METODE STATISTIKA Kode Matakuliah: STK211, 3(2-3) Tujuan Instruksional Umum: Setelah mengikuti mata kuliah ini selama satu semester, mahasiswa akan dapat menjelaskan prinsip-prinsip dasar metode statistika, dan mampu mengerjakan beberapa analisis statistika sederhana.

Pokok Bahasan Minggu Ke Pokok Bahasan Daftar Pustaka I Pendahuluan 1(1-10); 2(1-13) II Deskripsi Data 1(13-69);2(33-71);3(44-119) III Konsep Dasar Peluang 1(73-131);2(72-146);3(122-224) IV-V Konsep Peubah Acak dan Sebaran Peluang Acak 1(135-235); 2(147-204) VI Sebaran Penarikan Contoh VII Ujian Tengah Semester VIII-IX Pendugaan Parameter 1(135-235);2(147-204) X-XI Pengujian Hipotesis 1(135-235);2(147-204);3(225-339) XII Analisis Korelasi dan Regresi Linear Sederhana XIII Analisis Data Kategori XIV Topik Khusus I XV Topik Khusus II XVI Ujian Akhir Semester

Kepustakaan Fleming, M.C. dan J.G. Nellis. 1994. Principles of Applied Statistic. Routledge. London. Hamburg, M. 1974. Basic Statistics: A Modern Approach. Harcourt Brace Jovanovich, Inc. New York. Koopmans, L.H. 1987. Introduction to Contemporary Statistical Methods 2nd ed. Duxbury, Press. Boston.

PENDAHULUAN Apa itu statistika? Statistika berasal dari kata statistik  penduga parameter Ilmu yang mempelajari dan mengusahakan agar data menjadi informasi yang bermakna

Statistika Populasi Sampling Pendugaan Contoh Deskriptif Tingkat Keyakinan Ilmu Peluang Statistika Deskriptif vs Statistika Inferensia

Langkah-langkah Analisis Statistika Studying a problem through the use of statistical data analysis usually involves four basic steps. Defining the problem Collecting the data Analyzing the data Reporting the results

Defining the Problem An exact definition of the problem is imperative in order to obtain accurate data about it. It is extremely difficult to gather data without a clear definition of the problem.

Collecting the Data Designing ways to collect data is an important job in statistical data analysis. Two important aspects of a statistical study are: Population - a set of all the elements of interest in a study Sample - a subset of the population Statistical inference is refer to extending your knowledge obtain from a random sample from a population to the whole population.

The purpose of statistical inference is to obtain information about a population form information contained in a sample. It is just not feasible to test the entire population, so a sample is the only realistic way to obtain data because of the time and cost constraints. Data can be either quantitative or qualitative. Qualitative data are labels or names used to identify an attribute of each element. Quantitative data are always numeric and indicate either how much or how many.

Data can be collected from existing sources or obtained through observation and experimental studies designed to obtain new data. In an experimental study, the variable of interest is identified. Then one or more factors in the study are controlled so that data can be obtained about how the factors influence the variables. In observational studies, no attempt is made to control or influence the variables of interest. A survey is perhaps the most common type of observational study.

Analyzing the Data Statistical data analysis divides the methods for analyzing data into two categories: exploratory methods Exploratory methods are used to discover what the data seems to be saying by using simple arithmetic and easy-to-draw pictures to summarize data confirmatory methods Confirmatory methods use ideas from probability theory in the attempt to answer specific questions. Probability is important in decision making because it provides a mechanism for measuring, expressing, and analyzing the uncertainties associated with future events.

Reporting the Results Through inferences, an estimate or test claims about the characteristics of a population can be obtained from a sample. The results may be reported in the form of a table, a graph or a set of percentages. Because only a small collection (sample) has been examined and not an entire population, the reported results must reflect the uncertainty through the use of probability statements and intervals of values. To conclude, a critical aspect of managing any organization is planning for the future. Statistical data analysis helps us to forecast and predict future aspects of a business operation. The most successful leader and decision makers are the ones who can understand the information and use it effectively.

Perkembangan Analisis Statistika Analisis statistika telah banyak digunakan pada berbagai bidang. Analisis statistika yang digunakan mulai dari analisis statistika yang paling sederhana (statistika deksriptif) sampai analisis statistika lanjutan Beberapa ilustrasi analisis statistika: Statistik Deskriptif Analisis statistika yang bertujuan untuk menyajikan (tabel dan grafik) dan meringkas (ukuran pemusatan dan penyebaran) data sehingga data menjadi informasi yang mudah dipahami.

