Basicdefinition
Inferentialstatisticsistouseprobabilitynumberstodeterminethepossibilityofacertainrelationshipbetweentwo(orseveralgroups)ofnumbers,andtoinferoverallcharacteristicsfromsamplecharacteristicsStatisticalmethods.
Educationalscientificresearchisgenerallyimpossibletoexaminealltheobjectstobestudiedonebyone,buttodrawacertainsamplefromthewholeforresearch.Forexample,tounderstandthedemographiccharacteristicsofaregion,itisimpossibletomeasurethecharacteristicsofeachperson.
Intheresearchdesign,thesubjectsareoftendividedintodifferentgroupsaccordingtocertainrequirementstofacilitatetheresearchandstatisticalprocessing,sothatproblemssuchasestimatingthepopulationfromthesampleandinferringthepopulationarise.
Forexample,tounderstandthedemographiccharacteristicsofanarea,itisimpossibletomeasurethecharacteristicsofeachpersononebyone,andtoinspectthequalityoffinishedproducts,whichisoftendestructive,anditisimpossibletoinspecteachproduct..Thisrequiressamplingindividualsamplesformeasurement,andinferringtheoverallcharacteristicsbasedontheobtaineddata.Thisistheproblemthatinferencestatisticsmustsolve.Inferentialstatisticsisveryusefulbecauseitallowsustogivelimitedinformation(samples)todrawconclusionsaboutthepopulation.
Step
Hypothesistest:nullhypothesisandoppositehypothesis;one-sidedtestandtwo-sidedtest.
One-sidedinspectionandtwo-sidedinspection;
Samplingerrorcalculation;
P-valuedecision-making;
Effectsizecalculation.
Maincontent
Inferredstatisticsincludetwoaspects:overallparameterestimationandhypothesistesting.
Globalparameterestimation
Whenasetofdataisobtainedfromasampleintheresearch,howtousethissetofinformationtoestimatetheoverallcharacteristics,thatis,howtoinfertheoverallsituationfromthelocalresults,Calledtheoverallparameterestimation.Theoverallparameterestimationcanbedividedintopointestimationandintervalestimation.
Pointestimationistousesamplestatisticstoestimatetheoverallparameters,becausethesamplestatisticsarethevalueofacertainpointonthenumberaxis,andtheestimatedresultisalsorepresentedbythevalueofapoint.Sincethisestimateisasinglevalue,thereisalwaysanerror,andtheerrorcannotbeaccuratelycalculated.Inaddition,thepointestimatecannotindicatetheprobabilityofgivingacorrectestimateoftheoverallparameter.Therefore,thispointestimatecanonlybeusedasanimpreciseroughestimate,andabetterwayistoestimatetheoverallparametersinaninterval.
Intervalestimationisbasedonsamplestatistics,usingtheprincipleofsamplingdistribution,andusingprobabilitytoindicatethattheoverallparametermayfallwithinacertainnumericalinterval.Therearemanytypesofintervalestimation,mainlytheintervalestimationoftheoverallaverage,theintervalestimationoftheoverallpercentage,theintervalestimationofstandarddeviationandvariance,andtheintervalestimationofcorrelationcoefficient.
Hypothesistesting
Instatistics,generalconclusionsaredrawnfromthedifferencesinsamplestatisticstodeterminewhethertherearedifferencesbetweenoverallparameters.Thisinferenceprocessiscalledhypothesistest.Hypothesistestingisdividedintoparametrictestingandnon-parametrictesting.
Ifthedistributionofthepopulationisknownwhenthehypothesistestisperformed,itisnecessarytoperformahypothesistestonthelocationparameterofthepopulation,whichiscalledaparametrichypothesistest.Ifyouknowlittleabouttheoveralldistribution,youneedtoperformhypothesistestingontheformoftheunknowndistributionfunctionandothercharacteristics,usuallycallednonparametrichypothesistesting.
