Published by The Institute of Applied Statistics Sri Lanka · The Institute of Applied Statistics...

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APPSTAT NEWSLETTER Published by The Institute of Applied Statistics Sri Lanka 2nd floor of the OPA building ‘The Professional Center’ No. 275/75 Prof. Stanley Wijesundera Mawatha Colombo 07 Sri Lanka Tel/Fax : 011 2588291 Email: [email protected] ISSN -1391-4995 July 2012 FIRST ANNUAL GENERAL MEETING of IASSL First Annual General Meeting of the Institute of Applied Statistics, Sri Lanka (IASSL) has been scheduled to be held on Saturday 24th November 2012 at the Audito- rium of the Organization of Professional Associations, OPA, in Colombo. Although an agenda for the event has not yet been finalized, there are few significant fea- tures are to be included in the agenda. The AGM will be followed by a Technical session where Sri Lankan researchers are provided with a chance to discuss and share their research findings with others. House and Finance Management Committee of the IASSL will be organizing this event. The Executive council, on the recommendation of the Research & Development Com- mittee has decided to recognize the research activities of our young researchers by awarding the Best under- graduate and postgraduate awards at the AGM. The de- tails are published in our website. The council invites applications from suitable candidates for these awards. On the recommendation of the Statistics Popularization Committee, a National Statistics Olympiad has been or- ganized by the IASSL to popularize statistics among school children. Details are found in the website. It is a well known fact that there is a large percentage of failures in Mathematics at the GCE (AL) Examina- tions as they fail to answer two statistics questions well. Therefore this Statistics Olympiad is expected to encour- age the students to study statistics in the future. The awards and certificates for the successful candidates of this Statistics Olympiad will be distributed at the Tech- nical Sessions of the AGM. Currently we have only one Honorary Fellow; Prof. C. R. Rao, who was awarded an Honorary Fellow at the International Statistics Confer- ence last year. As per section 1( C) of Rules adopted at the Inaugural General Meeting, several distinguish members who held life membership over 10 years and had done immense service to the statistics discipline and/or to the IASSL/ASASL will be awarded Fellows of the Institute. The Executive Council advises its mem- bers to use the title MIAS(SL) which identifies you as a member of our Professional Organization. This is ad- vantageous to both the member and to the IASSL. For members it will identify them as professionals; that is a member of a professional organization, and for the in- stitute it will publicize the title MIAS(SL) among other professions. More details about the AGM will be pub- lished in our next Newsletter Eminent Statisticians for the Editorial Advisory Board and the Board of Associate Editors of the SLJAS The following Eminent Statisticians make honorary con- tributions as the Editorial Advisory Board of the SLJAS: Prof. C.R. Rao Penn State University, Pennsylva- nia, USA Prof. Nitis Mukhopadyay, University of Connecti- cut, USA Prof. Tim Swartz, Simon Fraser University, Canada Prof. Shelton Peiris, The University of Sydney, Australia The following Eminent Statisticians make honorary con- tributions as the Associate Editors of the SLJAS: Prof. Rahul Mukerjee Indian Institute of Manage- ment, Calcutta, India Prof. Aera. Thavaneswaran University of Mani- toba, Canada Dr. S. Ganesalingam Massy University, Welling- ton, NZ Dr. Samaradasa Weerahandi Pfizer , USA Prof. S. Huda University of Kuwait Prof. Neville Weber University of Sydney, Aus- tralia ISSN -1391-4995 Appstat Newsletter July 2012 Page 1

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APPSTAT NEWSLETTERPublished by

The Institute of Applied Statistics Sri Lanka2nd floor of the OPA building

‘The Professional Center’No. 275/75

Prof. Stanley Wijesundera MawathaColombo 07

Sri LankaTel/Fax : 011 2588291 Email: [email protected]

