Univariate Analysis

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MULTIVARIATE ANALYSIS

Multivariate analysis Elaborasi contingency tables split correlation analysis high-order partial correlation path analysis

Regressi/ Prediksi multiple regression

Differensiasi discriminant analysis manova

Eksplorasi/ identifikasi factor analysis cluster analysis

Elaborasi98/10/28/08

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Elaborasi • Elaborasi:

vr.

Memasukkan (mengontrol/membuat konstan) variabel ketiga dalam analisis hubungan antara independent vr. dan dependent guna merinci hubungan tsb.

•

Variabel ketiga:

test factor/variable, intervening vr., antecedent vr., specifying vr., dsb.

(tergantung Kerangka Teori)

•

(merubah konstanta)

Pengontrolan variabel:

membuat konstan suatu vr. suatu variabel menjadi

• Beberapa teknik elaborasi: 1. contingency tables Elaborasi98/10/28/08

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2. split/differential analysis 3. high-order partial correlation

Kemungkinan Hasil Suatu Elaborasi: Konstan

Replication Melemah

Explanation 3rd vr = antecedent

vr.

Interpretation

3rd vr = intervening vr.

Terbelah

Specification 3rd vr = specifying vr.

Menguat

Antecent Elaborasi98/10/28/08

3rd vr = suppressor vr.

Independent Intervening

4

Dependent variable(s) variable(s)

variable(s)

extraneous variable(s)

Elaborasi98/10/28/08

variable(s)

Specifying variable(s)

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Elaborasi98/10/28/08

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Elaborasi 1

CONTINGENCY TABLES Tabel Silang SES dan Konservatisme ( Zero-order Table )

n = 500 Pria & Wanita

SES Konservatisme Tinggi Rendah

Rendah 33% 67% 100%

Tinggi 78% 22% 100%

Tabel Silang SES dan Konservatisme Dalam Kelompok Pria ( First-order Table )

n = 300 Pria

SES Konservatisme Tinggi Rendah

Rendah 48% 52% 100%

Tinggi 49% 51% 100%

Tabel Silang SES dan Konservatisme Dalam Kelompok Wanita ( First-order Table )

n = 200 Wanita

SES Konservatisme Tinggi Rendah

Elaborasi98/10/28/08

Rendah 13% 87% 100%

Tinggi 81% 19% 100%

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Elaborasi 1

Contingency Tables Zero-order Table

LMIDSTAT minat statistik by LMPS minat mps

LMPS

Count ” Row Pct ”tidak be berminat Col Pct ”rminat Row ” 1” 2” Total LMIDSTAT ““““““““•““““““““•““““““““› 1 ” 18 ” 50 ” 68 tidak berminat ” 26.5 ” 73.5 ” 60.7 ” 75.0 ” 56.8 ” š““““““““•““““““““› 2 ” 6 ” 38 ” 44 berminat ” 13.6 ” 86.4 ” 39.3 ” 25.0 ” 43.2 ” –““““““““ﾝ ““““““““˜ Column 24 88 112 Total 21.4 78.6 100.0 Chi-Square ---------------------------Continuity Correction Likelihood Ratio Minimum Expected Frequency -

Elaborasi98/10/28/08

Value ----------1.90682 2.73749 9.429

DF

Significance ---1 1

.16732 .09802

8 08 May 96 SPSS for MS WINDOWS Release 6.0

First-order Tables ( controling for sex ) SEX:

1

LMIDSTAT

pria minat statistik

by

LMPS

LMPS

minat mps

Page 1 of 1

Count ” Row Pct ”tidak be berminat Col Pct ”rminat Row ” 1” 2” Total LMIDSTAT ““““““““•““““““““•““““““““› 1 ” 8 ” 24 ” 32 tidak berminat ” 25.0 ” 75.0 ” 55.2 ” 100.0 ” 48.0 ” š““““““““•““““““““› 2 ” ” 26 ” 26 berminat ” ” 100.0 ” 44.8 ” ” 52.0 ” –““““““““ﾝ ““““““““˜ Column 8 50 58 Total 13.8 86.2 100.0 Chi-Square -------------------Continuity Correction Likelihood Ratio Fisher's Exact Test:

Value ----------5.58407 10.54857 One-Tail Two-Tail Minimum Expected Frequency 3.586 Cells with Expected Frequency < 5 2 OF

8 May 96 SPSS for MS WINDOWS Release 6.0

Elaborasi98/10/28/08

DF ---1 1

4 ( 50.0%)

Significance --------.01812 .00116 .00549 .00630

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First-order Tables ( controling for sex ) SEX:

