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标准差和标准误的选择(SD)和(SEM).doc

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标准差和标准误的选择(SD)和(SEM) Whicherrorbarshouldyouchoose? Itiseasytobeconfusedaboutthedifferencebetweenthestandarddeviation(SD)andstandarderrorofthemean(SEM). TheSDquantifiesscatter-howmuchthevaluesvaryfromoneanother. TheSEMquantifieshowaccuratelyyouknowthetruemeanofthepopulation.TheSEMgetssmallerasyoursamplesgetlarger.Thismakessense,becausethemeanofalargesampleislikelytobeclosertothetruepopulationmeanthanisthemeanofasmallsample. TheSDdoesnotchangepredictablyasyouacquiremoredata.TheSDquantifiesthescatterofthedata,andincreasingthesizeofthesampledoesnotincreasethescatter.TheSDmightgouporitmightgodown.Youcan'tpredict.Onaverage,theSDwillstaythesameassamplesizegetslarger. Ifthescatteriscausedbybiologicalvariability,yourprobablywillwanttoshowthevariation.Inthiscase,graphtheSDratherthantheSEM.YoucouldalsoinstructPrismtographtherange,witherrorbarsextendingfromthesmallesttolargestvalue.Alsoconsidergraphingeveryvalue,ratherthanusingerrorbars. Ifyouareusinganinvitrosystemwithnobiologicalvariability,thescattercanonlyresultfromexperimentalimprecision.Inthiscase,youmaynotwanttoshowthescatter,butinsteadshowhowwellyouhaveassessedthemean.GraphthemeanandSEMorthemeanwith95%confidenceintervals. Ideally,thechoiceofwhicherrorbartoshowdependsonthesourceofthevariabilityandthepointoftheexperiment.Infact,manyscientistsalwaysshowthemeanandSEM,tomaketheerrorbarsassmallaspossible.