Prsteedingrof

The ?th lJrlT-GT Internati*nsl Esnfsrsnce on lrfitrtherustirl,ftstirtitr snd itt fipplicstionr

rErur sA 2t111

"InteIlTgunt $nIutlonr rhn,ru0h fttlathenatirr, *nd,1f*t?rt[n"s'

Iuly Il-E3, 3trll

Eunghoh, Thailsnd

The 7th IMT-GT lnternational Conference on Mathematics, Statistics and its Applications(rcMSA20ll)

Table of Contents

Message from NIDA President

Message from Dean, the Graduate School ofApplied Statistics, NIDA

Message from the ICMSA 201I Chair

Conference Sponsors

Organizing Committee

Full Paper/ Abstracts

Development of Statistical System to Support Effective Decision Making: A Case in Thailand(Abstract Only)

$ra*a@ra

Dynamical Modeling of Delay Mechanisms in Nonlinear Systems in Human Physiolory:Delineating Disease and Health (Abstract Onl)

Exponents and Vertex Exponents of Two-colored digraphs (Abstract Only)tuibSur.ila_

Closed-orbit Counting on Shift Spaces: FromZ to Z" -actions (Abstrrct Anfu)MMSdai Mdl,I.M$ri

Estimation and Model Selection Based on Maximum Product of Spacings for Multivariate Skew NormalFanily (Abstract Only)

ArjwKGrytn

8

9

IO

tl

I2

t4

l5

t6

I7

18

Leavitt Path Algebras over Graphs (Abstract Only)G'ardaAtw& ?bw

Ra$twt t4,lli d 11 *aveMwz

20

21

I9

22

23

24

25

Uniformly Convex Univalent Functions (Abstract Onfu)

Laguerre and Isotropic Surfaces (Abstract Only)Y*$AfuMdw*a*-**-

A Value Function of Discrete Time Surplus Process in Insurance under Investment and ReinsuranceCredit Risk (Abstract Only)

fatu*Wqwtu

More Pomo, More Sex Crimes? Econometric Analysis of Causal Relationships (Abstract Only)W*uiVatryswawal

Out of Crisis Models: An Application of Total Quality Management (TQM) (Abstract Onl)DnltCrw*zt--

The Statistical Analysis of Self Exciting Point Processes with Applications to Market Research(Abstract Only)

WW*deua 26

The 7th IMT-GT lnternational Conference on Mathematics, Statistics and its Applications(rcMSA 20r 1)

Lyapunov Functionals vs Lyapunov Functions for Various Types ofStability ofHybrid StochasticDifferential Equation (Abstract Only)

*{almdArdto*i

On Riemann-Liouville and Caputo Impulsive Fractional CalculusM- Dz lflS"r,

On The Pair of Operations With The Generalized Entropic PropertyAvldr{:la&fi**--

Applicability of Central Limit Theorem on Machine Generated Random Variables forRegression Model

ANiiwT- ?driic@r__

Hybrid Parameters Methods for The Second Order Initial Value ProblemserypAtui

History Matching Reservoir Parameter to Diftrent Type of Reservoirfu**anjl' Mvis , Agw Yod Gww,Arrlrg Kurwd&x A*Wia,NrwW

Modeling Frailty Survival DataWr II*wa, Tatbairt Yry Zufubi-__

Evaluating Advance Efficiency of Bangladeshi Online Banks Using Stochastic Frontier AnalysisMd-,{zrzrd Wn, Antsz Abfutfufu Kqarl_--__-

Love between Two Individuals in a Romantic Relationship: A Newly Proposed Mathematical ModelXg,ls,lri*Gfur,

Least Squares Cubic B-spline Finite Element Approach to Advection Diffirsion EquationS-Dh*@r,S-Kuw,S"KW

Heat Transfer and Fluid Flow Characteristic in a Rectangular Cavity with Partial Heatingand Cooling at Side Walls

?ruveztLila:a, S.fir{r$trd $, KW.

