metode statistika

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

StatistikaPopulasi

Contoh

Sampling Pendugaan

Tingkat Keyakinan

Ilmu Peluang

Statistika Deskriptif vs

Statistika Inferensia

Deskriptif

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

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.

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

Vo

lum

e

80

70

60

50

40

30

20

10

Boxplot of Volume

Volume

Fre

qu

en

cy

806040200

14

12

10

8

6

4

2

0

Mean 30.17

StDev 16.44

N 31

Histogram of VolumeNormal

Stem-and-Leaf Display: Volume

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

10 1 0005688999(9) 2 11122445712 3 134687 4 26 5 115581 61 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 peubah

Analisis Korelasi & Regresi Linier

x1

12

10

8

1050

x2

10

5

0

12108

35

30

25

Y1

353025

Matrix Plot of x1, x2, Y1


Correlations: x1,

x2, Y1

x1 x2

x2 -0.016

0.948

Y1 0.891 0.391

0.000 0.088

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

Fitted Value

Re

sid

ua

l

38363432302826242220

1

0

-1

-2

-3

Residuals Versus the Fitted Values(response is Y1)

Residual

Pe

rce

nt

210-1-2-3

99

95

90

80

70

60

50

40

30

20

10

5

1

Normal Probability Plot of the Residuals(response is Y1)


Analisis Regresi LogistikBinary 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: NXX

MM NTTTT)(

1

Bentuk umum:

Ilustrasi: Forecasting dengan Metode

Smoothing Eksponensial

ttt FXF )1(1

Ilustrasi Metode Winter

(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 Constants

Alpha (level) 0.2

Gamma (trend) 0.2

Delta (seasonal) 0.2

Accuracy Measures

MAPE 60

MAD 267

MSD 101122

Variable

Actual

Smoothed

Winters' Method Plot for xAdditive Method

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

SEKIAN

DAN

TERIMA KASIH

metode statistika

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