpopulasidirumuskan:

  4. Unequal Cluster Sampling • Misalkansatugugussampel yang berukuran n cluster yang ditarikdari N cluster secarasimple random sampling wor. • Notasiyang dipergunakansamadengancluster berukuransama, hanyamenggantidengan. : banyaknya unit dalamcluster ke-i • Estimasi rata-rata unit untuk cluster ke-i dirumuskan: • Untukestimasi rata-rata unit populasiterdapat 3 pendekatan: • Rata-rata sederhanadantidakmempertimbangkanukurancluster • Rata-rata denganmemperhitungkanukuran cluster darisampel • Rata-rata denganmenggunakanukuran cluster dalampopulasi

  5. Unequal Cluster Sampling 1. Rata-rata karakteristik per unit darisebanyaknsampelcluster, yang diperhitungkandari rata-rata cluster tanpaditimbangdengan banyaknya elemen dalam cluster terpilih . Keterangan: --> Estimasi rata-rata menggunakanpendekataninimenghasilkannilaiestimasi yang bias

  6. Unequal Cluster Sampling • Untuk populasidengannilaitidakbervariasiantara cluster satudengan cluster lainnya, besarnya bias tidakterlalusignifikan. • Jikadantidakberkorelasi, biasnyaakanbernilainoldanakanunbiased • Sebaliknya, jikabervariasi antara cluster satudengancluster ataulainnyaataujikadanberkorelasikuatmakabesarnya bias akansangatsignifikansehingga estimator inisebaiknyatidakdigunakan. Bukti bahwaadalah estimator yang bias: Besarnya bias dirumuskan:

  7. Unequal Cluster Sampling • Pembuktian sampling varians Unbiased estimator untuk Keterangan:

  8. Unequal Cluster Sampling 2. Rata-rata karakteristik per unit darisebanyaknsampelcluster, yang diperhitungkandarikarakteristikseluruh unit dalamsampel Keterangan: --> Estimasi rata-rata menggunakanpendekataninimenghasilkannilaiestimasi yang bias konsisten

  9. Unequal Cluster Sampling 3. Rata-rata karakteristik per unit darisebanyaknsampelcluster, denganmemperhitungkan rata-rata unit unit per cluster daripopulasi Keterangan: • Estimasirata-rata menggunakanpendekataninimenghasilkannilaiestimasi yang unbiased, tetapimembutuhkaninformasi rata-rata unit per cluster populasi. • Bukti:

  10. Unequal Cluster Sampling • Misalkanadalahmerupakansuatunilaivariabelkualitatif, tidakmempunyaisatuanukur, danterdiriataskategori-kategori yang yangkongkrit. • Elemen-elemendenganciritermasuksuatukategori (yang diperhatikan) masing-masingdiberinilai dummy samadengan 1, sedangkanselainnyadiberinilai 0. • Denganpengertianini, P (proporsi) dapatdipandangsebagai rata-rata populasi data variabeldarisuatukategoritertentu. • Proporsielemen-elemenpopulasi yang memilikisuatukategoritertentuadalah

  11. Unequal Cluster Sampling 1. Proporsikarakteristikdarisebanyaknsampelcluster, yang diperhitungkandari rata-rata cluster tanpaditimbangdengan. Keterangan:

  12. Unequal Cluster Sampling 2. Proporsikarakteristikdarisebanyaknsampelcluster, yang diperhitungkandarikarakteristikseluruh unit dalamsampel Keterangan:

  13. Unequal Cluster Sampling 3. Proporsikarakteristikdarisebanyaknsampelcluster, denganmemperhitungkan rata-rata unit unit per cluster daripopulasi Keterangan:

  14. Unequal Cluster Sampling Relative Efficiency Unequal Cluster Sampling terhadap SRS Jikamenggunakanestimasipendekatancara 3, makaefisiensiunequal cluster samplingterhadapSRSdirumuskan: Berdasarkanrumus di atas, tampakbahwa cluster sampling akanefisienjikavariasibetween cluster bernilaikecil.

  15. Unequal Cluster Sampling ContohSoal 1: Suatuwilayah yang terdiridari 10 cluster diambilsampelsecaraacaksebanyak 3 cluster, kemudiandilakukanpengukuranterhadapjumlah ART padasemuarumahtanggapada cluster terpilih. Jumlahrumahtangga di wilayahtersebutadalah 42 rumahtangga. Perkirakan rata-rata jumlah ART tiaprumahtanggabesertastandarerrornya !

