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INSTYTUT BADAē SYSTEMOWYCH

POLSKIEJ AKADEMII NAUK

TECHNIKI INFORMACYJNE

TEORIA I ZASTOSOWANIA

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ANALIZA SYSTEMOWA W FINANSACH

I ZARZĄDZANIU

P od redaką A nd rzeja MyĞĔskgo

Warszawa 2014

iBS PAN

ISBN 83-894-7555-3

GRADE DATAANALYSIS

APPLIED TOTHEEUR OPEANA GRICULTURE

StanisławLenkie wicz

Systems ResearchInstitute ,PolishAcadem yofSciences,

Ph. D.Studies, Warsaw, Poland

stan@lenkiewicz.eu Abstract.The paperpres entsresultsofthe analysisof agriculturein theEuropean Union. Basedon 15k ey characteristics,membercountrieshave beendi videdinto groups consistingof countrieswith asimilar conditionof agriculture.As aresearch method theGrade DataAnalysis hasbeen applied,and totreat thedata theGrade-

Stat softwarehasbeen used.

The textiscomposed offour parts.The rstpart isa briefanalysis ofagriculture as a sectorof theeconomy ,while thesecondisdedicated tothe measurement ofthe condition ofagriculture. Thethird partpresents theresearch tools:cluster analysis and GradeData Analysis,and thefourth shows theresults ofusing thesetoolsfor the assessmentof EUagriculture. Keywords:agriculture, productivity,clusteranalysis, GradeDataAnalysis,o ver - representation, outlier

1 AGRICULTUREASASECT OROF THEECONOMY

Agriculture constitutesan importantsector ofeconomy inalmost ev ery while insome otherones itspurely economicrole maybe quitelimited. The latteris thecase formost ofthe dev elopedw orld.Y et,with onlyfew exceptions,agriculture isconsidered tobe ofhigh importance,if notfor just economicreasons, thenfor thesocial, cultural, and,most ofall, politi- cal ones.Agri cultureprovidesfood, andisaproducer ofra wm aterialsfor manyindustries, but itisalsothe reservoir ofv eryimportant resources,in- cluding land,landscape, culturalheritage, people,and theirspecic know- how.Thusit isin thecentre ofinterest ofcountries' gov ernments,as well as ofv ariousinternationalcommunities,such asthe EuropeanUnion (EU) or theF AO. Because ofits importanceand complexity ,agriculture isalsoanarea of manystudies.Ho wev ercomplextheymayget andhowmanyf actors theytak eintoaccount,the yall hav etwomain purposes.First, theytry to assessthe "health"of agriculture.Secondly ,the yaim -onthebasis of assessments -at identifyingthe ways ofimpr ovingits condition.In partic- ular,within theEU, amajor shareof theCommunity' sb udgethas alw ays

GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE57been goinginto agriculture;first, inorder tok eepthe Europeanagriculture

aliveinthe face ofcompetition fromtheoutside(the dev elopingw orld), and fromthe inside(t heother sectorsofeconomy, includingconstruction, transport, etc.),and secondly, toretaintherural economyand society, as well aslandscape, asan elementof theEuropean cultureand identitythat has beende velopingovermillennia.

1.1 Specific

Agriculture is"based onthe ground",i.e. ituses theland asits primary resource. Theland, ev enifinthecaseof highlyintensi ve farming itsarea can beminimised, constitutesthe sinequa noncondition ofagricultural production, whateverthe"nationalspecialisation" ororientation ina giv en country.This fact makesagriculturedif ferentfromamajority ofsectors of the economy. Agriculture isdependent onman yf actorsover whichpeoplehav eno influence orwhich canbe formedby peopleto alimited degree. Themost important ofthem are:climate, surface relief,soil quality,precipitation. Another setof factors isrelatedtot hef armingpopulation -its skills,tra- ditions andattachment tof armingand toland.Asa result,agricultural production isal waysspecifictoaparticular countryand agricultural prod- ucts arethe subjectof intensetrading, especiallybetween countrieswith differentnatural conditionsand different farming cultures.

