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 BahasanMinggu 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 1(135-235); 2(147-204)

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

1. Fleming, M.C. dan J.G. Nellis. 1994. Principles of Applied Statistic. Routledge. London.

2. Hamburg, M. 1974. Basic Statistics: A Modern Approach. Harcourt Brace Jovanovich, Inc. New York.

3. 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

Contoh

Sampling Pendugaan

Tingkat Keyakinan

Ilmu PeluangStatistika Deskriptif

vs Statistika Inferensia

Deskriptif

Langkah-langkah Analisis StatistikaStudying 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

Statistik DeskriptifAnalisis statistika yang bertujuan untuk menyajikan (tabel dan grafik) dan meringkas (ukuran pemusatan dan penyebaran) data sehingga data menjadi informasi yang mudah dipahami.

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:

Ilustrasi

Diameter

20

15

10

807060

Height

80

70

60

201510

70

45

20

Volume

704520

Matrix Plot of Diameter, Height, Volume

Volu

me

80

70

60

50

40

30

20

10

Boxplot of Volume

Volume

Frequency

806040200

14

12

10

8

6

4

2

0

Mean 30.17StDev 16.44N 31

Histogram of VolumeNormal

Stem-and-Leaf Display: Volume

Stem-and-leaf of Volume N = 31Leaf Unit = 1.0

10 1 0005688999(9) 2 111224457 12 3 13468 7 4 2 6 5 11558 1 6 1 7 7

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 peubahAnalisis Korelasi & Regresi Linier

x1

12

10

8

1050

x2

10

5

0

12108

35

30

25

Y1

353025

Matrix Plot of x1, x2, Y1

Ilustrasi Hubungan antar peubah

Correlations: x1, x2, Y1

x1 x2x2 -0.016 0.948

Y1 0.891 0.391 0.000 0.088

Regression Analysis: Y1 versus x1, x2

The regression equation isY1 = 2.20 + 2.46 x1 + 0.565 x2

Predictor Coef SE Coef T PConstant 2.200 1.416 1.55 0.139x1 2.4621 0.1353 18.19 0.000x2 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 PRegression 2 411.21 205.61 196.93 0.000Residual Error 17 17.75 1.04Total 19 428.96

Fitted Value

Re

sid

ua

l

38363432302826242220

1

0

-1

-2

-3

Residuals Versus the Fitted Values(response is Y1)

ResidualP

erc

en

t210-1-2-3

99

95

90

80

70

605040

30

20

10

5

1

Normal Probability Plot of the Residuals(response is Y1)

Ilustrasi Hubungan antar peubahAnalisis Regresi LogistikBinary Logistic Regression: Y2 versus x1, x2

Link Function: LogitResponse Information

Variable Value CountY2 1 12 (Event) 0 8 Total 20

Logistic Regression Table

Odds 95% CIPredictor Coef SE Coef Z P Ratio Lower UpperConstant 3.87448 3.38365 1.15 0.252x1 -0.516801 0.357665 -1.44 0.148 0.60 0.30 1.20x2 0.396576 0.211489 1.88 0.061 1.49 0.98 2.25

Log-Likelihood = -10.017Test that all slopes are zero: G = 6.886, DF = 2, P-Value = 0.032

Goodness-of-Fit Tests

Method Chi-Square DF PPearson 21.7994 17 0.193Deviance 20.0347 17 0.272Hosmer-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: N

XXMM NTT

TT

)(1

Bentuk umum:

Ilustrasi: Forecasting dengan Metode Smoothing Eksponensial

ttt FXF )1(1

Ilustrasi Metode WinterIlustrasi Metode Winter(Kasus data musiman)(Kasus data musiman)

Index

x

454035302520151051

1400

1200

1000

800

600

400

200

0

Time Series Plot of x

Index

x

454035302520151051

1400

1200

1000

800

600

400

200

0

Smoothing ConstantsAlpha (level) 0.2Gamma (trend) 0.2Delta (seasonal) 0.2

Accuracy MeasuresMAPE 60MAD 267MSD 101122

VariableActualSmoothed

Winters' Method Plot for xAdditive Method

Xt = b1+b2 t + ct + t Xt = (b1+b2 t) ct + t

SEKIAN DAN TERIMA KASIH