ISSN -1391-4995 July 2012

FIRST ANNUAL GENERAL MEETINGof IASSL

First Annual General Meeting of the Institute of AppliedStatistics, Sri Lanka (IASSL) has been scheduled to beheld on Saturday 24th November 2012 at the Audito-rium of the Organization of Professional Associations,OPA, in Colombo. Although an agenda for the eventhas not yet been finalized, there are few significant fea-tures are to be included in the agenda. The AGM willbe followed by a Technical session where Sri Lankanresearchers are provided with a chance to discuss andshare their research findings with others. House andFinance Management Committee of the IASSL will beorganizing this event. The Executive council, on therecommendation of the Research & Development Com-mittee has decided to recognize the research activitiesof our young researchers by awarding the Best under-graduate and postgraduate awards at the AGM. The de-tails are published in our website. The council invitesapplications from suitable candidates for these awards.On the recommendation of the Statistics PopularizationCommittee, a National Statistics Olympiad has been or-ganized by the IASSL to popularize statistics amongschool children. Details are found in the website. Itis a well known fact that there is a large percentageof failures in Mathematics at the GCE (AL) Examina-tions as they fail to answer two statistics questions well.Therefore this Statistics Olympiad is expected to encour-age the students to study statistics in the future. Theawards and certificates for the successful candidates ofthis Statistics Olympiad will be distributed at the Tech-nical Sessions of the AGM. Currently we have only oneHonorary Fellow; Prof. C. R. Rao, who was awarded anHonorary Fellow at the International Statistics Confer-ence last year. As per section 1( C) of Rules adoptedat the Inaugural General Meeting, several distinguishmembers who held life membership over 10 years andhad done immense service to the statistics disciplineand/or to the IASSL/ASASL will be awarded Fellows ofthe Institute. The Executive Council advises its mem-bers to use the title MIAS(SL) which identifies you asa member of our Professional Organization. This is ad-

vantageous to both the member and to the IASSL. Formembers it will identify them as professionals; that is amember of a professional organization, and for the in-stitute it will publicize the title MIAS(SL) among otherprofessions. More details about the AGM will be pub-lished in our next Newsletter

Eminent Statisticians for the EditorialAdvisory Board and the Board of Associate

Editors of the SLJAS

The following Eminent Statisticians make honorary con-tributions as the Editorial Advisory Board of the SLJAS:

• Prof. C.R. Rao Penn State University, Pennsylva-nia, USA

• Prof. Nitis Mukhopadyay, University of Connecti-cut, USA

• Prof. Tim Swartz, Simon Fraser University,Canada

• Prof. Shelton Peiris, The University of Sydney,Australia

The following Eminent Statisticians make honorary con-tributions as the Associate Editors of the SLJAS:

• Prof. Rahul Mukerjee Indian Institute of Manage-ment, Calcutta, India

• Prof. Aera. Thavaneswaran University of Mani-toba, Canada

• Dr. S. Ganesalingam Massy University, Welling-ton, NZ

• Dr. Samaradasa Weerahandi Pfizer , USA

• Prof. S. Huda University of Kuwait

• Prof. Neville Weber University of Sydney, Aus-tralia

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• Prof. Nader Tajvidi Lund University, Sweden

• Prof. G. Shmuali University of Maryland, USA

• Prof. David Allen Edith Cowan University, West-ern Australia

• Prof. Richard Gerlach University of Sydney

• Prof. Alan Hutson University at Buffalo, NY, USA

• Prof. Karunarathna B. Kulasekera, University ofLouisville, Louisville, USA

• Prof. Sarma Yadavalli - University of Pretoria,South Africa

• Prof. A. Nanthakumar - State University of NewYork at Oswego, Oswego, NY, USA

The contributions of these eminent statisticians will un-doubtedly help the IASSL to bring the SLJAS to a levelof an indexed journal within a short period of time.The IASSL greatly appreciates their invaluable contri-butions.

Calling Papers for SLJAS

The Volume 12 (2011) of the Sri Lankan Journal ofApplied Statistics (SLJAS) is now available on-line athttp://www.iappstat.lk. It is expected to publish twoissues of volume 13 in 2012. The first issue of volume13 will be published soon. Research papers are now ac-cepted for the second issue of volume 13.

