1 MODUL STATISTIKA BISNIS DAN INDUSTRI ANALISIS DISKRIMINAN HARYONO, dkk PROGRAM MAGISTER MANAJEMEN TEKNOLOGI PROGRAM PASCA SARJANA ITS
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1
MODUL
STATISTIKA BISNIS DAN INDUSTRI
ANALISIS DISKRIMINAN
HARYONO, dkk
PROGRAM MAGISTER MANAJEMEN TEKNOLOGIPROGRAM PASCA SARJANA
ITS
2
TUJUAN
Setelah mempelajari modul ini diharapkan peserta
dapat :
a) Memahami konsep analisis diskriminan dan mampu menerapkannya
b) Memahami konsep analisis diskriminan multiple dan mampu menerapkannya
3
MANFAAT
Analisis diskriminan adalah bagian dari Statistika
Multivariate, yang bermanfaat untuk :
a) Mangidentifikasi variabel-variabel independen yang “mampu” membedakan 2 (dua) kelompok atau lebih
b) Menentukan variabel independen mana yang mempunyai peranan paling penting terhadap perbedaan antar kelompok
c) Menentukan suatu sampel akan masuk kelompok mana berdasarkan variabel-variabel independen
4
LANGKAH-LANGKAH ANALISIS
Analisis Diskriminan
Mengetahui variabel-variabel yang mampu membedakan 2 kelompok atau lebih
DiskriptifMean dan Variansi
Diperkuat oleh Uji F (Analisis Variasi)
Membuat Fungsi DiskriminanManfaat :Mengetahui variabel yang paling dominanMengetahui besar kontribusi variabel pengelompokkan
Validitas : Tingkat kebenaran dengan melihat klasifikasi
Gambar 1 : Langkah-Langkah Interpretasi Hasil Analisis Diskriminan
5
Contoh 1 : ANALISIS DISKRIMINAN 2 KELOMPOK
Andaikan suatu perusahaan ingin mengetahui karakteristik keluarga yang berkunjung ke daerah wisata tertentu untuk 2 tahun terakhir ini. Data diberikan pada Tabel 1. Berdasarkan output komputer yang diberikan, simpulkan variabel-variabel mana yang paling dapat membedakan antara 2 kelompok pengunjung tersebut. (Output komputer pada Tabel 1)
6
Tabel 1 : Data Karakteristik Keluarga yang Berkunjung Ke Daerah Wisata Tertentu
Visit Income Travel Vacation Hsize Age Amount
11111111111111
50.270.362.948.552.775
46.257
64.168.173.471.956.249.3
56776852776514
87556734567882
34654536455463
4361523655686251574544645456
23313322333323
7
Lanjutan Tabel 1
Visit Income Travel Vacation Hsize Age Amount
12222222
6232.136.243.250.444.138.355
55425661
64352662
23224322
5858555737424557
31122213
8
Lanjutan Tabel 1
Visit Income Travel Vacation Hsize Age Amount
22222222
46.135
37.341.857
33.437.541.3
36258633
54713823
35432232
4264545636504842
11122111
9
Visit Income Travel Vacation Hsize Age Amount
111111222222
50.863.6544568
62.135
49.639.437
54.538.2
476565456272
747466335632
374363453533
455558604656543944513749
232233113121
10
Tabel 1 RESULT OF TWO-GROUP DISKRIMINANT ANALYSIS
Group Statistics
60.5200 9.83065 15 15.000
5.4000 1.91982 15 15.000
5.8000 1.82052 15 15.000
4.3333 1.23443 15 15.000
53.7333 8.77062 15 15.000
41.9133 7.55115 15 15.000
4.3333 1.95180 15 15.000
4.0667 2.05171 15 15.000
2.8000 .94112 15 15.000
50.1333 8.27101 15 15.000
51.2167 12.79523 30 30.000
4.8667 1.97804 30 30.000
4.9333 2.09981 30 30.000
3.5667 1.33089 30 30.000
51.9333 8.57395 30 30.000
INCOME
TRAVEL
VACATION
HSIZE
AGE
INCOME
TRAVEL
VACATION
HSIZE
AGE
INCOME
TRAVEL
VACATION
HSIZE
AGE
VISIT1.00
2.00
Total
Mean Std. Deviation Unweighted Weighted
Valid N (listwise)
11
Tests of Equality of Group Means
.453 33.796 1 28 .000
.925 2.277 1 28 .143
.824 5.990 1 28 .021
.657 14.636 1 28 .001
.954 1.338 1 28 .257
INCOME
TRAVEL
VACATION
HSIZE
AGE
Wilks'Lambda F df1 df2 Sig.
