Basic-statistics

Basicstatistics郜战莹外国语言学及应用语言学硕士研究生ContentAbriefdescriptionofstatisticsDescriptionstatisticsInferentialstatistics1.Abriefdescriptionofstatistics1.1Definitions1.2Twoimportantterms1.1Definitionsdescriptivestatisticsinferentialstatistics1.1.1DescriptivestatisticsIfareseacherisinterestedonlyindescribingagroupfromwhichthedataaregathered,thestatisticsinvolvediscalleddescriptivestatistics.Note:Inmanycasesdatainthefieldofappliedlinguisticsarepriamrilydescriptiveinnature.c1.1.2InferentialstatisticsIfhisorherinterestgoesbeyonddescribingthegroupfromwhichthedataarecollectedands/hetriestodrawconclusionsaboutthepopulationfromwhichthegroupwasselected,thestatisticsneededinthiscaseininferentialstatistics.Note:Itsadvantageistoallowthereseachertomakedecisionsaboutthepopulationwithoutstudyingtheentirepopulation.1.2TwotermsparameterstatisticParameterisadescriptivemeasureofthepopulation,whichisdenotedbyGreekletterssuchasPage180.e.g:populationmeanpopulationvariancepopulationstandarddeviationParameterStatisticisadescriptivemeasureofasample,whichisdenotedbyaRomanletter,suchastheexamplesinpage180e.g.samplemeansamplevariancesamplestandarizationdeviationStatisticDiferentiationbetweenparameterandstatisticisimportantonlyintheuseofinferentialstatistics.Thestatisticianoftenwantstoestimatethevalueofaparameter.However,therearesomefactorscanaffectthevalues,especially:NotetimemoneyAnexample:SupposeyouareanEnglishteacheratNanjingUniversityandyouwanttoknowtherelationshipbetweentheuseofstrategiesandtheEnglishproficiencyofalltheNanjingUniversitystudents.Therearemorethan10,000studentsontwocampuses.Obviously,youcannnotaffordthemoneyandtimetotakeacensus.Whatyoumaydoistosurvey400studentsasasamplebyaquestionnaire.Then,howdowedo?descriptivestatisticsinferentialstatisticsYouusedescriptivestatisticstogettoknowwhichstrategiesaremorefrequentlyusedbythese400students.Theresultsyouhavegotareonsample.YoumayuseinferentialstatisticstoexaminetherelationbewteentheuseofstrategiesandEnglishachievement,ortoseewhetherthemalestudentsdifferfromthefemalestudentsintheiruseofstategiesbasedonthenotionprobabilityDescriptiveanalysisorstatisticsdescribesthegeneralpatternortendencyemergingfromthedatacollected.Inferentialanalysisorstatistics,morecomplicatedthandescriptive,aimsatpredictionsbeyondthesampledata.ConclusionDescriptiveStatisticsfrequenciescentraltendencyvariabilityFrequenciesThesimplestwaytoorganizethedataistodescribetheirfrequencydistributionwhichcanreduceandsummarizedataeffectivelyandefficiently.frequencydistributionbargraphpolygonpiechartIfthetotalpossiblevaluesareverylimited.forexample:ifthestudents'responsestoquestionnaireitemsarenomorethanfive:1,2,3,4,5,frequencydistributioncanbeobtainedsimplybytallyingupalltheresponses,asshownintable1.ChoicesFrequencyPercentage1(Stronglydisagree)3030%2(Disagree)4545%3(Neitherdisagreenoragree)1010%4(Agree)55%5(Stronglyagree)1010%Table1:FrequencydistributionIfthetotalpossiblevaluesarevarious,suchaspeople'sageandstudents'testscores,weneedtogrouptherawdataintoclasses.Inthiscase,thefrequencydistributionisconcernedwithclassesratherthanwitheachindividualscore.Howdowedescribethefrequencydistributionintermsofclasses?Therearenohard-and-fastrulestofollow.Generallyspeaking,wemayconstructthefrequencydistributionofthesedatainthreesteps:1.Determinetherangeoftherawdata2.Determinethenumberoftheclasses3.Determinethewidthoftheclassinterval58,65,84,70,90,75,86,76,80,82,83,84,69,84,85,86,72,89,75,92Attention1.Therangeoftherawdata:definedasthedifferencebetweenthelargestandsmallestnumbers.2.Thenumberofclassestoomany:cannotachievegeneralizationtoofew:cannotseetheimportantdifferencestheappropriatenumberofclassesbetween5and1092-58=34Attentionrange3.thewidthoftheclassinterval=—————————thenumberofclasses组距=全距/组数Asusual,itis5,10,15andsoon.4.Thefrequencydistributionmustincludeallthedatagiven.Therefore,thefrequencydistributionshouldstart:atavalueequaltoorlowerthanthelowestnumberoftheungroupeddataend:atavalueequaltoorhigherthanthehighestnumber.ClassIntervalFrequency50—under60160—under70270—under80580—under901090—under1002Total20Table2:FrequencydistributionintermsoffiveclassesClassIntervalFrequency50—under65165—under80780—under9512Table3:FrequencydistributionintermsofthreeclassesIfyouwanttoknowtherelativestandingofanyparticularscoreinagroupofscores,youcanshowitbyapercentilescore.formula:CumulativeFPercentile=——————×（100）N1.Cumulativefrequency(F):referstothefrequencyofthescoreorthescoreswithintheclassjustbelow.2.N:representsthetotalnumbelofscores.3.Percentile:definedasanumberwhichrepresentsthepercentofscoresthataparticularrawscoreexceeds.ClassIntervalFrequencyCumulativeFrequenciesPercentage50—under60115%60—under702310%70—under805825%80—under90101850%90—under10022010%Total2020100%Table4:FrequencydistributionwithcumulativefrequenciesandpercentagesPercentileInterpretations95thThescoreconcernedexceeds95%ofthescores.90thThescoreconcernedexceeds90%ofthescores.75thThescoreconcernedexceeds75%ofthescores.60thThescoreconcernedexceeds60%ofthescores.50thThescoreconcerne