The SLJAS publishes papers of practical or theoreticalimportance to researchers in mathematical or appliedsciences. Only papers that address application of newor modified important statistical methods, or that makeeven the smallest contribution to statistical theory ormethodology, will be considered. Illustration of the the-ory/methodology developed using real data are stronglyencouraged in the latter case.

Applications of Statistics in the area of Agriculture &Forestry, Finance, Economics, Medical, Dental and Vet-erinary Sciences, Actuarial Science, Natural, Physicaland Social Sciences fall within the scope of the jour-nal. The journal also welcomes critical reviews includ-ing conceptual discussions, opinions and book reviews.

Each paper is reviewed by experts in the particular sub-ject area of the paper. Papers recommended by at leasttwo reviewers are accepted for publication. Review pro-cess is carried out completely independently and anony-mously.

Instructions to authors are available at http://www.

iappstat.lk. Manuscripts should be sent to editor@

iappstat.lk.

Prof C.R. Rao and the InternationalStatistics Conference, 28-30December 2011, Colombo

Prof. Shelton Peiris,Chair, International Program Committee,

School of Mathematics and Statistics,The University of Sydney,

NSW2006, Australia.

We have all heard the name of a great statistician,C.R. Rao since our early stages of statistics education viaCramer-Rao inequality and Rao-Blackwell theorem. Asmany others, I also had the dream of meeting him dur-ing my academic career. It became a reality in 2002 dur-ing my visit to the Department of Statistics at Pennsyl-vania State University where I was fortunate enough towitness all statements about this renowned statistician.I have come to the understanding that he is not only agreat statistician (in both academic and non-academic)but also a very humble gentleman with a good heart.He has a personality of helping his fellow statisticiansto develop skills and to reach their full potential.

Prof. Shelton Peiris with Prof. C. R. Rao

On the first day of the conference, 28 December2011 at the Waters Edge, Battaramulla, Sri Lanka, Pro-fessor Rao delivered a very interesting and elegantkeynote address on "Importance sampling and cross-entropy with applications to problems of large devia-tions and optimization problems and no one believedthat he was 91 years of age at that time.

The organising committee of this conference waspleased to report that the University of Colombo hadalready offered him his 34th honorary doctorate forthe great contributions he had made to statistical sci-ence. This degree had been conferred in absentia atthe University of Colombo postgraduate convocation, inJuly 2011, and was offered in person on 28 December2011, at the conference venue by Professor Kshanika

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Hirimburegama, the Vice Chancellor of the Universityof Colombo. On behalf of the conference organisingcommittee, I am very grateful to the Faculty of Science,The Senate and, in particular to Professor Kshanika Hir-imburegama of the University of Colombo for recogniz-ing Professor Raos contributions and making all neces-sary arrangements to award his honorary degree. Inaddition, on behalf of the Institute of Applied StatisticsSri Lanka (IASSL), its president Mr Palitha Sarukkali of-fered the first IASSL Fellowship to Professor Rao, at thesame conference.

All Sri Lankan and other participating statisticianswere very fortunate to meet Professor Rao, who was ac-tively solving many current problems in statistics as hehad done at Cambridge University in 1948/1949 withRA Fisher.

Other eminent statisticians who participated at thisconference are Dr Nancy Geller, ASA president 2011who was the second Keynote Speaker, and the Spe-cial Guest speakers: Professor John Robinson, The Uni-versity of Sydney, Australia, Professor Martin Hazel-ton, Massey University, Palmerston North, New Zealand,Professor Neville Weber, The University of Sydney, Aus-tralia, Professor Rahul Mukerjee, Indian Institute ofManagement, Kolkata, India, Professor Tim Swartz, Si-mon Fraser University, Canada, Professor David Allen,Edith Cowan University, Perth, Australia, Dr Sama-radasa Weerahandi, Director in Analytics, Pfizer, USA,and Professor Alan Hutson, University at Buffalo, NewYork, USA.

