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Inferential statistics



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

  1. Hypothesistest:nullhypothesisandoppositehypothesis;one-sidedtestandtwo-sidedtest.

  2. One-sidedinspectionandtwo-sidedinspection;

  3. Samplingerrorcalculation;

  4. P-valuedecision-making;

  5. 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.

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