1.2 InternallyandExter nallyDiffer entiated

There aretw omainactivities inagriculture: thecultivation ofplants and livestockhusbandry. Theyarev erydiversified. Someplants areusedfor food production,some ofthem serve asanimal feed,whileothersbecome industrial rawmaterials(e.g. forthe productionof medicines,f abrics,or biofuels). Animalsalso canbe bredto producefood (meat,milk, eggs, honey,etc.),or topro videra wmaterials (e.g.wool,leather ,orsilk). There are,also inEurope, "traditional"f arms,dealing withboth plant cultivationandanimal husbandry, aswell asthespecializedones: focused on oneparticular activity (e.g,dairyfarms). Thereare highlymechanized farms,as wellas thosethat usemechanization toa lessere xtent.Some farmsuse large quantitiesofchemicals,while others- smallor notat all. Little useof machineryand chemicalsdoes notnecessarily resultfrom backwardness;on thecontrary ,may betheresultof adecision tostart organicfarming activity,which isincreasinglypopularinhighlyde veloped countries.

58StanisławLenkie wiczThus, agricultureis very diversifiede venwithinonecountry. Further-

more, itis generallyhighly div erseamong variouscountries,especially when theyhave differentnaturalconditionsforf arminganddifferent farm- ing traditions.

1.3 CriticallyImportant

It ishard tobelie ve thatinthe21stcentury, many peoplesti llsuf ferfrom hunger.Though thenumber ofundernourished personsdropped from15% at thebe ginningofthecentury to12% now ,it issti llunacceptable. 1Even a short-termfood shortageis aserious problemand canbe asource of social unrest.This isan explanation asto whyagriculture isin thefocus of nationalgo vernments,aswellasof internationalcommunities,

2one of

which isthe EU. Although oneof characteristicsof thede veloped countriesis somekind of marketeconomy, agriculture-asits specific andparticularly important sector -is subjectto specialrules, whichare usuallypresented inthe form of so-called"agricultural policy". Oneofitselements arev ariousforms of i.e. exertinganexplicit influenceon onebranchofthe economythrough administrativedecisions,is thesubject ofdispute amongpoliticians, as well asamong researchersdealing withthe problemsof agriculture.

1.4 Hardto Assess

It isv eryhardtoassess thecondition ofagriculture. Firstof all,one should explainwhat ismeant bythe notionof "condition".Is itjust aglobal value of agriculturalgoods producedby acertain countryor region? Orshould it bepresented asa setof values describingv ariousareas ofagricultural activity?Ho wtotake intoaccount objectiveconditions suchas climateor soil quality?Ho wtodealwith thele vel ofmechanization andfertilizer use? Some countriesha vegreatercapacityofagricultural productionthan their demandforagricultural products.Man yof themintroduced various limits, forcingor motiv atingfarmstoproducebelo wtheircapacities.In such acase canan ev aluationbe fair?1 Source: FAO"sHungerPortal(http://www.f ao.org/hunger/en/, access:June 27th,2014).

2There areman ystudiesofthe stateof agriculturein dev elopingcountries whichare conducted

by scientistsfrom thosere gions(e.g. [9],[11]),aswell asnumerous analysesof agriculturein those regionsdone byw orld-renowned scholarsfromEuropeandtheUS (e.g.[13]). Thisis notsurprising.

GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE59Forman y,theefficiency -i.e. theratioofproduct(value) tocosts (re-

sources used)- isthe codew ord.Y et,again,bothnaturalconditions and the (local)specificity ofproduct mixand technologiesmay make there- spectivecomparisonshighly doubtful. These arethe mostimportant questionsthat mustbe answeredfor an assessment toha veanyvalue. Wewilldeal withtheminmore detailsin the followingsection.

2 CONDITIONOF AGRICUL TURE.CANITBEMEASURED?

Let usput itclearly: any assessmentismor eor lesssubjective . Itis al- waysa particularperson (ora groupof people)who preparesrules forthe evaluation.We allfollowour own perceptionsofthew orld,thus: ourindi- vidual hierarchiesof values, sotheassessments wemak eare notobjective ones; theyareour assessments. Someonewho claimsto beobjecti ve, is naive-or simplyis lying. It isdif ficulttobeobjecti ve (or, strictlyspeaking:nottoosubjectiv e) eveninassessing simplesubjects. Itis very hardto beso whendealing with complexproblemsof greatimportance -and thecondition ofagricul- ture isone ofthem. Sowe arenot tryingto pretendthat westri ve tomak e a fullyobjecti veassessmentofagriculture; weonlyaimat ane valuation the leastmark edbyourpersonal convictions. Indeed,we candeal away with atleast animportant partof the"subjecti vity"approach bymaking explicitthe criteriaof ev aluation,and/or thecharacteristicsthataretaken into account( "theassessmentismade fromTHIS pointof view"). Suchan explicitspecification ofthe elementsof assessmentis particularlyproper for thecase ofEU agriculturalpolic y, wherethe goalsandcriteriahave been changingfrom periodto period.In therecent periods,care was taken to avoidoverproduction thatmighthaveresulted fromapplication ofsub- sidies, whilepreserving therural farming activities throughoutEuropeand leavingroom forcompetition interms ofproduction costsand technology- and-product mix.