The conference covered many topics including,Asymptotic Statistics, Bayesian Statistics, Bio-statistics,Bioinformatics, Clinical Trials, Computational Statis-tics, Data Mining , Decision Theory, Design of Exper-iments, Econometrics, Environmental Statistics, Mul-tivariate Statistics, Option Pricing Models, ReliabilityTheory, Re-sampling, Sample Surveys, Sequential Anal-ysis, Software Reliability, Spatial Statistics, Statistics inSports, Statistical Modelling , Statistics in Finance, Sta-tistical Quality Control, Survival Analysis, and Time Se-ries Analysis. There were more than 260 participantsfrom over 20 countries who attended the Conference.As a result of the success of this conference, the Insti-tute of Applied Statistics, Sri Lanka is planning to holda similar large scale International Statistics conferencein 2014.

The 2011 International StatisticsConference: an American’s

Perspective

Dr. Nancy L. Geller

The 2011 International Statistics Conference tookplace 28-30 December, 2011 at a state-of the art con-ference center located on the outskirts of Columbo.The American Statistical Association (ASA) was a silversponsor of the conference, and that is why I, the 2011ASA President was invited to present a plenary talk. As Ihad met a good number of the attendees at the two sem-inars I gave the previous week, it was quite gratifying tonot feel like a stranger.

The conference began with a traditional openingceremony. The Vice-Chancellor of U Columbo and theSri Lankan Senior Minister of Science and Technologywere the high officials who were present. All honoredguests lit the opening torch (including me). Then themelodious national anthem, and the presentation of thehonorary degree to Professor CR Rao, who is 91 nowand who was a student of RA Fisher. This was his 34thhonorary degree. Professor Rao’s degrees are from 18countries and include the Guy medal (Britain), mem-bership in the U.S. Na Academy of Sci, and the U.S.National Medal of Science. Professor Rao was alsoawarded the first Fellowship of the newly created In-stitute of Applied Statistics of Sri Lanka. Making the SriLankan Applied Statistical Association into an Institutetook an act of parliament, a recent achievement of itspresident, Palitha Sarrukali who was one of my hosts.

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The Chief Guest, the Sri Lankan Senior Minister ofScience and Technology Hon Prof Vitarana, spoke aboutglobal warming through human intervention and its po-tentially disastrous effect on island nations. He urgedmaking policy makers and the general population moreaware of the magnitude of the problem and urged usas statisticians to contribute to this effort. He spoke ofstatisticians’ contributions to modeling after the 2004tsunami. He expressed optimism that this meeting willstrengthen applied statistics and its contributions to sci-entific research.

The first plenary talk was given by Professor Rao.His title was "Importance sampling and cross-entropywith applications to problems of large deviations andoptimization problems." Cross entropy is a measure ofloss of information when one uses a probability den-sity g to make inference on a probability density f. Onechooses g by minimizing cross entropy and then one canuse Monte-Carlo techniques to find such things as prob-ability of large deviations or the maximum of a functionover a given subset.

I gave the second plenary talk on the morning ofthe second day. The talk, on prognostic and predic-tive biomarkers, was well received with some questionsand a number of inquiries from students who want tostudy or do post-docs in the United States. Most of thetalks were mathematical statistics and mine was moreapplied. The conference overall was very interestingwith a wide range of topics, such as robust statistics,Bayesian methods, cancer research and sequential anal-ysis.

My husband and I attended the conference dinnerfollowing the second day of the meeting, an elegant SriLankan buffet with many choices of both curries andwestern food. At the informal party following dinner,many of the students asked to be photographed withme. It was very gratifying, and somewhat unexpected. Iwill always remember the wonderful hospitality I expe-rienced in Sri Lanka, especially at the conference.

Note: A similar summary appeared in AmStat News,March, 2012.