Evaluating Environmental Performance in Highway Construction Using Neuro-firzzySystern and logistic Regression Analysis

Tk*&i&fi,iryar_**

Queueing System with Service Channels Lirtked Under Pre-emptive Priority Service RuleS- Agr*ead LM I:rw@i" *KW, A- Crrueffi, 8. fl. Stryrr-..-...-.-__

Two Levels Regression Modeling of Trading Day and Holiday Effects for ForecastingRetail Data

$dwtw MalwMl{irywle

Sequential 'Fixed-Ratio Width' Conhdence Interval for Reliability Function: Case ofWeibull Distribution

R**ad Gupu, Ydrt &di, Su*ril Xord

Power of Two-tailed M Test*ass itaM{tw S@iarry.Klna_ _ - -

Statistical Analysis of Various Risk Factors of Tuberculosis (TB) in District Mardan

27

28

40

46

56

66

76

8J

97

t05

126

t36

il2

t50

t65

t72

178e- fuM* Latrka K*aa Nsi*e_

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 201l)

Estimation in a Random Effects One-way Model: A Multi Stage ApproachJ P StuqftJoorcl" XdurGupts, Sclwn*-____

Strategizing Planning using MCDM: a Case of Malaysian Local AuthortiesMahd Sa*rrl" Sar$n4 ?narbaiaso Kwt&in, Rillqe Arwr, Ndsiah Mfuwd

Motion Planning and Control of a n-LinkNonholonomic Mobile ManipulatorShorel SWh Bibfry $wra Aviws$ Prwd

Break-And-Fit Strategy for Bezier and Beta-Splines CurvesNarni,&&l IIdi" A"st?Mh lbrahim, Fatilnalz Yalqn" J&wlrdia Md Ali

On Upper and Lower Boundaries of Real Log Canonical Threshold and Free EnergyTafushiMatsafu

Parametric Programming and Its Effects in Determining the Feasible Regionfor the Projects in the Developing Countries

HesfuwAww_-

Outliers Detection inFvzy Regression Approach with Asymmetric Trapezoidal Fwzy DataA- Mde*i-

Approximate Bayes Estimators of the Parameters of Weibull Model under Squared andEntropy Loss Frmction

Utw*ipryjow

A dynamically Consistent Numerical Method for Sirs Epidemic Model with Non-monotonelncidence Rate

Agn$ Srtwnto

Complex Function Bergman Classes with Measures!*F- *ei'effis O-. L-&{- Tavs S-. Rslre& 7fu

Mathematical Modelling of Love Wave in an Anisotropic Porous layerSsrrri, Xurw Yis*wa*srazq Srt shbcu#fl-

Nonlinear Extension of Sliced Inverse Regression using the Geodesic Distance Approximation

Trapezoidal FtzzyData in Hybrid Fuzzy Regression Analysisf. Rmzahnia-

Statistical Modeling on Area, Production and Productivity Trends of Mustmd(Brassica juncea L. Czern) Crop

R4! ar*hirwa 4 X knt{ta*woi Kw,twz

Optimal Sliding Mode Control for Spacecraft Approaching a Tumbling TargetChatipfun Pufuboon____

Statistical Inference on Minimax Distribution in the Presence of OutliersI*wtMaWs*a, Pwiz Nrcil

Formation Types of a Flock of l-Trailer Mobile RobotsK Sqlrrrwliju,S' Strylr B " Slzwtsw, G- {iWM _-- - --

203

218

226

236

251

273

283

t84

t9r

2s8

297

312

323

346

337

359

368

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 201r)

Infant Growth Card by Using Weighted SplineJ€""y fuiTrgry ?w*wo, I llprw fuf*awa" Ms,eWw4AfiWw

New Results for Global Asymptotic Stability ofNeutral-Type Delayed Neural NetworkstuyaJrodr,M"idri**__

A Cyclic Constrained-Search Algorithm for a Two-Stock Universal PortfolioClwa Petg Ta lw l{eag Pe*,

Failure Inference of Marker Process Based on Bivariate Gamma ModelSadMzktwMs

Vertex Exponents of 2-digraphs with Largest Exponentsageai Stdw@r{ Sa& &tft o-

Fish Processed Production Planning Under UncertaintyRilae Wi@asw| Modi*ta lruwaty, it*rtwt l{aretgftatg*

Endomorphism Monoid and Group of Cycle Graphs

i94

383

442

412

424

438

450

457

464

474

489

5u

525

539

547

WirddRw,ltriwEie*ss*i 496

Yulia ksd, Nryiszsa lsrvril, Sa4fal l{@ze Jw,**__

Interval Estimation for Quantile on One Parameter Exponential Distribution under MultipleType-II Censoring