2.1 AnAssessment -What IsIt?

Toassess something,one shouldcollect dataand constructa methodto process them.T odothis,he orshe should: -Prepare alist ofcharacteristics thatwill beco vered bythe assessment.

-Prioritisethesecharacteristics,i.e.decidewhethertheyshouldbeequallyweighted ortheir weightsshould bedif ferent.

60StanisławLenkie wicz-If necessary:normalize weightedcharacteristics.

-Choose thew aytotreatpre-processed characteristicsto obtaina mea- sure (ormeasures) ofthe phenomenonof hisor herinterest. These elementsdetermine theentir estudy ,highlyinfluencingits outcome.Describing these"pillars" means:presenting themethod ofre- search.

2.2 Conditionof Agriculture

As statedin Section1.4, theterm "condition"is abstract.Before weget to the methodsof itsmeasurement, weha ve tobe morespecific.Formany researchers itis asynon ymof theagriculturalproductivity. Productivity is understoodas theratio ofoutputs toinputs in production;thus agricul- tural productivityisthe ratioof agriculturaloutputs toagricultural inputs. 3 There arealso many publicationswherethew ord"producti vity"has been replaced by" efficiency

4Sometimes thesetermsare usedinterchange-

ably. 5 There isa messin terminology;ho wev er, ineachanalysisofagriculture we mayfind thesame basicelement: ite xaminesho wwell outlays(inputs) are processedi ntheresults(outputs), andtries topresent itin numerical form. Most researcherslist asinputs of"agricultural production system"three elements:land, labour,andcapital . Someof themperform forthem sepa- rate analysis,highlighting productivity ofland,productivity ofl abour, and productivityof capital. Analysis forcertain regions (e.g.forEUor NAFT A)become abasis for comparison ofagricultural productivity inthecountriesof thesere gions. Theypermit toidentify strengths andweaknesses ofeachcountryand to suggest waysforimpro vement.

6Assessments madefor agriculture may

also serveforcomparison ofits productivity andproducti vitiesobserv ed in othersectors.

7The resultsmay besurprising. 83

See [9].

4See [30].

5See [7].

6See [3],[25], [27],[28], [33].

7See [12],[13].

8As Gollin,Lag akosandWaughobserv edin [12],accordingto nationalaccounts data,value

added perwork erismuch higherin thenon-agricultural sectorthan ina griculture inthetypical country,and particularlyso inde velopingcountries. Tak enatfacevalue ,this "agriculturalproduc- tivity gap"sug geststhatlabourisgr eatlymisallocate dacr osssector s.[.. .]even afterconsidering sector differencesinhours worked andhumancapitalper worker,as wellas alternativemeasur es of sectoroutput constructedfr omhousehold surveydata,a puzzlinglylar gegapr emains. GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE612.3 MeasuringAgricultural Producti vity There area greatnumber ofmethods usedfor agriculturalproducti vity assessment. Inthis paperit isnot possible neitherto presentall ofthem, nor todelv edeeplyintothe details.Some examples maybe foundin [3], [7], [9],and [23]. In allmethods wemay findthese commonelements (seeSection 2.1):

-Choosingcharacteristics(attributes)tobeanalysed(e.g.totalcropsout-put perhectare, fertilisersusage perhectare, totalsubsidies oncrops).

-Pre-processing thesecharacteristics (weighting,normalizing). -Processing thedata toobtain productivity metric(s).

-Analysis ofthe results.V eryoften: groupingtheobjectswith similarprofiles (e.g.di visionoftheEU membersinto groupsof countrieswith a similarprofile ofagriculture).

Such aprocedure, andespecially itslast step,mak esit naturalto con- sider theapplication ofdata miningand clusteranalysis. Itis surprising that thereare very fewpublicationsrelated toagriculturewhichuse them. 9

3 CLUSTERAN ALYSISANDGDA

The aimof ev eryresearchistoincreasekno wledge.This maymean either discoveringnew facts,ordeeper understandingoffacts alreadykno wn.In both cases:we want toknowmore abouta certainsubject. Wemay divide allresearchmethodsinto two groups:quantitati ve and qualitativeones.Ho wev er,theboundariesbetweenthemareblurred;in fact,usually weuse amixture ofboth. Thebest exam pleof thisis data mining.