Awards for Best Undergraduate/ Post-graduate Research Projects

Institute of Applied Statistics, Sri Lanka (IASSL) an-nounces its 2012 scheme of awards for Best Under-graduate / Postgraduate Research Projects that havereached outstanding standard in utilization of STATIS-TICAL METHODS.

This award is open to all eligible Undergraduates /Postgraduates in the National Universities and Institutesof Sri Lanka. The award will bring an extra dimen-

sion to winners qualifications when he/she complete thestudies, enriching personal development and substan-tially boosting employment prospects.

The eligibility criteria for applying for Awards are asfollows:

• The applicants should be undergraduates / post-graduates in the National Universities of Sri Lankawho have successfully completed and submittedtheir research papers / dissertations / theses in theperiod from 01st January 2011 to 30 June 2012;

• The material submitted for Awards should demon-strate application of Statistical Methods and havereached outstanding standard;

• The applicants supervisor(s) should certify the Ap-plication (see below) to guarantee that the mate-rial submitted for Award is genuine output of theapplicant and have accepted as deemed to satisfythe fulfillment of the academic requirements.

For each category of undergraduates / postgradu-ates, the winner plus two runner-ups, will be selected bya Panel appointed by the Executive Council of IASSL andits decision will be final. Winners will be announced inOctober 2012. A certificate and a plaque with the win-ners name will be awarded to the winners at the AnnualGeneral Meeting of IASSL to be held in November 2012.

Application forms could be downloaded from IASSLwebsite: www.iappstat.lk. Duly completed applicationsand other relevant documents should reach the Secre-tariat, Institute of Applied Statistics - Sri Lanka, TheProfessional Centre, No. 275/75, Prof. Stanley Wijesun-dera Mawatha, Colombo 07 (Tel: 011-2588291; E-mail:[email protected]) on or before 15 August 2012. Pleaseindicate Award Application on the top left corner of theenvelope.

(Please publicize this scheme among undergradu-ate/ post graduate students of the Universities and Re-search Institutes)

Academic Training Committee

Dr. Chandani NawarathnaChairperson/ ATC

The Academic Training Committee (ATC) is a statu-tory committee appointed by the General Committeeof the Institute and the chairperson of the committeeis a member of the Executive Council of the Institute.The main functions of this committee are to design, de-velop and offer academic programs of the Institution

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and ensure the academic quality of the programs of-fered by the Institution. These academic programs in-clude Long-term programs leading to professional qual-ification, short courses and seminars as well as trainingprograms depending on the need of the country. Wher-ever relevant, the committee also bears the responsi-bility of appointing examiners on the recommendationof the council, holding examinations, marking/gradingand awarding certificates on the recommendation of theCouncil of the Institution.

Currently ATC has planned to conduct short termcourses on Basic Statistics, SPSS training, Businessstatistics and quality control, Geographic InformationSystems etc. Recently two well attended seminars onForecasting techniques were contacted by ATC. It is alsoplanning to conduct a one year Diploma course in Statis-tics for students who passed GCE(AL) but could not getinto the university system. This Diploma will be fol-lowed by a Higher Diploma course in Statistics in thesecond year for the successful candidates of Diplomain Statistics. Those who pass the Higher Diploma willbe entitled to follow the third year course and the suc-cessful students at the third year examinations will beawarded the title Chartered Statistician of the IASSL .

Statistics Popularization Committee

Mrs. Nimalshanthi AmarasekeraChairperson/ SPC

Main objective of the Statistics Popularization Com-mittee is to popularize the statistics discipline amongstudents and the general public. As the President men-tioned in his Presidential address at the Induction Cer-emony, this will remove the prevailing distrust of statis-tics among masses. During this period the StatisticsPopularization Committee has launched two importantprojects in view of achieving our objectives.

It was noted that the students are reluctant to an-swer the statistics questions in Combined Mathematicsand Mathematics papers at the GCE (AL) Examination.This can be attributed to the inability of majority of theAL teachers to teach statistics in a way it can be ab-sorbed by the students. The two activities launched byour committee are expected to erase this situation.