Al&MFry-

Towards an Optimal Allocation of the Fiscal Stimulus Package: A Linear Goal ProgrammingApproach

MabELA*an

Time*Reliazdwafo\71rdletJiaasNfuhta* _-____*=_Marginal Homogeneity Model for Open-ended Categories in Square Contingency Tables

*@tAtu$-_____

Exponential Extrapolation Method for the Solution of Initial Value Problems in OrdinaryDifferential Equations

AstwAli Elkte€, tut*M. Taib

Progressively Type-tl Hybrid Censoring Schemes with Log-Normal DistributionFwifu l{e*nwi, ilswile Kl*nwt

Vertex and Edge Independence Sets of N-gonal SystemsW@lffi Krsrdnbfu* Thit& Jtuwdrsbot

Imaginary Numbers as Quantum Superposition States and a Proof of Complex VectorConjugation

Zero-inflated Poisson Versus Zero-inflated Negative Binomial: Application to TheftInsurance Data

Atali*& Z*IWL Nqiwra lsgfEil A]erwd l,ddr *@di.

Development of Statistical Approximation Model Using Weighted Error Adjushent MethodsWri{rw, Xilrfug, Atwwi Na-&*, .fuast *wqrAszmM

Clayton Copula in Handling the Dependence of Claim Severities

555

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 201l)

Mode Choice Decision: an [nvestigation into Suvamabhumi Airport Rail Link ServiceIntroduction

Pad*aJit&m

Odds Ratio for Contingency Table with Fuzry CategoriesFllo Ro&crt F- @,8 fu____ -_

Interval Prediction for Pareto Lifetime Data of Known Shape Parameter under Type-IICensoring with Bayesian Method

ffuA*rwXtptd;_

Doubly Multivariate Model Analysis for High Dimensional Multivariate Repeated MeasuresXwu*gw ff*w*asi futtwa CbWcSwwa_

Analysis and Improvement of Non Repeatable Run out Disturbance from Head StackAssembly in Hard Disk Drive

Cfux@a arwaphryha Yryn M@__

AWell-Defined lnterpretation of the Rule of Thumb for the Bemoulli ParameterturyWcrrw*Wl*yaAryfie*-

Improving Error Control Using Stopping Sets of CodesCh&*kqTsad" Yw-{,aiXu

A Finite Capacrty Scheduling System for Assembly Flow Shop with MultipleCommon Due Dates: A Case Study

T?wie#Wtwh Pisd{sy&

Aggregate Production Planning with Workforce TransferringPlan under UncertainDemand and Cost

Khbfu Wr A{a*warytua Prwl {zw&i

Estimation of A Joined Point in Tobit-Piecewise Regression ModelTilirnt Tkipblwas__

Tweaking Narve Bayes Classifier for Intelligent Spam DetectionAnfua RMi, Suail ?racit tal_

Fuzry Constrained Minimization on Quadratic Programming Problem

WWta, Yos?n Dar;rtt" Iwait *in MoM_

On the Numerical Solution of Linear Stiff IVPs by Modified HomotopyPerturbation Method

M- S- t{- Clwdtary, I- Iflasldar--_--

Statistical Analysis on the Reliability Tests in the Resin Coated TransformerInsulation Systems

Niolwl Clseg. Clw-It lry{tu, W1*y*ritg{*mS6g

Saw Tooth Function for Enhancing Facial Pattems Detection Usiag Dynamic Time Warpingbry Ad*w, I{a,wah Arcf, I{n rza Ydd-_ __

Broadcast Group-oriented Encryption Based on Braid GroupsNwwaa @wua*dgaia PW l$"Mfubrrr__

647

626

562

575

586

s92

619

632

702

709

7t5

726

647

662

682

694

The 7th IMT-GT Intemational Conference on Mathematics, Statistics and its Applications

(rcMSA 2011)

Clustering of Regencies or Cities in Aceh Province with Prineipal Component Analysis

and Cluster AnalysisAwp Stryw,Nwlwswttdt--

English Mastery Level of FMIPA Unsyiah Graduates Using Binary Logistic

Regression Analysis{ifri&rwA-X._

Propensity Score Classification in Estimating the Difference between Two Means

Mwar&. $ismi&et:

