Elementary Statistical Methods Sahana Prasad Elementary Statistical Methods SahanaPrasad ChristUniversity Bangalore,India ISBN 978-981-19-0595-7 ISBN 978-981-19-0596-4 (eBook) https://doi.org/10.1007/978-981-19-0596-4 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SingaporePteLtd.2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface Statistics is basically a mathematical science wherein data is first collected, then analysed by using suitable tools, explanation/interpretation given, and then finally converted into a valid conclusion. Statistical techniques are used right from data collectiontofinalmeasurement.Differentexperimentaldesignsandsurveysampling techniqueshelpinobtainingthedatawhiledataqualityisimprovisedbystatisticians byusingdatacleaningtechniques.Variousforecastingandpredictiontoolsareavail- ableforprovidinginferences.Statisticalknowledgeisarelevantdisciplineinvarious academicorganizations—insocialandnaturalsciencesandinbusinessset-upsand governmentalorganizations. Theworldisproducingmorestatisticalinformationthaneverbefore,andmany peoplefeeloverwhelmedbyit.Itisimportanttoknowwhatinformationweshould payattentiontowhattodowithitandhowtousethem.Statisticsareinformationbut, as Albert Einstein put it, “information is not knowledge”. Yet, it is the knowledge thatleadstogooddecision-makingandspursprogress.Statisticsarerawmaterialfor thecreationofknowledge,andobviously,thequalityofstatisticsiscriticalforpublic policy.Flawedanalysisaffectsconclusionsandcanleadtopoorpolicydecisions,thus negatingthepurposeofdataanalysis.AsBenjaminFranklinsaid,“aninvestmentin knowledgepaysthebestinterest”. Awell-plannedprogramisessentialbeforecollectingthedata.Knowledgeabout alternative statistical methods, their assumptions, limitations and their usability is veryimportanttotheresearcher.Manytimes,aresearchermaynotbeabletodeter- minetheappropriatetooltousefordifferentkindsofdata.He/shemayapplyarigid theoreticalapproachwhichmaynotbecorrect.Whenstandardquestionsareused,it mayleadtostructuralbiasandfalserepresentation.Theymayalsocollectanarrow andsuperficialdataset,andtheresultscangetdistortedbecauseoffalseassumptions andinaccurateuseoftechniques. ix x Preface Since political, economic and other social conditions are rapidly changing, one hastobeequippedtodealwiththemandusetheappropriatetoolswithcaution.This requiresthattheresearcherhasenoughexposureandfamiliaritywithdifferenttools and techniques as the onus of selecting and implementing the right one rests with theresearcher.Inordertofulfilthisresponsibility,theresearcherhastopayattention toeverysmalldetailsofthestudy,rightfromdatacollection,measurementofdata, byusingtherighttoolfordifferenttypesofdataandmakingthecorrectinferences fromthedatabyusingthecorrectandvalidtechniquesofanalysis.Averyimportant aspectofthisisthattheresearchershouldbecomeconversantwiththeavailabletools andthesituationsinwhichtheycanbeused.Thus,heislikeaskilleddoctorwho knowsexactlywhathastobeprescribedandtowhom. Statisticsaidstheresearcheringivingvaluableandconcretesupportintermsof toolsandtheory.Themostimportantpointtobenotedisthatexperiments/researches havetobedesignedtousestatistics.Manyresearchersembarkonastudywithout pausing to think of how they can use statistics right from the design stage. If an experiment is designed and executed properly, as we would expect of an eminent scientist, then the results often speak for themselves. A good experimental design involveshavingaclearideaabouthowwewillanalysetheresultswhenwegetthem. That’swhystatisticiansoftentellusto“thinkaboutthestatisticaltestswewilluse beforewestartanexperiment”. Aresearcherinanyfieldwillsurelybenefitbytakingupacourseinbasicstatistics toknowtheusageandappropriatenessofvariousconcepts.Dependingonsoftware foranalysisand,thusonexpertsinthatareamaynotleadtoagoodanalysis,ifthe theory behind the problem has not been understood. It has been found that many research scholars use various measures without paying attention to data, its scale anditsvalidity.Thismayproducesomeresults,butitmayturnouttobeaskewed analysis. A wrong tool may lead to erroneous conclusions, which may affect the credibility of the researcher. It is a good principle, therefore, to remember that “a toolisgoodinthehandsofaskilledandknowledgeableresearcherbutmayturnout tobeadangerousweaponwhenusedbyanamateur”. Therearealargenumberofuser-friendlypackagesavailabletoaidresearch.SPSS (renamedPASW)STATA,SAS,EXCEL,R,etc.,aresomeothersoftwarewhichare usedtoanalysedata.However,usageoftheserequirescautionastheyoperatelike other software packages on the principle of “garbage-in, garbage-out”. Thus, it is essential to use the right statistical tools and to have at least a basic knowledge of statisticsbeforeusingsoftware. Preface xi Thisbookdealswiththeaboveissueswithreferencetostatisticaltools.Itassumes thatthereaderhasveryelementaryornoknowledgeaboutstatisticaltoolsandtries toexplainallconceptsbyusingcasestudies.Thereisjustenoughtheorytointroduce theconceptandthentakethereaderthroughavarietyofcasestudies.Theseanswer fourmainquestions,namelywhat,why,howandwhen.Allconceptsareexplained keeping these questions, which are likely to arise while understanding statistical concepts. A detailed list of figures as well as tables is appended in the book. The links giveninthebookareavailableinhttps://github.com/ElementaryStatisticalMethods/ Book1.git. Bangalore,India SahanaPrasad