Introduction of the National Statistics Olympiad isone such activity. Applications for the Olympiad 2012has been called from students and the examination willbe held just after GCE(AL) examination in August,2012.The first five students who performed well at the Na-tional Statistics Olympiad are expected to take part atthe International Statistics Olympiad 2013, to be heldin India.

National Statistics Olympiad will be held in six (6)examination centers (Colombo, Matara, Kandy, Jaffna,Anuradhapura and Batticaloa). This Olympiad will beheld annually in the future and will come under thepurview of the Statistics Popularization Committee ofthe IASSL.

The next project is to train teachers in teaching Com-bined mathematics, Mathematics and Business Statis-tics for AL students. This program will cover the entirecountry in several stages. The first training program willbe held in Matara during September, this year.

Research and Development (R & D)Committee

Dr. H. D. SumanasekeraChairperson/ R & D Committee

The R & D Committee decided to develop a Databaseof IASSL Members carrying information on individu-als such as qualifications, experience, areas of researchinterest, availability to undertake consultancy assign-ments, and etc. It is planned to upload the Databaseto IASSL website.

The Committee took steps to upload to the websiteinformation (such as, title of the presentation, affili-ated institute, contact details) about paper presenters atthe IASSL organized International Statistics Conferenceheld in January 2012.

The Committee formulated 2012 scheme of Awardsfor Best Undergraduate / Postgraduate ResearchProjects that have reached outstanding standard in uti-lization of Statistical Methods. Details of the schemeand the application form have been uploaded to thewebsite.

The Committee prepared the guidelines for estab-lishment and management of a Research and Consul-tancy Unit (RCU) under the R & D Committee of theIASSL with the primary aim to provide statistical ser-vices to business, industry, government, NGOs, and theacademic world including individual researchers in (a)research planning, (b) design of experiments, quanti-tative and qualitative data collection, and instrumentsand surveys, (c) statistical analysis, (d) interpretationof results, and (e) report preparation. This announce-ment will be posted on the website.

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House and Finance ManagementCommittee

Dr. B. L. PeirisChairperson/ H&FM Committee

Functions of the House and Finance Management (H& F Management) Committee are of two fold; Normaladministrative and management functions of the secre-tariat and of membership, and the management of Fi-nances of the IASSL. H&F Management Committee hasrecently recruited the first employee of the IASSL. Ms.Kalani Adikari, a graduate of the University of Wayambahas been recruited as the Administrative Officer (AO)who is in charge of implementing all the decisions takenby the Executive Council under the supervision of theSecretary. The Executive Council has decided to issueIdentity Cards to members (General members and fel-lows) of the IASSL. It is a statutory requirement thatnew members have to provide a colour passport sizephotograph along with the application form and an en-rolment fee. This will be used to issue the Identity Cardfor the new members. However this facility will be ex-tended to other members but is not a statutory require-ment. If anybody wishes to obtain an Identity card ofthe IASSL, he/she has to provide a passport size colourphotograph along with the cost of the ID (Rs. 250/-).The Identity cards will be available for issue in early Au-gust. The website of the IASSL (www.iappstat.lk) is be-ing developed and maintained by Dr. Dharshana Yapa,Assistant Secretary. Many improvements were done tothe site recently; the Journal of the IASSL, Sri LankanJournal of Applied Statistics, is published in the web-site and any author can submit papers for the future is-sues of the Journal online. The first AGM that has beenscheduled for 24th November with a Technical sessionwill be organized by the H & F Management Committee.Recognizing the services rendered by our senior mem-bers, the H & F Management Committee will nominatesome of them for award of Fellowships of the IASSL.