Comparativeanalysis
Theconfrontationaldebatebetweenthedescriptiveandinferentialschoolsinstatisticsinthe1920sand1940scanbasicallybesaidtobetherapiddevelopmentofstatisticalinferenceideas.Andit'sover.Butinthe1960s,withtheriseofBayesianstatisticalthinking,peoplewentbacktounderstandthewholestatisticsandvariousideasinitfromamoreobjectiveperspective,andtriedtofindthebasisofvariousstatisticalideas.Theexistenceofstatisticalknowledgeobjectsandmethodsthathavethesamefundamentalsignificanceiswhatwecallthegenerallawandprobabilitytheory.Thesetwopointshavebecomethemostessentialthingsthatvariouswesternstatisticalschoolsofthoughtadhereto,andtheyarethetwocoresoftheentirestatistics.However,this"generic"statisticalviewisstillbasedonthesignificantdifferencesbetweenvariousstatisticalschoolsofthought.Asfarasdescriptivestatisticsandinferentialstatisticsareconcerned,thisdifferenceismainlyreflectedinthefollowingthreeaspects:
Firstofall,differentthinkingandunderstanding.Descriptivestatisticsbelievesthatonlyalargenumberofobservations(notafewexperiments)canfullyandcorrectlyreflecttheregularityofappearancechanges,andifthisobservationislimitedtoafewsmall,partialexperiments,theconclusioncanbedrawnItmustbeone-sidedorevenwrong.Fromaphilosophicalpointofview,itadherestothetheoryofknowability,opposesthetheoryoflimitedhumanintelligence,andbelievesthathumanbeingsarefullycapableofmakingalargenumberofevencomprehensiveobservations.Onthecontrary,inferentialstatisticsstronglyopposetheextensiveandcomprehensivecollectionoflargeandcomplexrawdata,thinkingthatinsteadofthis,itisbettertofocusonexperimentsthatarepreciselydesignedandcontrolled.Thedatacanbetrulydescribedasinformativeandreliable,andthuscanitmoreaccuratelyreflecttheregularityofchangesinthephenomenon.
Secondly,theapproachisdifferent.Thisisexactlythedifferencethatisinevitablyderivedfromthedifferenceinthinkingandunderstanding.Descriptivestatisticsinsistonalargenumberofobservations,whileinferentialstatisticsinsistonsampleanalysis,anditsessenceissmallsampleanalysis.Therefore,itcanberoughlysaid:thelawofdescriptivestatisticsisdisplayed"directly"intheoverallinformation(comprehensivedata)andisdescribed(condensed);whilethelawofinferringstatisticsisthroughsampleinformation(partialdata).)Whatappears"indirectly"isinferred(estimatedortested).
Finally,thelogicalstructureisdifferent.Inferentialstatisticsadvocatesusingsamplestomakeinferences.Therefore,itmustfirstconstructthetwomostbasicstatisticalcategories,namelythepopulationandthesample.Otherstatisticalcategoriesorconceptsarerelativelyderivedfromtheirinferiorcategoriesorconcepts.Callitasubcategoryorsubconcept.Incontrast,fordescriptivestatistics,thisisnotindispensableforthebasiccategory(especiallythelatter).Ifyouwanttousethispairofbasiccategoriestoestablishtheentirestatisticalcategoryorconceptualsystem,youcanroughlysaythatdescriptivestatisticsbelongtolargesampleanalysis,whileinferentialstatisticsbelongtosmallsampleanalysis.
Teachingapplication
Selectthecasethatisclosesttothestudent’slife,throughthedesignofpracticalteaching,letstudentsparticipateintheacquisitionofoveralldata,randomsampleextraction,calculationofcommonstatistics,Toinferandtesttheoverallparameters,graduallygainanintuitiveunderstandingofsomekeyissuesandconceptsinstatisticalinferencetheoriessuchassamplingdistribution,parameterestimation,andhypothesistesting.ThismethodcanvisualizeabstractstatisticaltheoriesandisbeneficialtoDeepenstudents'understandingofstatisticalinferencetheory.