Feature Selection on community Health Development lndex in Indonesia using

Relief Algorithmhrmila Madi Xesuwa*

- - - -

The Approximation of Bootstrap Residual in Estimating Parameters of Regression Model

Novakryfu" M*z*i

Study on an EOQ Model with Three-Parameter Weibull Distribution Deterioration

without Shortage and Price-Dependent Demand

CWon Kuxw S&o, &islndr Kurrw Mwa

Generating Stock Trading Strategies

,Anawurla Pirw'* 0h ?rSsnil -*

736

752

771

781

758

766

The 7th IMT-GT lnternational Conference on Mathematics, Statistics and its Applications(rcMSA 20l l)

Message from NIDA President

& bdplf oflIatiorml lnstitute ofDeveloprnd Adarinistratim G\&DA)" it is a gred pleasrre for us tobc&shofit adwslcome aII pffiticipffitoffre ?e IhdTSTInterMisrt Curferwcc m}da*hunaics,SHis*ics" aud its Aspticatio*s (ICMSA 2OIII Ar urc ae aII preeirnd &at fu objective of thisfttun*imal c*rfmre is slmiag *rrow@c in mdremxics and #i$ics and discussing of tkirrylication to s€rve our life r*l*h Ming us &om setF&velopryre$, to rratisrall derrehFmmt ad torqimf nnd glokl &elapmddld- Thlii$ ahigh hontroft"ffDAtolpHslc& m iryuffiercnta its main @iective is ihe same as IIIIDA's $ril@ry'Wisdom fmCkprIffiomtr Insitr*e of Developmmt Adminisirat*m m e#lisH fonawing Hi$ Mflixty tk KingBhrrribol A&rly&j's visim of drarcirg mnrtr5r's fuelorynrer*- \Yc ue bsmd to the responsibihlyof pro&rcing dxxed agsmts of drage to serne ttc CICIrnry- This is ve4r impessirae mom€nt f.Hf atlagffibs of furge ftwtr difu angle of the wryld are aII togp$er twe d rniq fime- Na mdterditreent ra&6 s.e are, differcr* we r$s, ditrusrt religims urc fai$f ,ne all leve trhs sxrnegoal- I'o dwrp ud develop &is worHhy rning wisdoilr as a ktand teclmsl€ies as hands is theuhimate prpoee of rhis conferme-

I hve a @ beli€f tk ee f IGdSA Confmroe witl be a @c fs all dis€itrg$isrd sdralarprticiprtq ma&erndicians, sffiisicians, rmwclm and let*urem to dlare lmowl@s" discuss ofaosr:bilisies;E fuir ryIic4ims d driwet&e cmfuesse g@t- FimIIy, f smrld liketadelivermy5lassp lharrks to aI Organiziqg Corymittee fcr eeir cffort and lmrd wor*ing on hosting this pwiousEmHrL Iwi*ymrdI apleasirgadpkawrttrip&riryyorrsfay ieTh*iM\#ithrrwrnwelcome

Sincerely yours,

5-ffff-a-'.u*^p-Professor Dr. Sombat Thamrongthanyawong

President, National lnstitute of Development Administration

The 7th IMT-GT Intemational Conference on Mathematics, Statistics and its Applications

0CMSA 20ll)

Message from l)ean, the Graduate School of Apptied Statistics,NIDA

On behalf of the Graduate School of Applied Statistics, National Institute of DevelopmentAdministration (NIDA), it is a great honor and sincere pleasure to welcome all participants to the 7frIMT-GT International Conference on Mathematics, Statistics and Its Applications GCMSA 201 l).

This year, the Graduate School of fuplied Statistics has an horor to organize this meaningfulinternational conference. I believe that the pupose of dris conference is not only sharing knowledgeamong mathematician, statisticians, and scholars in related fields but also to hearten new generationof expertise in mathematics and statistics to realize the science and technology advancement.

Absolutely, it is undeniable that science and technology are the products of mathematics and statisticsapplications. Disciplines like computer science, information technolory, operational research,logistics management risk marugeinent" engineeriag and nmny olhers arc all tlrc products ofmathe,rratics and statistics. Thus, it is essential that we must hold this arurual conference as a stage forall scholars in finding new ideas and applications on Mathematics and Statistics.

