Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Matakuliah Tahun Versi : I0014 / Biostatistika : 2005 : V1 / R1 Pertemuan 9 Pendugaan Parameter (I) 1 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : • Mahasiswa dapat menjelaskan konsep pendugaan parameter populasi (C2) 2 Outline Materi • Sebaran penarikan contoh • Pendugaan titik • Pendugaan selang 3 <<ISI>> POPULASI DAN SAMPEL • POPULASI (N) parameter , , 2 • Pengambilan sampel (sampling) statistik • SAMPEL (n) 2 x, s , s 4 <<ISI>> BAGAIMANA SAMPLING ? • Random • Non-random Bagaimana Me-random ?? • Lotere / undian • Tabel / angka acak • Alat elektronik 5 <<ISI>> Penarikan Contoh (Sampling) • Penarikan Contoh Acak 1. 2. 3. 4. SIMPLE RANDOM SAMPLING SYSTEMATIC RANDOM SAMPLING STRATIFIED RANDOM SAMPLING CLUSTER RANDOM SAMPLING • Penarikan Contoh Non Acak 1. 2. 3. 4. ACCIDENTAL SAMPLING PURPOSIVE SAMPLING EQUOTA SAMPLING SNOWBAL SAMPLING 6 <<ISI>> Penarikan Contoh • Jika n diambil secara acak dari N dengan pengembalian, maka ada N n kemungkinan contoh • Jika n diambil secara acak dari N tanpa pengembalian, maka ada N kemungkinan contoh n • Oleh karena itu, suatu contoh berukuran n yang diambil dari N mempunyai statistik contoh yang tidak sama 7 <<ISI>> SIFAT SAMPEL • Rata-rata sampel = Rata-rata populasi • Ukuran penyebaran rata-rata sampel (mis: s dan dq) semakin menurun dengan meningkatnya ukuran contoh 8 <<ISI>> Sebaran Rata-rata Sampel • Sampling tanpa pengembalian N n s s N n 2 2 x • Sampling dengan pengembalian 2 atau N >> n s 2 x s n 9 <<ISI>> • Rata-rata sampel x E( X ) • Sampling tanpa pengembalian N n N 1 n 2 2 x • Sampling dengan pengembalian atau N >> n 2 2 x n 10 <<ISI>> Penduga Titik dan Sifat Penduga An estimator of a population parameter is a sample statistic used to estimate the parameter. The most commonly-used estimator of the: Population Parameter Sample Statistic Mean () is the Mean (X) Variance (2) is the Variance (s2) Standard Deviation () is the Standard Deviation (s) Proportion (p) is the Proportion ( p ) • Desirable properties of estimators include: – Unbiasedness – Efficiency – Consistency – Sufficiency 11 <<ISI>> Tidak Bias An estimator is said to be unbiased if its expected value is equal to the population parameter it estimates. For example, E(X)=so the sample mean is an unbiased estimator of the population mean. Unbiasedness is an average or long-run property. The mean of any single sample will probably not equal the population mean, but the average of the means of repeated independent samples from a population will equal the population mean. Any systematic deviation of the estimator from the population parameter of interest is called a bias. 12 <<ISI>> { Penduga Tak-bias dan Bias Bias An unbiased estimator is on target on average. A biased estimator is off target on average. 13 <<ISI>> Efisiensi An estimator is efficient if it has a relatively small variance (and standard deviation). An efficient estimator is, on average, closer to the parameter being estimated.. An inefficient estimator is, on average, farther from the parameter being estimated. 14 <<ISI>> Konsistensi dan Kecukupan An estimator is said to be consistent if its probability of being close to the parameter it estimates increases as the sample size increases. Consistency n = 10 n = 100 An estimator is said to be sufficient if it contains all the information 15 in the data about the parameter it estimates. << CLOSING>> • Sampai saat ini Anda telah mempelajari sebaran penarikan contoh dan pendugaan titik dan selang • Untuk dapat lebih memahami penggunaan pendugaan tersebut, cobalah Anda pelajari materi penunjang, dan mengerjakan latihan 16