2

wanita

LMIDSTAT

minat statistik

by

LMPS

LMPS

minat mps

Page 1 of 1

Count ” Row Pct ”tidak be berminat Col Pct ”rminat Row ” 1” 2” Total LMIDSTAT ““““““““•““““““““•““““““““› 1 ” 10 ” 26 ” 36 tidak berminat ” 27.8 ” 72.2 ” 66.7 ” 62.5 ” 68.4 ” š““““““““•““““““““› 2 ” 6 ” 12 ” 18 berminat ” 33.3 ” 66.7 ” 33.3 ” 37.5 ” 31.6 ” –““““““““ﾝ ““““““““˜ Column 16 38 54 Total 29.6 70.4 100.0 Chi-Square ------------------Pearson Continuity Correction Likelihood Ratio Mantel-Haenszel test for linear association Minimum Expected Frequency -

Value ----------.17763 .01110 .17574 .17434

Elaborasi98/10/28/08

5.333

DF 1 1 1 1

----

Significance --------.67342 .91609 .67506 .67628

10 08 May 96 SPSS for MS WINDOWS Release 6.0

Elaborasi 2 SPLIT CORRELATION ANALYSIS Zero-order Correlation MIDSTAT

MPS

MIDSTAT

1.0000 ( 112) P= .

.5928 ( 112) P= .000

MPS

.5928 ( 112) P= .000

1.0000 ( 112) P= .

First-order Correlation (controlling for sex) SEX:

1

pria MIDSTAT

SEX:

2

MPS

MIDSTAT

1.0000 ( 58) P= .

.8099 ( 58) P= .000

MPS

.8099 ( 58) P= .000

1.0000 ( 58) P= .

wanita

MIDSTAT

MPS

MIDSTAT

1.0000 ( 54) P= .

.2321 ( 54) P= .091

MPS

.2321 ( 54) P= .091

1.0000 ( 54) P= .

Elaborasi98/10/28/08

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Contoh HIGH-ORDER P A R T I A L ANALYSIS

CORRELATION

Zero-order Correlation Coefficient MIDSTAT

MPS

MIDSTAT

1.0000 ( 112) P= .

.5928 ( 112) P= .000

MPS

.5928 ( 112) P= .000

1.0000 ( 112) P= .

First-order Partial Correlation Coefficient Controlling for..

LOGIKA MPS

MIDSTAT

MPS

1.0000 ( 0) P= .

.1687 ( 109) P= .077

MIDSTAT

.1687 ( 109) P= .077

1.0000 ( 0) P= .

Elaborasi98/10/28/08

12

- -

Matrix

Correlation Coefficients

- -

MIDSTAT

MPS

LOGIKA

MIDSTAT

1.0000 ( 112) P= .

.5928 ( 112) P= .000

.8054 ( 112) P= .000

MPS

.5928 ( 112) P= .000

1.0000 ( 112) P= .

.6407 ( 112) P= .000

LOGIKA

.8054 ( 112) P= .000

.6407 ( 112) P= .000

1.0000 ( 112) P= .

(Coefficient / (Cases) / 2-tailed Significance) " . " is printed if a coefficient cannot be computed

Elaborasi98/10/28/08

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Elaborasi 3

HIGH-ORDER PARTIAL CORRELATION ANALYSIS • Zero-order Coefficient

Partial

N∑ xy

-

Correlation

(∑x) (∑y)

rxy = [ N∑x2 - (∑x)2 ] [ N∑y2 - (∑y)2 ]

•

First-order Coefficient

Partial Correlation (Controling for A)

rXY - (rXA)(rYA) rXY/A = (1- rXA2) (1- rYA2)

•

Second-order Partial Correlation Coefficient (Controling for A and B) r

XY.A

-

(rXB.A) (rYB.A)

rXY/AB = (1- rXB.A2) (1- rYB.A2) Elaborasi98/10/28/08

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• Third-order Partial Coefficient etc. etc.

Correlation

Uji Signifikansi Statistik Perbedaan Dua Koefisien Korelasi (Marascuilo and Serlin, 1988; p.646)

H0 : ρ = 0

t=

r

N-2-V 1 - r2

Tolak H0 bila t > tN-2-V; α

(two-tailed test)

H0 : ρ = ρ 0 dengan transformasi ke nilai Z

Z = Zr - Z 0

1/ √N-3-V tolak H0 bila Z ≥ 1.96 (bila ∝ = 0.05)

H0 : ρ 1 = ρ 2 dengan transformasi ke nilai Z

Z r - Z0 Z

Elaborasi98/10/28/08

=

1

+

1

15

N1-3

N2-3

tolak H0 bila Z ≥ 1.96 (bila ∝ = 0.05)