International Year of Statistics

The International Statistical Institute invites all Sta-tistical institutes/ organizations to participate in a part-nership among societies and organizations around theglobe to celebrate 2013 as the International Year of

Statistics. The ISI joins four other societies (RSS, IMS,IBS, and ASA) to form the organizing group for the In-ternational Year of Statistics. The purpose of this In-ternational Year, which we are abbreviating as IYStat(Eye-stat), is to promote the importance of Statistics,through the combined energies of societies and organi-zations worldwide, to the broader scientific community,business and government data users, the media, pol-icy makers, employers, students, and the general public.The goals of IYStat include:

• increasing public awareness of the power and im-pact of Statistics on all aspects of society;

• nurturing Statistics as a profession, especiallyamong young people; and

• promoting creativity and development in the sci-ences of Probability and Statistics

Institute of Applied Statistics, Sri Lanka is amongover 500 Statistical Organizations of the world whojoined the partnership to celebrate 2013 as the Inter-national Year of Statistics. In fact we are the only SriLanka based organization among the participants. Mr.Palitha Sarukkali, President of the IASSL will serve asthe liaison between IASSL and the IYStat Steering Com-mittee. We have already identified to organize a five daySeminar on Medical Statistics towards the end of thisyear. Statistics Olympiad will be another activity iden-tified for the next year 2013. We hope this will placespecial emphasis on activities to engage students andpotential students of statistics, helping them to becomemore aware of statistics as a key scientific discipline.We will publish other activities of the IYStat in future.Also it should be noted that 2013 will be the 300th an-niversary of the publication of the Ars Conjectandi, writ-ten by Jakob Bernoulli (and published after his death),which is considered a foundational work in probability.The Bernoulli Society has already planned a rich varietyof activities in 2013 to celebrate this anniversary. Alsonote that 2013 is the 250th anniversary of the first pub-lic presentation of Thomas Bayes famous work.

The most annoying question

Q: What’s the question the Cauchy distributionhates the most?A: Got a moment?

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Use of Z scores to rank the performance of students in A/L

Sarath Banneheka

According to Wikipedia [1], in Statistics, a standard score indicates by how many standard deviations an obser-vation or datum is above or below the mean. It is a dimensionless quantity derived by subtracting the populationmean from an individual raw score and then dividing the difference by the population standard deviation. Standardscores are also called Z-values, Z-scores, normal scores, and standardized variables.

Let x1, x2, . . . , xN be a set of N real numbers. When this set is considered as a population, the population meanand the the population standard deviation are defined as

µ =1

N

N∑i=1

xi and σ =

√√√√ 1

N

N∑i=1

(xi − µ)2

respectively. Then, zi = xi−µσ is called the Z-score of the value xi (i = 1, 2, . . . , N).

The University Grants Commission of Sri Lanka uses Z scores to select students to universities since 2001.According to one of its publications [2],

• It has been confirmed from various research that when selecting students based on the raw marks, somestudents gain an unfair advantage. The reason for this is that the difficulty levels of all the questions papersare not the same.

• For example, the students who follow the subject combination chemistry, biology and physics as well as thosewho follow the subject combination chemistry, biology and agriculture for A/L can enter in to the bio-sciencestream in the universities. Often the students score higher marks for agriculture than for physics. Under thissituation, among the students who compete for the same subject stream in university, some students gain anunfair advantage, when the students are selected based on the raw marks.

• This problem can be eliminated by converting the raw marks in to a standard scale using the Z score.

The UGC calculates the Z-scores within each subject and the Z-score of a given student is calculated as themean of the 3 subject Z-scores of that student.

ExampleIn a certain examination, the means of the marks of all the students who faced examinations in Physics, Chemistry,Biology, and Agriculture were 37, 36, 44, and 41 respectively. The standard deviations of the marks for thosesubjects were 16, 16, 15 and 12 respectively. Suppose the marks obtained by 5 students who sat for examinationsin Physics, Chemistry and Biology and 5 students who sat for examinations in Physics, Chemistry and Agricultureare as in the following table. Then, their Z-scores are also shown in the table.