Greatly thank to all supportive session including organizing committee, keynote speakers, invitedspeakers, paper reviewers, participants and sponsors. This event will not achieve without you all.Lastly, I hope that the outcome of ICMSA this year will be pleasing and most useful to everybody.

Sincerely yours,

J***3rr***Dr. Lersan Bosuwan

Dean, the Graduate School of Applied Statistics

I

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 20ll)

t0

Message from the ICMSA 2011 Chair

On behalf of the organizing committeg it is my great pleasure to welcome all participants of the 7tr

IMT-GT International Conference on Mathematic, Statistics, and ib Applications. This conference

had been held for six times in Indonesia and Malaysia. It is the first time that Thailand hosts theconference and the School of Applied Statistics, National Institute of Development Administration, is

honoredto organize this irnporhnt event

Mathematics and Statistics are the major tools for solving problerns and making the right decisions.They play vital roles to the development of science and technolory in the IMT-GT region and beyond.

The regular meeting among researchers in the fields like this conference will promote the progress

and advancement of the fields. This conference will surely serve as a venue for researchers in thefields to present their works, exchange ideas and soek collabomtion Participants from {he IMT-GTregion and many cotmtries around the world will attend the conference. More than 10 distinguishedspeakers from many counkies are invited to give talks in the conference. So I hop all participantswill enjoy attending to the talks and paper presentations as well as have very fruitful discussions.

I would like to take this opportunity to thank all the keynote and invited speakers for coming andsharing lheir lvrowledge with us. tr arn also very gmtefirl to all i{teraaJional scienlific committce,paper reviewom and sponsors. Without their helps and supports, the preparation for the conferencewould deem impossible to complete. Fioally, I would like to thank all participants for joining theconference. I do hope all participants will have opportrmity to explore Bangkok City and eqioystaying in the City of Angel.

Sincerely yours,

5 #e*Associate Professor Dr. Surapong Auwatanamongkol

Chair of the ICMSA 20fi Orgarttzing Committee

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA2011)

ll

Conference Sponsom

.*ffiffi#" *o,urro' center co., Ltd. (scM)

National Research Council of Thailand

Government Savings Bank

Ocean Life Insurance Co., Ltd.

The 7th IMT-GT lntemational Conference on Mathematics, Statistics and its Applications(ICMSA 201l)

t2

Organizing Committee

International Scientific Committee

Prof. Dr. Herman Mawengkang

Prof. Dato Dr. Rosihan M. Ali

Prof. Dr. Yongwimon Lenbury

Assoc. Prof. Dr. Anton Abdulbasah Kamil

Assist- Prof- Dr- Kanchana Kumnungkit

Assoc. Prof. Dr. Pachitjanut Siripanitch

Assoc. Prof. Dr. Surapong Auwatanamongkol

Assoc. Prof, Adam Bahmum

Assoc. Prof, Putipong Bookkamana

Dr. Hizir Soffan

Dr. Saib Suwilo

Dr. Tarmizi Usman

Dr. Yosza Dasril

Itrat Orgauising Committee

Chair: Assoc. Prof. Dr. Surapong Auwatanamongkol

Advisory board:

Prof. Dr. Prachoom Suwattee

Assoc. Prof. Dr. Anumongkol Sirivedhin

Assoc. Prof, Dr. Vichit Lorchirachoonkul

Dr. Lersan Bosuwan

University of Sumatera Utara,

bfunesia

Universiti Sains Malaysi4 Malays ia

Mahidol Univ wsity , Thailand

Universiti Sains Malaysia, Malaysia

King Mongkut's Institute of

Technolory, Ladlcabang Tluil and

National Institute of Development

Administrati on, Thail and

National Institute of Development

Administratiorq Thailad

Universiti Sains Malaysi4 Malays ia

Chiang Mai University, Thailand

Syiah Kuala University, Indonesia

University of Sumatera Utara,

Indonesia

Syiah Kuala University, Indonestq.