Simple Regression • The use of sample statistics to predict population parameters • The use of past and current data to predict future results linear simple regression equation

y| = a +

= the value of y when x

y-intercept (constant) =0

a =

bx

y- b(x)

slope =the number of unit changed in y for every increase (or decrease of one unit in x

N∑ xy b =

Elaborasi98/10/28/08

-

(∑x) (∑y) = N ∑x2 - (∑x)2

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linear simple regression equation

y| = a +

bx

Trend Analysis The use of past and current data to predict future results Tahun saham 1989 1990 1991 1992 1993 1994 1995 1996

Keuntungan per satuan 0.96 1.03 1.23 1.15 1.10 1.40 2.10 ?

2000

Tahu n 1989 1990 1991 1992 1993 1994

?

x

y

x2

y2

xy

1 2 3 4 5 6

.96 1.03 1.23 1.15 1.10 1.40

1 4 9 16 25 36

.92 1.06 1.51 1.32 1.21 1.96

.96 2.06 3.69 4.60 5.50 8.40

Elaborasi98/10/28/08

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1995

7 ∑x = 28

2.10 ∑y = 8.97

49 ∑x2 = 140

4.41 ∑y2 = 12.39

14.70 ∑xy = 39.91

Trend Analysis Tahu n 1989 1990 1991 1992 1993 1994 1995 N= 7

x

y

x2

y2

xy

1 2 3 4 5 6 7 ∑x = 28

.96 1.03 1.23 1.15 1.10 1.40 2.10 ∑y = 8.97

1 4 9 16 25 36 49 ∑x2 = 140

.92 1.06 1.51 1.32 1.21 1.96 4.41 ∑y2 = 12.39

.96 2.06 3.69 4.60 5.50 8.40 14.70 ∑xy = 39.91

N∑ xy

- (∑x) (∑y)

rxy =

= [ N∑x2 - (∑x)2 ] [ N∑y2 - (∑y)2 ] N∑ xy - (∑x) (∑y)

b =

= 0.14 N ∑x - (∑x) 2

Elaborasi98/10/28/08

2

0.81 reject H0

(r0.05;5= 0.75)

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a = y- b(x)

= 0.721

y| = a + bx

•

)

Estimasi profit 1996 (tahun ke-8) = bx = 0.721 =

•

+ 0.14 ( 8

1.84

Estimasi profit 2001 (tahun ke-12) + 0.14 ( 12 ) = 2.41

Elaborasi98/10/28/08

y| = a +

=

0.721

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13 May 96 SPSS for MS WINDOWS Release 6.0

Page 1

****REGRESSION **** Listwise Deletion of Missing Data Equation Number 1 Dependent Variable.. Block Number 1. Method: Enter YEAR

PROFIT

Variable(s) Entered on Step Number 1.. YEAR Multiple R R Square Adjusted R Square Standard Error

.80125 .64199 .57039 .25434

Analysis of Variance DF 1 5

Regression Residual F =

8.96623

Sum of Squares .58003 .32345 Signif F =

Mean Square .58003 .06469

.0303

---------------------- Variables in the Equation -------------Variable Beta YEAR .801245 (Constant)

B

SE B

95% Confdnce Intrvl B

.143929

.048066

.020372

.267485

.705714

.214960

.153151

1.258277

End Block Number

Elaborasi98/10/28/08

1

All requested variables entered.

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Standard Error of Estimate

Sest

= Sy

1 - r2

∑ y2 Sy =

-

( y )2 = 0.36

N

Sest

= 0.36

1 - ( 0.81)2 = 0.21

Accuracy Limits / Confidence Interval Limits ( alpha= 0.05 confidence interval = 95%)

AL.95 = = =

y| [ ± 1.96 ) (Sest ) ] 1.84 [ ± 1.96 ) ( 0.21 ) ] 1.84 ± 0.41

95% confidence y| (1996 profit per satuan saham) = 1.42 ≤ y| ≤ 2.25

Elaborasi98/10/28/08

21 12 May 96 SPSS for MS WINDOWS Release 6.0

Page 1

M U LT I PLE R E G R E S S I O N (Method: Enter) Equation Number 1

Dependent Variable..