Pooled Within-Groups Matrices
1.000 .197 .091 .089 -.014
.197 1.000 .084 -.017 -.197
.091 .084 1.000 .070 .017
.089 -.017 .070 1.000 -.043
-.014 -.197 .017 -.043 1.000
INCOME
TRAVEL
VACATION
HSIZE
AGE
CorrelationINCOME TRAVEL VACATION HSIZE AGE
12
Summary of Canonical Discriminant Functions
Eigenvalues
1.786a 100.0 100.0 .801Function1
Eigenvalue % of Variance Cumulative %CanonicalCorrelation
First 1 canonical discriminant functions were used in theanalysis.
a.
Wilks' Lambda
.359 26.130 5 .000Test of Function(s)1
Wilks'Lambda Chi-square df Sig.
13
Standardized Canonical Discriminant Function Coefficients
.743
.096
.233
.469
.209
INCOME
TRAVEL
VACATION
HSIZE
AGE
1
Function
Structure Matrix
.822
.541
.346
.213
.164
INCOME
HSIZE
VACATION
TRAVEL
AGE
1
Function
Pooled within-groups correlations between discriminatingvariables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function.
14
Functions at Group Centroids
1.291
-1.291
VISIT1.00
2.00
1
Function
Unstandardized canonical discriminantfunctions evaluated at group means
Canonical Discriminant Function Coefficients
.085
.050
.120
.427
.025
-7.975
INCOME
TRAVEL
VACATION
HSIZE
AGE
(Constant)
1
Function
Unstandardized coefficients
15
Classification Statistics
Classification Function Coefficients
.678 .459
1.509 1.381
.938 .628
3.322 2.218
.832 .768
-57.532 -36.936
INCOME
TRAVEL
VACATION
HSIZE
AGE
(Constant)
1.00 2.00
VISIT
Fisher's linear discriminant functions
Classification Resultsb,c
12 3 15
0 15 15
80.0 20.0 100.0
.0 100.0 100.0
11 4 15
2 13 15
73.3 26.7 100.0
13.3 86.7 100.0
VISIT1.00
2.00
1.00
2.00
1.00
2.00
1.00
2.00
Count
%
Count
%
Original
Cross-validateda
1.00 2.00
Predicted GroupMembership
Total
Cross validation is done only for those cases in the analysis. Incross validation, each case is classified by the functions derivedfrom all cases other than that case.
a.
90.0% of original grouped cases correctly classified.b.
80.0% of cross-validated grouped cases correctly classified.c.