Universiti Teknikal Malaysia,

Malaysia

The 7th IMT-GT lntemational Conference on Mathematics, StatisticsgcMSA20ll)

and its Applications

13

Members:

Assoc. Prof. Dr. Duanpen Teerawanviwat

Assoc. Prof. Dr. Jirawan Jitthavech

Assoc. Prof. Dr. Pachitjanut Siripanitch

Assoc- Rof Dr. Pipat Hiranvanichakom

Assoc. Prof. Dr. Patcharaporn Neammanee

Assoc. Prof. Dr. Raweewan Auepanwiriyakul

Assoc. Prof. Dr. Samruam Chongcharoen

Assist. Prof. Dr. Jugkarin Sukmok

Assist Prof. Dr- Kannapha Amaruchkul

Assist. Prof. Dr. Nithinant Thammakoranonta

Assist. Prof. Dr. Ohm Sornil

Assist. Prof. Dr. Pramote Kucharoen

Assist. Prof. Dr. Preecha Vichitthatnaros

Assist. kof. Dr. Sukanya Suranauwarat

Assist. Prof. Dr- Supoj Sutanthavibul

Assist. Prof. Dr. Warapom Jirachiefoattana

Assist. Prof. Patrawadee Tanawongsuwan

Assist. Prof. Weena Chaisilaparungruang

Dr. Rattakom Poonsuph

Dr. Siwiga Dusadenoad

fh. Sutep Tongngarn

Dr. Watchareepom Chaimongkol

Mr. Worathep Chantakanakakom

The 7th IMT-GT lnternational Conference on Mathematics, Statistics and its Applications(rcMSA20ll)

752

Propensity Score Classificationin Estimating the Difference between Two Means

Marzukil and Nazaruddinl

t Syiah Kuala University, Banda Aceh, Indonesiamarz_ukie@yahoo. com

AbstracL The result of comparison of a parameter among two populations willbe bias ifthe objects in both population are different in their background. Directestimation method assumed that there is no influence of other variable(covariate) or in the other word, it can be said that each observation objects havethe same background except observation variable. One ofthe ways which used tocontrol the difference is divide the background ofthe objects to the classes basedon observation characteristic. One ofthe characteristics is propensity score. Theaim of this research is to evaluate mean difference of graduates GPA betweengraduates who school origin at urban area and rural area, and between male andfemale graduates by using propensity score technique. There are 7 variables ineach group ofdata. Those variables are graduates GPA asI, School origin or

sex as Z, and 5 others ( X, to X5 ) as X (length of study, length of thesis

completiorq batch (irrcoming year), fields of interes! and sex or school(SMA/SMK/IUA) origin). Alleged of GPA differences batween graduates whostudied ai senior high school in urban areas and in rural areas is -0.16187. GPAof graduates who have school origin in rural areas is higher than in the urbanareas.

Kelrvords : propensity score, classihcation, estimating, covariate

l.Introduction

The estimation of mean difference among two populations using regressionanalysis can be done by one independent variable, namely indicator vafiable Zto the model. Meanwhile, covariate variables can be entered to the model as

other independent variables. The expectation the difference between the meansof two populations is presented by coefficient fuatn Z, for sxample 6.However, the conclusion which taken is based on all other constant variable.

The result of comparison of a parameter among two populations will bebias if the objects in both population are different in their background. Forinstance, a research is to estimate the difference of GPA between graduateswho was school origin (SMA/SMK/MA) at urban area and rural area, orbetryeen male and female graduates. The estimation will be diffrcuh if it isdone directly because among those graduates have different field of interest ordifferent batch.

ISBN: 978 - 974 - 231- 812 - 3

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 201l)

753

Direct estimation method assurned that there is no influence of othervariable (covariate) or in the other word, it can be said that each observationobjects have the same background except observation variable. One of theways which used to control the difference is divide the background of theobjects to the classess based on observation characteristic. One of thecharacteristics is propensity score. The estimation of propensity estimation isdone through the logistic model.

This researsh ryas done by collecting graduates data in the last 4 (four)year at Mathematics Department, Faculty of Sciences, Syiah Kuala University.Evaluation of graduates data is done in two cases, based on school origin andgender.Numberofsampledatausedis 146. The aim of this research is toevaluate mean difference of graduates GPA between graduates who schoolorigin at urban area and rural area, and between male and female graduates byusing propensity score technique.