3.1 DataMining

There isno cleardefinition ofdata mining.It isone ofthe stagesof ac- quiring knowledgefromthedata: analysinglar gesets ofra wv alues(very often havingtheform ofdatabases ordata warehouses), retrieving new val- ues andi nterpretingthem.We maysay: dataminingisa way todisco vering patterns inlar gedatasets,it isthe searchfor orderin chaos.As almoste v- ery studybe ginswithandeep analysisof data,data miningis largely used in variousareasof research. Data miningis aset ofmethods, heuristics,and algorithms,and itis usually placedbetween computerscience andstatistics. 109

Some examples:[1],[22], and[26].

10See [10].

62StanisławLenkie wicz3.2 ClusterAnalysis

11 Wecalled datamining discoveringpatterns inlar ge datasets. Veryoften discoveringpatternsmeans puttingobjects underin vestig ationinto groups to eachother thanto theobjects inother groups.Such anapproach iscalled cluster analysis. Grouping similarobjects (clusteringthem) hastw oadv antages.First, it makespossibletoanalyse datastructure, todisco ver relationsbetween variousobjects, andfinally: toget informationabout theproblem beingin- vestigated.Secondly, itcanpointout thedirection offurther study, allow- ing researchersto focustheir attentionon selectedgroups, thus:to reduce the searcharea. Theanalysis ofdisco vered clustersis bidirectional.Onone hand wein vestigatetheinternalstructureofclusters, onthe other- wetry do findsimilarities anddif ferencesbetween variousclusters. Toapply the clusteranalysisonemust decidewhich attributes ofthe investigatedobjectswillbe taken intoaccount. Moreov er,someof them may becorrelated, sothe yshould notbeincludedin thesame research.An opinion ofa researcher, thoughimportant,itis notsuf ficient;there must be aclear ruleof decidingwhich attributes ofthe objectsare important, whicharenotandwhy. becomes muchmore complicated.W eightsha veastrong influenceonthe result ofthe analysisshould thereforebe chosenwith greatcare. The resultofclustering theobjects, i.e.determining whichones are "close" (orsimilar) toeach other, dependson themeasureof similarity (sometimes alsocalled resemblancecoef ficient).Its choiceisoneof the most importantsteps inthe wholeanalys is,and notan easyone.Attributes of objectsmay hav evariousnatures:they canbenominal(e.g. countryof residence), ordinal(e.g. educationle vel), orinterval(e.g.age),sometimes theyare ratios(e.g. inflationor unemployment rate).

13Theycan bemea-

sured ondif ferentscales,soan initialnormalisation maybe necessary. The purposeof any clusteranalysisisto identifyclusters. Sothe ques- tion:how manyshould they be?is natural.Unfortunately ,thereisno one clear answer.Thenumber ofclusters dependsbasically onthe purposeof the research,as wellas... onthe preferencesof theresearcher . 1411

See [21].

12This procedureis alsocalled choosing inputv ariables. [20]co versthisproblemindetails.

13See [29],p. 93-177.

14[5] presentsa detailedanalysis ofthis issue.

GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE63Weha vebrieflydiscussedonlythe mostimportant problems ofthe clus-

ter analysis.A detaileddescription ofthis methodis beyond thescope of this article.More informationmay befound in[2] and[29].

3.3 GradeData Analysis

As statedin Section3.1, datamining isa setof various methods.In this article wewill lookat oneof them,less known but very useful:Grade Data Analysis (GDA).Ithas beende veloped atthe InstituteofComputerSci- ence -Polish Academyof Sciences.

15Its maincomponent isthe Grade

Correspondence Analysis(GCA)- analgorithm whichhas beenimple- mented inGradeStat program. 16 GDAa llowsforacomprehensiv eanalysis ofthe dataincludingcluster analysis anda detectionof outliers.Here wepresent onlyan outlineof this method; adetailed descriptionmay befound in[19], andsome examples of itsapplication: in[14], [17],and [36]. As wementioned inSection 3.2,one ofcritical parametersof eachclus- ter analysisis ameasure ofsimilarity ofobjects. InGD Athese areconcen- tration indexeswhich playthis role.The concentrationinde xis associated with theconcentration curve. Wewillno we xploreboththesenotions.

