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# Inferential statistics

## Basicdefinition

Inferentialstatisticsistouseprobabilitynumberstodeterminethepossibilityofacertainrelationshipbetweentwo(orseveralgroups)ofnumbers,andtoinferoverallcharacteristicsfromsamplecharacteristicsStatisticalmethods.

Educationalscientificresearchisgenerallyimpossibletoexaminealltheobjectstobestudiedonebyone,buttodrawacertainsamplefromthewholeforresearch.Forexample,tounderstandthedemographiccharacteristicsofaregion,itisimpossibletomeasurethecharacteristicsofeachperson.

Intheresearchdesign,thesubjectsareoftendividedintodifferentgroupsaccordingtocertainrequirementstofacilitatetheresearchandstatisticalprocessing,sothatproblemssuchasestimatingthepopulationfromthesampleandinferringthepopulationarise.

## 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.

Intervalestimationisbasedonsamplestatistics,usingtheprincipleofsamplingdistribution,andusingprobabilitytoindicatethattheoverallparametermayfallwithinacertainnumericalinterval.Therearemanytypesofintervalestimation,mainlytheintervalestimationoftheoverallaverage,theintervalestimationoftheoverallpercentage,theintervalestimationofstandarddeviationandvariance,andtheintervalestimationofcorrelationcoefficient.

### Hypothesistesting

Instatistics,generalconclusionsaredrawnfromthedifferencesinsamplestatisticstodeterminewhethertherearedifferencesbetweenoverallparameters.Thisinferenceprocessiscalledhypothesistest.Hypothesistestingisdividedintoparametrictestingandnon-parametrictesting.

## Comparativeanalysis

Secondly,theapproachisdifferent.Thisisexactlythedifferencethatisinevitablyderivedfromthedifferenceinthinkingandunderstanding.Descriptivestatisticsinsistonalargenumberofobservations,whileinferentialstatisticsinsistonsampleanalysis,anditsessenceissmallsampleanalysis.Therefore,itcanberoughlysaid:thelawofdescriptivestatisticsisdisplayed"directly"intheoverallinformation(comprehensivedata)andisdescribed(condensed);whilethelawofinferringstatisticsisthroughsampleinformation(partialdata).)Whatappears"indirectly"isinferred(estimatedortested).