Z.Data and Method

This research is use primary data, sourced from a database in mathmaticsdepartment, Syiah Kuala Universit5r in Aceh. There are 7 variables in eachgroup of data Those variables are graduxes GPA asI, School origin or sex asZ, and 5 others (Jf, to Xr) * X (length of study, length of thesis

completion, batch (incoming year), fields of interest, and sex or school(SMA/SMK/MA) origin).

Variable of sex is used in the comparison of graduated GPA, betweengraduates who have school origin in the urban areas and rural areas, as one ofit's covariate. lilhereas, when the differences of graduated CPA between maleand female is allegedly, then variable of school origin is used as one of it'scovariate in addition to four other covariates (length of study, length of thesiscompletion, batch, and fields of interest).

The estimation of mean difference in these two populations is done withthis following steps:

l' o-t'z -lrrz-..\ \l. tngistic model in hl --:lY-ril-1-:'l- l: *'P is checked based on rhe

[l-P(Z=tlX=x\) --r '-

sample data for covariate and group indicator (Xu Z,), i: 1,2,..., n.. Then

logistic model parameter estimation (B)is searched.

2- Propensity score estimation is calculated for each observafion which use

01x1 : .*Gl ?o and put it in the smallest score to the biggest score.1+exp(x'B)

3. Objects were divide to be K class based on the propensity score for thewhole observation with these following steps:

ISBN: 978 - 974 - 231- 812 - 3

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(rcMSA 2ol r)

754

(1) Determine the range of propensrty score which is the differencebetween the maximum score and the minimum score.

(2) Determine the wide of each class interval which is the division betweenthose regions and the number of classes.

The result of the alleged differences using propensity score technique is then tobe compa.red with the allegation by using the classical method (t-test) withoutapplying vector of covariates in the calculations. The software which is used togenerate and data processing is done with MATLAB 7.0.

3. Result and Discussion

3.1 Data Description

The number of graduates collecGd arc 146 samples which are consisted of 118samples obtained from schools located in urban areas and 28 are from ruralareas. Data are also consisted of 43 males and 103 females. Graduates databased on fields of interest is comprised into mathematics is 41 samples,statistics 62 samples, and computing is 43 samples. If the data is observedbased on incoming year (batch), then the incoming year 2000 and 2001respectively are 8 graduates, and.incoming year 20O2 to 2006, respectively 28,52,22,15, and 13 graduates.

Based on the samples collected, the graduates GPA is 2.9778. Whilst theaverage of length of thesis completion is 8.2329 months and it's standarddeviation is 5.2378 months. The average of length of study and the averagestandard deviation respectively 67.7397 months and 11.5699 months.

32 Estimalion of Difrerence using Propensity Score

Evaluation using propensity score classification was done by determining theregion of propensity score. For comparison on the basis of school origin,territory acquired by 0-2976- Table 1 show that the interval value of sampleswas divided into 5 classes.

Table l- The values ofthe partition (school origin)

Kelas (k) Batas Kelas v,o Yrorltt

I 0,6296<11<0,68922 0,6892 <12<0,74873 0,7487 < I3< 0,80824 0,8082 <t4<0,86775 0,8677 <l\<0.9272

45

8

92

68

384t25

2,666"1

2,73252,87032,99003.t912 3.3000

2,81152,92403,08373,1 156

Jumlah 28ll8

ISBN: 978 - 974 - 231- 8t2 - 3

i

i

;

:

i

!

I

t

i

i

i

I

I

I

tII

I

I

II

IiI

I

tI

I

iIII

I

The 7th IMT-GT Intemational Conference on Mathematics, Statistics and its Applications

0CMSA 2011)755

The approach, which to have the result as is shown in table 1, was doneby using steps of creating partition of subject into 5 classes interval. Theclasses interval was created in order to meet the assumption that at least there is

one subject in each class derived from each population.Based on Table 1, the estimation of GPA differences between graduates

who come from urban high school and outer urban, using the equation

" J-( tn., +n^,. - )

'=)[' " *- <fr-'rrr) is -0'16187' lt means that applving of five

covariate variables can be resulted the mean differences of GPA betweengraduate coming from the school origin in urban areas and rural areas

approximately is -0. 16187.