3.3.1 ConcentrationCur ve

Let usconsider thefollo wing example.Table1presents theresultsofa surveyconductedby Eurostatin 2011:self-percei ved healthstatus ofre- sponders. Thestudy includedthe EuropeanUnion countries, Iceland,Nor - wayand Switzerland.

17Each columnsho wsthepercentageof respondents

who assessedtheir healthas very bad,bad, fair,good, orv erygood. We may easilynotice thatresults forGreece andNetherlands differ .But how much? Toanswerthis questionwe shouldplot aconcentration curve of

Dutch resultsrelati vetoGreekresults.

Each valueinT able 1maybeinterpretedasa probabilitythat aperson randomly selectedfrom acountry indicatedin thefirst columnpercei ves his orher healthstatus asv erybad, bad,f air,etc.Such aprobability tableis 15 Websiteof theInstitute: http://www2.ipipan.wa w.pl/inde x.php/en/(access:July5th,2014).

16The CDwith theprogram isincluded in[17]. To unlocksome offunctions itis necessaryto

July 5th,2014).

17[17] usessimilar datato show theidea ofGDAand how GradeStatapplication works.

64StanisławLenkie wiczTable1.Self-perceivedhealthin 2011(% oftotal responders)CountryVerybad BadFairGoodVerygood

Austria1.97.221.538.231.2

Belgium2.17.416.943.929.7

Bulgaria2.59.321.150.117.0

Croatia5.322.227.529.615.4

Cyprus2.55.516.428.647.0

Czech Republic2.410.128.040.519.0

Denmark2.55.820.942.828.0

Estonia2.214.032.044.07.8

Finland1.26.223.747.321.6

France1.27.623.645.022.6

Germany1.56.727.048.216.6

Greece2.76.314.625.850.6

Hungary4.012.227.939.916.0

Iceland1.64.716.036.241.5

Ireland0.42.514.040.143.0

Italy3.010.122.251.613.1

Latvia3.513.835.942.74.1

Lithuania3.816.136.237.36.6

Luxembourg1.56.419.646.526.0

Malta0.73.425.147.123.7

Netherlands0.84.917.955.221.2

Norway1.27.318.348.824.4

Poland2.512.427.539.717.9

Portugal4.913.232.240.39.4

Romania1.87.821.042.227.2

Slovakia3.010.523.344.119.1

Slovenia2.910.426.341.818.6

Spain2.05.517.453.621.5

Sweden1.03.715.441.438.5

Switzerland0.72.915.249.831.4

United Kingdom1.04.716.842.035.5

GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE65a startingpoint whendra wingeach concentrationcurve.

18Starting fromit,

we createa tableof cumulativ edistrib utionsforallresponsesin allcoun- Each valuemaybe interpretedas aprobability thata personrandomly se- lected froma giv encountryperceiveshis orher healthstatusasverybad, at leastbad, atleast fair ,etc. Table2.Cumulativedistributions forGreeceandNetherlands CountryVerybad BadFairGoodVerygood

Greece0.0270.0900.2360.4941.000

Netherlands0.0080.0570.2360.7881.000

Wedra wpoints:(0,0), (0,027,0,008), (0,090,0,057), (0,236,0,236), (0,494, 0,788),(1, 1)and connectthem withse gments.W erecei ve acon- centration curveofDutch opinionsrelati ve toGreek opinionsC(Nether- lands:Greece) -see Fig.1. In asimilar way wecouldplotthe concentrationcurv efor thein verse relationship, i.e.C(Greece:Netherlands). Thiscurv ewouldbe areflec- tion ofthe firstone ov erthe diagonalofthecoordinatesystem. A concentrationcurv eiscomposedof asman yse gmentsas thereare characteristics ofthe objectsbeing analysed.Each segment illustrates a comparison ofa "concentration"of onecharacteristic inboth objects.If a segmenthas aslope lower than45 , the"concent ration"ofacharacteris- tic isgreater inthe "horisontal"object thanin the"v ertical"one; aslope greater than45 illustrates anin verserelation;aslopeequal to45 - iden- tical "concentration"in bothobjects. InFig. 1we cannotice thatpeople perceivingtheir healthstatus asv erybad orbad aremorenumerousin

Greece (slopelo werthan45

), thosewho perceiv etheirhealthstatusas fairor goodare morenumerous inNetherlands (slopegreater than45 and responderspercei vingtheirhealthas very goodare morenumerous in Greece.W ewillsay, inGD Aterminology,that responses"V erybad", "Bad", and"V erygood"areoverrepresentedin Greece,and responses "Fair"and "Good"are overrepresentedin Netherlands.1918 Note: Ithappens very oftenthatweha ve atable withabsolute valuesandnotprobabilities(e.g. here wecould hav eatablewithnumbersof respondents).In thiscase weobtain aprobability table by dividingeachv alueby thesumofits row .