Ilustrasi Stem-and-Leaf Display: Volume Stem-and-leaf of Volume N = 31 Leaf Unit = 1.0 10 1 0005688999 (9) 2 111224457 12 3 13468 7 4 2 6 5 11558 1 6 1 7 7 Untuk kebutuhan ekplorasi data, bentuk penyajian data yang paling banyak digunakan adalah diagram dahan daun (stem and leaf), histogram, diagram kotak garis (box-plot), dan plot antar peubah. Diagram dahan daun atau histogram dapat digunakan untuk menelusuri pola sebaran data (simetrik atau menjulur). Box-plot dapat juga digunakan untuk melihat sebaran tetapi penggunaan lebih spesifik adalah untuk mengidentifikasi keanehan-keanehan data. Plot antar peubah digunakan untuk melihat pola hubungan antar variabel (tidak berhubungan, ada hubungan linier atau non linier)

Statistika Inferensia Perbandingan Rataan Populasi Satu populasi  Uji t atau uji z Dua populasi  Uji t atau uji z Lebih dari dua populasi  anova Hubungan antar variabel Hubungan dua arah  Analisis Korelasi Hubungan satu arah (sebab akibat)  Analisis Regresi

Ilustrasi Hubungan antar peubah Analisis Korelasi & Regresi Linier

Ilustrasi Hubungan antar peubah Regression Analysis: Y1 versus x1, x2 The regression equation is Y1 = 2.20 + 2.46 x1 + 0.565 x2 Predictor Coef SE Coef T P Constant 2.200 1.416 1.55 0.139 x1 2.4621 0.1353 18.19 0.000 x2 0.56531 0.06884 8.21 0.000 S = 1.02180 R-Sq = 95.9% R-Sq(adj) = 95.4% Analysis of Variance Source DF SS MS F P Regression 2 411.21 205.61 196.93 0.000 Residual Error 17 17.75 1.04 Total 19 428.96 Correlations: x1, x2, Y1 x1 x2 x2 -0.016 0.948 Y1 0.891 0.391 0.000 0.088

Ilustrasi Hubungan antar peubah Analisis Regresi Logistik Binary Logistic Regression: Y2 versus x1, x2 Link Function: Logit Response Information Variable Value Count Y2 1 12 (Event) 0 8 Total 20 Logistic Regression Table Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant 3.87448 3.38365 1.15 0.252 x1 -0.516801 0.357665 -1.44 0.148 0.60 0.30 1.20 x2 0.396576 0.211489 1.88 0.061 1.49 0.98 2.25

Log-Likelihood = -10.017 Test that all slopes are zero: G = 6.886, DF = 2, P-Value = 0.032 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 21.7994 17 0.193 Deviance 20.0347 17 0.272 Hosmer-Lemeshow 14.8216 8 0.063

Analisis Data Lanjutan Analisis Multivariate Manova Analisis Komponen Utama Analisis Faktor Analisis Cluster Analisis Diskriminan Analisis Korelasi Kanonik Analisis Biplot

Analisis data time series Data time series merupakan data yang dikumpulkan secara sequensial menurut periode waktu tertentu. Peranan ramalan (forecasting) data ke depan memegang peranan penting dalam menyusun kebijakan strategis perusahaan/lembaga Metode Forecasting yang berkembang saat ini, antara lain: Metode Rataan Kumulatif Metode Pemulusan (Smoothing) ARIMA (AutoRegressive Integrated Moving Average) Fungsi Transfer (Bivariate ARIMA) MARIMA (Multivariate ARIMA)

Pola Data Time Series

Ilustrasi: Forecasting dengan Metode Smoothing Moving Average Formula:

Ilustrasi: Forecasting dengan Metode Smoothing Eksponensial Bentuk umum:

Ilustrasi Metode Winter (Kasus data musiman) Xt = b1+b2 t + ct + t Xt = (b1+b2 t) ct + t Metode Winter digunakan untuk data time series yang mengandung unsur musiman. Model winter yang dapat digunakan ada dua yaitu: Model aditif : Xt=b1 + b2 t + Ct + et Model multiflikatif : Xt=(b1 + b2 t)Ct + et

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