Student Raw marks for subjects Z-scores for subjects Student’sPhysics Chemistry Biology Agriculture Physics Chemistry Biology Agriculture Z-scoreµ = 37 µ = 36 µ = 44 µ = 41σ = 16 σ = 16 σ = 15 σ = 12

1 70 80 85 2.063 2.750 2.733 2.5152 37 52 70 0.000 1.000 1.733 0.9113 53 70 44 1.000 2.125 0.000 1.0424 70 36 59 2.063 0.000 1.000 1.0215 21 36 59 -1.000 0.000 1.000 0.0006 80 85 70 2.750 2.733 2.417 2.6337 52 70 37 1.000 1.733 -0.333 0.8008 70 44 53 2.125 0.000 1.000 1.0429 36 59 70 0.000 1.000 2.417 1.139

10 36 59 21 0.000 1.000 -1.667 -0.222

Table 1:

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Several researchers have examined the z-scoremethod. According to Yajni and Karishma [3],“it is clearthat using the z score method in determining universityadmissions in Sri Lanka is disadvantageous to most stu-dents". According to Ariyaratne and Rosa [4], “becauseof the dependence of the standard deviation on the na-ture of subjects, students doing well in subjects having alarge value of standard deviation will have a disadvan-tage when the aggregated is taken under the Z scoremethod". According to Dayananda [5], due to skewnessthat is present in scores of some subjects, the Z methodis not the best replacement for raw aggregate. Do youagree or disagree with these ideas?

In the recent past, various ideas/statements havebeen expressed about the Z-scores. The following aresome of those ideas/statements. What do you thinkabout them? True or False?

• The Z value transforms variables with differentdistributions into a common distribution.

• In order to compare marks from two subjects, acommon scale can be obtained by using the Zscore.

• Regardless of the distribution of the marks (x val-ues), the Z score can be viewed as a scaling tech-nique that makes the location and dispersion pa-rameters for the marks of all subjects the same.

• Z score eliminates the unfair advantage that can

be gained by the students who follow subject com-binations with relatively easy subjects. (Hint: seeTable 1)

Your views are invited for the future newsletters. Sendyour views to [email protected]

References

1. http://en.wikipedia.org/wiki/Z-score.

2. Selection of students to universities from 2001.University Grants Commission, 2011.

3. Yajni Warnapala and Karishma Silva. Z-score de-mystified: a critical analysis of the sri lankan uni-versity admission policy. Journal of Case Stud-ies in Education. accessed from www.aabri.com/

manuscripts/10741.pdf on 30/07/2012.

4. T. R. Ariyaratne and S. R. D. Rosa. Use of z-scoresfor the admission to sri lankan universities. InProceedings of the Technical Session of Instituteof Physics, Sri Lanka, volume 18, pages 45 -51,2002.

5. R.A. Dayananda. Statistical study of criteria foradmission to national universities in sri lanka. InProceedings of the International Statistics Confer-ence, 2011: Contributed Papers, pages 27 - 36.Institute of Applied Statistics, 2011.

New Editor for IASSL

Dr. Sarath Banneheka resignsfrom the post of Editor of the IASSLon the 31st of July 2012 as he isdue to go abroad on a Common-wealth Academic Fellowship. Dr.Banneheka served as the editor ofthe SLJAS for volume 11 (2010) andvolume 12 (2011) and took part ofthe work for the issue 1 of volume13 (2012), which will be publishedsoon. He also served as a memberof the board of editors of the pro-

ceedings of the International Statis-tics Conference 2011. He published2 newsletters in 2010, 3 newslettersin 2011 and 2 newsletters in 2012during his term. He also modifiedthe ‘guidlines for authors’ and pre-pared a format for a paper of theSLJAS, which are now available on-line at the IASSL website. The exec-utive council of the IASSL appointedProf. Pushpa Wijekoon of the uni-versity of Peradeniya as the new Ed-itor of the IASSL effective from 1stof August 2012.

INSTITUTE OF APPLIEDSTATISTICS SRI LANKA

(IASSL)

Editor:Dr. B.M.S.G. BannehekaE-mail: [email protected]

ISSN -1391-4995 Appstat Newsletter July 2012 Page 8