Block Number 1. Method: Enter LOGIKA METODE TOEFL TPA Variable(s) Entered 1.. STATSOS 2.. TPA 3.. TOEFL 4.. METODE 5.. LOGIKA

STATSOS

.76899 .59135 .57208 .25410

Analysis of Variance

F =

indeks prestasi kumulatif

on Step Number test statistik test potensi akademik predict TOEFL test metodologi riset test logika

Multiple R R Square Adjusted R Square Standard Error

DF 5 106

Regression Residual

IPK

Sum of Squares 9.90429 6.84428

30.67831

Signif F =

Mean Square 1.98086 .06457

.0000

---------------------- Variables in the Equation ----------------------Variable LOGIKA METODE TOEFL TPA STATSOS (Constant)

B .016074 9.01291E-04 4.23286E-04 .003154 -.034613 1.169435

SE B

95% Confdnce Intrvl B

.006239 .003704 .003307 -.005655 5.8488E-04 -7.36286E-04 5.1792E-04 .002127 .084556 -.202254 .179047 .814457

.028443 .007457 .001583 .004181 .133029 1.524414

Beta .289058 .029872 .074931 .547330 -.044034

----------- in -----------Variable LOGIKA METODE TOEFL TPA STATSOS (Constant)

T

Sig T

2.576 .273 .724 6.090 -.409 6.531

.0114 .7857 .4708 .0000 .6831 .0000

Equation Number 1 End Block Number

Elaborasi98/10/28/08

Dependent Variable.. 1

IPK

indeks prestasi kumulatif

All requested variables entered

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12 May 96 SPSS for MS WINDOWS Release 6.0

Page 2

M U LT I PLE R E G R E S S I O N (Method: Stepwise) Equation Number 1 kumulatif

Dependent Variable..

Block Number 1. Method: Stepwise .1000 LOGIKA METODE TOEFL TPA

IPK

Criteria

indeks prestasi PIN

.0500

POUT

STATSOS

Variable(s) Entered on Step Number 1.. TPA test potensi akademik Multiple R R Square Adjusted R Square Standard Error

.72113 .52003 .51567 .27033

Analysis of Variance

DF 1 110

Regression Residual F =

119.18174

Sum of Squares 8.70979 8.03879 Signif F =

Mean Square 8.70979 .07308

.0000

---------------------- Variables in the Equation ----------------------Variable TPA (Constant)

B

SE B

.004155 1.117701

3.8064E-04 .158138

----------- in -----------Variable TPA (Constant)

T

Sig T

10.917 7.068

.0000 .0000

Elaborasi98/10/28/08

95% Confdnce Intrvl B .003401 .804309

.004910 1.431094

Beta .721132

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12 May 96 SPSS for MS WINDOWS Release 6.0

* * * *

Page 3

M U L T I P L E

Equation Number 1 kumulatif

R E G R E S S I O N

Dependent Variable..

IPK

* * * *

indeks prestasi

Variable(s) Entered on Step Number 2.. LOGIKA test logika Multiple R R Square Adjusted R Square Standard Error

.76642 .58740 .57983 .25179

Analysis of Variance DF 2 109

Regression Residual F =

77.58984

Sum of Squares 9.83814 6.91043 Signif F =

Mean Square 4.91907 .06340

.0000

--------------------- Variables in the Equation ----------------------Variable LOGIKA TPA (Constant)

B

SE B

.015826 .003483 1.230336

.003751 3.8875E-04 .149691

95% Confdnce Intrvl B .008391 .002712 .933652

.023261 .004253 1.527019

----------- in -----------Variable LOGIKA TPA (Constant)

T

Sig T

4.219 8.959 8.219

.0001 .0000 .0000

------------- Variables not in the Equation ------------Variable METODE TOEFL STATSOS

Beta In

Partial

Min Toler

T

Sig T

.061428 .061758 .080414 .086330 -.020683 -.019048

.417039 .475540 .335437

.643 .901 -.198

.5216 .3698 .8434

Elaborasi98/10/28/08

Beta .284609 .604377

24 End Block Number

1

PIN =

.050 Limits reached.

12 May 96 SPSS for MS WINDOWS Release 6.0

Page 5

Multiple r

r1y2 + r2y2 - 2(r1y r2y r12) r 12.y = 1 - r122

y = midstat 1 = MPS

2 = Logika

r1y = 0.5928

r2y = 0.6407

r12 = 0.8054

(0.5928)2 + (0.6407)2 - 2[(0.5928)(0.6407)(0.8054) r 12.y = 1 - (0.8054)2

Elaborasi98/10/28/08

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Multiple Regression y| = a + b1x1 + b2x2 + . . . Sy

r1y - r2y r12

S1

1 - r122

Sy

r2y - r1yr12

S2

1 - r122

b1 =

b2 =

a =

y - b1x1 - b2x2

Standard Error of Multiple Estimate

Sm.est =

1 - r 12.y2

AL.95 =

y| ± 1.96 (Sm.est)

Elaborasi98/10/28/08

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Elaborasi98/10/28/08