  16. 1. Pendugarata-rata sederhana (tanpapenimbang)

  17. 2. Penduga rata-rata tertimbangukuran cluster darisampel

  18. 3. Penduga rata-rata tertimbangukuran cluster daripopulasi

  19. Penghitungan Sampling Error denganStata(Estimasitidaktertimbang) use "D:Bahan Ajar MPC\unequal cluster.dta” collapse (count) household_id (sum) art, by(cluster_id) renhousehold_idruta gen art_per_ruta= art/ruta gen N=10 svysetcluster_id, fpc(N) vce(linearized) singleunit(missing) pweight: <none> VCE: linearized Single unit: missing Strata 1: <one> SU 1: cluster_id FPC 1: N svylinearized : mean art_per_ruta (running mean on estimation sample) Survey: Mean estimation Number of strata = 1 Number of obs = 3 Number of PSUs = 3 Population size = 3 Design df = 2 Linearized Mean Std. Err. [95% Conf. Interval] art_per_ruta 4,744445 ,247531 3,679404 5,809485

  20. PenghitunganSampling Error denganStata(Estimasitertimbangdenganukuran cluster dari data sampel) use "D:Bahan Ajar MPC\unequal cluster.dta” gen N=10 gen weight=10/3 svysetcluster_id [pweight=weight], fpc(N) vce(linearized) pweight: weight VCE: linearized Single unit: missing Strata 1: <one> SU 1: cluster_id FPC 1: N svy linearized : mean art (running mean on estimation sample) Survey: Mean estimation Number of strata = 1 Number of obs = 12 Number of PSUs = 3 Population size = 40 Design df = 2 Linearized Mean Std. Err. [95% Conf. Interval] art 4,666667 ,2130032 3,750188 5,583146 Sampling weight

  21. Penghitungan Sampling Error denganStata(Estimasitertimbangdenganukuran cluster dari data populasi) use "D:Bahan Ajar MPC\unequal cluster.dta” collapse (count) household_id (sum) art, by(cluster_id) renhousehold_idruta gen art_per_ruta= art/ruta gen N=10 gen art_per_ruta2= ruta/4.2* art_per_ruta svysetcluster_id, fpc(N) vce(linearized) singleunit(missing) pweight: <none> VCE: linearized Single unit: missing Strata 1: <one> SU 1: cluster_id FPC 1: N svylinearized : mean art_per_ruta2 (running mean on estimation sample) Survey: Mean estimation Number of strata = 1 Number of obs = 3 Number of PSUs = 3 Population size = 3 Design df = 2 Linearized Mean Std. Err. [95% Conf. Interval] art_per_ruta2 4,444444 ,3513642 2,932646 5,956243

  22. Unequal Cluster Sampling ContohSoal 2: Sebanyak 3.510 rumahtanggapeternakan di suatukecamatandialokasikankedalam 90 cluster denganjumlahrumahtanggapeternakanuntuktiap cluster tidaksama. Sebuah random sampelsebanyak 15 cluster dipilihsecaraacakdandilakukanpengukuranterhadapjumlahternakuntuktiap cluster terpilih. Tujuandarisurveiiniadalahuntukmemperkirakan rata-rata jumlahternakuntuktiaprumahtanggapeternak.

  23. 1. Pendugarata-rata sederhana (tanpapenimbang)

  24. 2. Pendugarata-rata tertimbangukuran cluster darisampel

  25. 3. Pendugarata-rata tertimbangukuran cluster daripopulasi

  26. SoalLatihan 1 The new candy Green Globules is being test-marketed in an area of upstate New York. Total number of supermarkets is 230. The market research firm decides to sample 6 of the 45 cities in the area and then to sample supermarkets within those cities, wanting to know the number of cases of Green Globules sold. Estimate the total number of cases sold and the average number sold per supermarket, along with the standard errors of your estimates. (use three methods of estimation).

  27. SoalLatihan 2 A researcher wants to study the prevalence of smoking and other hight-risk behaviors among male students in a high school with 36 class. The total numbers of male students is 932. She intend to drive to 8 of the class and then interview all male students in the selected class.The results were as follows: Estimate the percentage and total of male students who smoke, along with the standard errors of your estimates. (use three methods of estimation).

  28. TERIMA KASIH Have A Nice Sampling

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