16
Contoh 2 : ANALISIS DISKRIMINAN 2 KELOMPOKLihat kembali Contoh 1. (Output komputer pada Tabel 2)
Tabel 2 : Result of Three-Group Discriminant AnalysisGroup Statistics
38.5700 5.29718 10 10.000
4.5000 1.71594 10 10.000
4.7000 1.88856 10 10.000
3.1000 1.19722 10 10.000
50.3000 8.09732 10 10.000
50.1100 6.00231 10 10.000
4.0000 2.35702 10 10.000
4.2000 2.48551 10 10.000
3.4000 1.50555 10 10.000
49.5000 9.25263 10 10.000
64.9700 8.61434 10 10.000
6.1000 1.19722 10 10.000
5.9000 1.66333 10 10.000
4.2000 1.13529 10 10.000
56.0000 7.60117 10 10.000
51.2167 12.79523 30 30.000
4.8667 1.97804 30 30.000
4.9333 2.09981 30 30.000
3.5667 1.33089 30 30.000
51.9333 8.57395 30 30.000
INCOME
TRAVEL
VACATION
HSIZE
AGE
INCOME
TRAVEL
VACATION
HSIZE
AGE
INCOME
TRAVEL
VACATION
HSIZE
AGE
INCOME
TRAVEL
VACATION
HSIZE
AGE
AMAOUNT1.00
2.00
3.00
Total
Mean Std. Deviation Unweighted Weighted
Valid N (listwise)
17
Tests of Equality of Group Means
.262 37.997 2 27 .000
.788 3.634 2 27 .040
.881 1.830 2 27 .180
.874 1.944 2 27 .163
.882 1.804 2 27 .184
INCOME
TRAVEL
VACATION
HSIZE
AGE
Wilks'Lambda F df1 df2 Sig.
Pooled Within-Groups Matrices
1.000 .051 .307 .380 -.209
.051 1.000 .036 .005 -.340
.307 .036 1.000 .221 -.013
.380 .005 .221 1.000 -.025
-.209 -.340 -.013 -.025 1.000
INCOME
TRAVEL
VACATION
HSIZE
AGE
CorrelationINCOME TRAVEL VACATION HSIZE AGE
18
Summary of Canonical Discriminant Functions
Eigenvalues
3.819a 93.9 93.9 .890
.247a 6.1 100.0 .445
Function1
2
Eigenvalue % of Variance Cumulative %CanonicalCorrelation
First 2 canonical discriminant functions were used in theanalysis.
a.
Wilks' Lambda
.166 44.831 10 .000
.802 5.517 4 .238
Test of Function(s)1 through 2
2
Wilks'Lambda Chi-square df Sig.
19
Standardized Canonical Discriminant Function Coefficients
1.047 -.421
.340 .769
-.142 .534
-.163 .129
.495 .524
INCOME
TRAVEL
VACATION
HSIZE
AGE
1 2
Function
Structure Matrix
.856* -.278
.193* .077
.219 .588*
.149 .454*
.166 .341*
INCOME
HSIZE
TRAVEL
VACATION
AGE
1 2
Function
Pooled within-groups correlations between discriminatingvariables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function.
Largest absolute correlation between each variable andany discriminant function
*.
20
Canonical Discriminant Function Coefficients
.154 -.062
.187 .422
-.070 .261
-.127 .100
.059 .063
-11.094 -3.792
INCOME
TRAVEL
VACATION
HSIZE
AGE
(Constant)
1 2
Function
Unstandardized coefficients
Functions at Group Centroids
-2.041 .418
-.405 -.659
2.446 .240
AMAOUNT1.00
2.00
3.00
1 2
Function
Unstandardized canonical discriminantfunctions evaluated at group means
21
Classification Statistics
Classification Resultsb,c
9 1 0 10
1 9 0 10
0 2 8 10
90.0 10.0 .0 100.0
10.0 90.0 .0 100.0
.0 20.0 80.0 100.0
7 3 0 10
4 5 1 10
0 2 8 10
70.0 30.0 .0 100.0
40.0 50.0 10.0 100.0
.0 20.0 80.0 100.0
AMAOUNT1.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
3.00
Count
%
Count
%
Original
Cross-validateda
1.00 2.00 3.00
Predicted Group Membership
Total
Cross validation is done only for those cases in the analysis. In cross validation,each case is classified by the functions derived from all cases other than that case.
a.
86.7% of original grouped cases correctly classified.b.
66.7% of cross-validated grouped cases correctly classified.c.
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