19Note: Ithas noimpact onthe interpretationof theo verrepresentation value whethera certain

segmentof theconcentrati oncurv eisunderor abovethe diagonal.It isits slopewhat representsthe overrepresentation.I I I I I I I

66StanisławLenkie wiczFig.1.Concentration curveofDutch opinionsrelati ve toGreek opinions

There areas many concentrationcurvesas permutations ofsegments which buildthem.

20All concentrationcurves carrythesame information

about theo verrepresentationofevery particularattrib uteincomparedob- jects. Thereis, howe ver,onecurvewhichalsocarries additionalinforma- tion: itsho wstotaldissimilarityof two objects,taking intoaccount alltheir attributes.It isa maximalconcentration curve.

3.3.2 MaximalConcentration Curv e

Some segmentsofthe concentrationcurv eare underthe diagonal,some others -abo veit.Letusreorder segments basedon theirslopes, fromthe smallest slopeto largest one.Weobtain thecurv epresentedinFig. 2.It is themaximal concentrationcu rve. Itis conv exandliestotallyunderthe diagonal. The areabounded fromthe bottomby themaximal concentrationcurv e and fromthe top- bythe diagonalhas aspecial meaning.It isthe largest of all theareas boundedby any concentration curveandthe diagonal(proof20 This isalso anumber ofpermutations ofobjects" attributes. (I,:

GRADE DATAANALYSISAPPLIEDT OTHEEUROPEAN AGRICUL TURE67Fig.2.Maximal concentrationcurv eofDutchopinions relativ eto Greekopinions

may befound in[19]), soit isa measureof dissimilarityof comparedob- jects. Itis anequi valent ofadistanceofobjectsused inmore "traditional" cluster analysismethods. Here: thisarearepresentsdissimilarity ofpercep- tions oftheir healthby Greeksand bythe Dutch. Wecan comparethe resultsof thesurv ey foreach pairof countries. Comparison ofthe areasbetween eachmaximal concentration curve and the diagonalwill tellus thei nhabitantsof whichtw ocountriespercei ve their healthstatus themost dissimilarly.

3.3.3 ConcentrationCur veForColumns

Wecompared two rowsofthe table,i.e.two countries.But wecan also compare twocolumns,i.e. two perceptionsof healthstatus.For instance let uscompare theanswer "Very good"and theanswer"Very bad".

21Fig. 321

In Section3.3.1 wecompared resultsof thesurv ey fortw ocountries. Inthiscomparisoncoun- tries werefor usobjects andanswers ofresponders wereattrib utesof theseobjects. Herewe are going tocompare two answers,soresponders"answers areobjects andcountries areattrib utes."·"

68StanisławLenkie wiczpresents theconcentration curve forthiscomparison,

22and Fig.4 -the

maximal concentrationcurv e. Fig.3.Concentration curveofthe answer"V erygood" relativ etotheanswer "Very bad" Because wecan comparepairs ofro wsof thet ableaswellas pairsof columns, wecan findbot h:dissimilar objectsanddissimilarattrib utesof these objects. Measuring dissimilarityofobjects willbe cov eredin moredetail in

Section 3.3.4.22

Note: Todra wthiscurve,firstwe need tohave cumulativ edistrib utionsforbothanswers. To obtain them,we divide eachvalueby thesum ofitscolumn,thus obtainingprobabilities forboth answers: "Verybad"and "Very good". It isimportant tounderstand thedif ferencebetween probabilitiesfor countries(rowsof thetable, no datatransformation necessary)and probabilitiesfor healthstatus perceptions (columnsof the table afterthe operationdescribed abov e).V aluesinrowsareprobabilities thatarandomlychosen responder froma giv encountryhasgiven acertain answer(e.g. thataresponderfromGreecehas answeredI perceivemyhealth statusas verygood ). Valuesincolumns areprobabilities thata randomly chosenanswer hasbeen giv enby aresponderfromagiv encount ry(e.g. thata responseI perceivemy healthstatus asvery goodhas beengi venbyaresponderfrom Greece).,;11 • 1 c.s

C,; C.2

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