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(122224)
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(225339)
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.
2.
3.
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?
berasal dari kata statistik 
penduga parameter
 Statistika
 Ilmu
yang mempelajari dan mengusahakan
agar data menjadi informasi yang bermakna
Statistika
Populasi
Sampling
Pendugaan
Contoh
Deskriptif
Statistika Deskriptif
vs
Statistika Inferensia
Tingkat Keyakinan
Ilmu Peluang
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
Matrix Plot of Diameter, Height, Volume
Stem-and-leaf of Volume N = 31
Leaf Unit = 1.0
60
70
80
20
15
Diameter
10
10 1 0005688999
(9) 2 111224457
12 3 13468
7 4 2
6 5 11558
1 6
1 7 7
80
Height
60
70
45
10
60
Normal
Mean
StDev
N
Frequency
30.17
16.44
31
Volume
Histogram of Volume
50
40
30
10
20
8
10
6
4
2
0
0
20
40
Volume
60
80
15
Boxplot of Volume
70
12
Volume
20
80
14
70
20
20
45
70
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
Matrix Plot of x1, x2, Y1
0
5
10
12
x1
10
8
10
5
x2
0
35
30
Y1
25
8
10
12
25
30
35
Ilustrasi Hubungan antar peubah
Correlations: x1,
x2, Y1
x2
Y1
x1
-0.016
0.948
x2
0.891
0.000
0.391
0.088
Regression Analysis: Y1 versus x1, x2
The regression equation is
Y1 = 2.20 + 2.46 x1 + 0.565 x2
Predictor
Constant
x1
x2
Coef
2.200
2.4621
0.56531
S = 1.02180
SE Coef
1.416
0.1353
0.06884
R-Sq = 95.9%
T
1.55
18.19
8.21
P
0.139
0.000
0.000
R-Sq(adj) = 95.4%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
17
19
SS
411.21
17.75
428.96
MS
205.61
1.04
F
196.93
P
0.000
Residuals Versus the Fitted Values
Normal Probability Plot of the Residuals
(response is Y1)
(response is Y1)
99
1
95
90
80
Percent
Residual
0
-1
70
60
50
40
30
20
-2
10
5
-3
20
22
24
26
28
30
Fitted Value
32
34
36
38
1
-3
-2
-1
0
Residual
1
2
Ilustrasi Hubungan antar peubah
Analisis Regresi Logistik
Binary Logistic Regression: Y2 versus x1, x2
Link Function: Logit
Response Information
Variable
Y2
Value
1
0
Total
Count
12
8
20
(Event)
Logistic Regression Table
Predictor
Constant
x1
x2
Coef
3.87448
-0.516801
0.396576
SE Coef
3.38365
0.357665
0.211489
Z
1.15
-1.44
1.88
P
0.252
0.148
0.061
Odds
Ratio
0.60
1.49
95% CI
Lower Upper
0.30
0.98
1.20
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
Pearson
Deviance
Hosmer-Lemeshow
Chi-Square
21.7994
20.0347
14.8216
DF
17
17
8
P
0.193
0.272
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:
M T  M T 1 
( X T  X T N )
N
Ilustrasi: Forecasting dengan Metode
Smoothing Eksponensial

Bentuk umum:
Ft 1  X t  (1   ) Ft
Ilustrasi Metode Winter
(Kasus data musiman)
Xt = b1+b2 t + ct + t
Xt = (b1+b2 t) ct + t
Time Series Plot of x
1400
1200
1000
x
800
600
Winters' Method Plot for x
400
Additive Method
200
Variable
Actual
Smoothed
1400
0
5
10
15
20
25
Index
30
35
40
45
1200
Smoothing C onstants
A lpha (lev el)
0.2
Gamma (trend)
0.2
Delta (seasonal)
0.2
1000
800
Accuracy Measures
MAPE
60
MAD
267
MSD
101122
x
1
600
400
200
0
1
5
10
15
20
25
Index
30
35
40
45
SEKIAN
DAN
TERIMA KASIH