GPA comparison based on sex, obtained an area of 0.7036. Table 2

shows that samples is comprised into 5 classes interval.

Table 2. The value ofthe partition (sex)

Ratas Kelas YouY,11rtKelas&)

472t24l0

1

76t47

9

I2

-1

45

0,0418<Ir<0,18250,1825 < 1230J2320,3232 < I3< 0,46400,4640 < t4<0,60470,6047 <ts<0,7454

3,15713,01332,96502,8t43) 1q))

3,14702"88712,88292,77602_7300

Jumlah

By using the same approach, graduate GPA of alleged differencesbetween male and female approximately is 0.057165. The result is obtained byconsidering the background (covariate) of each sample, such as the length ofstudy, length of thesis completion, incoming year, fields of interest, and sex.

3.3 Estimation of Difference using l-Test

Estimation of GPA difference between graduates who coming from the schoolin urban areas and rural areas by using t-test approximately is 0.1310. Byusing 957o of confidence interval, the result of prediction differences are(0.0233;0.2388). The use of 5%o of a is lead to the conclusion that the GPAbetween the two populations (school origin) were significantly different. TheGPA of graduates who used to attend school in urban areas is higher (0.1310)compared to graduates who used affend the school in rural areas. The resultingdifference is assumed that the background (covariate) ofeach graduate is notaddressed.

10343

ISBN: 978 - 974 - 231- 812 - 3

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applications(ICMSA 201l)

756

Similarly, it is also true for the prediction difference of GPA betweenmale and female. Without considering other factors, differences of GPA amongmale and female graduates approximately is -0.1846. GPA of female graduateswas higher than male graduates, that is equal to 0.1846. Whilst, by using 95%of confidence interval, the difference is (-0.2683; -0.1009).

4. Conclusion

Estimation of GPA difference of two populations was done for two cases

based on the population of school origin and population by sex. Covariateswere included for the first case study is a length of study, length of thesiscompletion, incoming year (batch), fields of interest, and sex. Whilst thecoyariate for the second case is same as the first case, except is sex covariatevariable that was replaced by the school origin variable. There are severalthings that can be concluded in relation to the study, that are:1) Alleged of GPA differences between graduates who studied at senior high

school in mban areas and in rural areas is -0.16187. GPA of graduates whohave school origin in rural areas is higher than in the urban areas.

2) Alleged of GPA differences between male and female graduates is0.057165. GPA of male graduates is slightly higher than the GPA of femalegraduates.

3) If the prediction does not consider the vector of covariates, the resultsobtained were contrary, whereas the differences of the average of GPA ofgraduates for the first case is 0.1310. GPA of graduates who have schoolorigin in urban is higher than in rural areas- For the second case, thedifference is (-0. 1846).

5. Acknowledgements

We conveyed many great thanks for Department of Mathematics of Math andNatural Science Faculty, University of Syiah Kuala which had support thefacility to do this research.

ReferencesHosmer DW, Lemeshow S. 1989. Applied Logistic Regression. John Wiley & Sons, New York

Marzuki Faldrrurrazi. 2006. Pengkelasan dengan Skor Propensitas, Jurnal Statistika Vol. 6 No. 2,Nopember 2006, Jumsan Statisik FMIFA UnisbE 81 - 86

Parsons LS- 2001. Reducing Bias in a Propensity Score Matched-Pair Sample Using Greedy MatchingTechniques. Onration Research Group paper 214-26

Rosenbaum PR, Rubin DB. l9M. Reducing Bias in Observational Studies Usiag Subclassification on thePropensity Score. Joumal of the American Statistical Association 79318-328

ISBN: 978 - 974 - 231- 812 - 3

The 7th IMT-GT International Conference on Mathematics, Statistics and its Applicatims(ICMSA 2011)

75,7

Supardi A. 2003- Metode Grafls untuk Pemeriksaan Model Regresi Logistrlc Skripsi tll&dipublikasikan. Jurusan Statistika Universitas lslam Bandung

Tu W, Zhou XH. 2003. A Bootstrap Confldence Interval Procedure for the Treatment Effec Lr-gPropensity Score Subclassification. UW Biostatistics Working Paper Series paper 200

ISBN: 978 - 974 - l3I- 3rl - 3