Uses and abuses of logarithmic axes - GraphPad Software

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Notethatwhenanexponentialdissociationcurveplateausatavalueotherthanzero,itwillnotbelinearonalogarithmicaxis.ThegraphontherightbelowhasalogarithmicYaxis,buttheexponentialdecay(greencurve)isnotastraightline.Lognormal distributionsPlotting lognormal distributions on a logarithmic axisThetwographsbelowplotthesame50values.Thegraphonthelefthasalinear(ordinary)Yaxis,whilethegraphontherighthasalogarithmicscale.Thedataaresampledfromalognormaldistribution,whichisveryasymmetrical. 8
Whenshownonalinearscale(graphontheleft),itisimpossibletoreallygetasenseofthedistribution,sinceabouthalfofthevaluesareplottedinpileatthebottomofthegraph.Anotherproblemisthatifyousawonlythegraphontheleft,youmightthinkthehighestfourvaluesareoutliers,sincetheyseemtobesofarfromtheothers.Whenplottedwithalogarithmicaxis,thedistributionappearssymmetrical,thehighestpointsdon’tseemoutofplace,andyoucanseeallthepoints.Thesedatacomefromalognormaldistribution.ThatmeansthatthelogarithmsofvaluesfollowaGaussiandistribution.Plottingsuchvaluesonalogarithmicplotmakesthedistributionmoresymmetricalandeasiertounderstand.The mean and geometric meanThegraphsbelowshowthesamedata,andalsoshowthemeanandgeometricmean.Thegeometricmeaniscomputedbyfirsttransformingallthevaluestologarithms,findingthemeanofthoselogarithms,andthenreversetransformingthatmeanbacktotheoriginalunits.Withanasymmetricaldistribution,themeanandgeometricmeancanbequitedifferentasshownhere.Whenplottedonalogscale(right),themeanisnotnearthemiddleofthedata.Thatisbecausethepointsabovethemeanhavemuchlargervaluessobringupthemeanvalue.Onalogarithmicaxis,thegeometricmeanisnearthemiddleofthedistribution.Thisgraphshowsthattheconceptofanaverageormeanissomewhatambiguouswhendataareplottedonalogarithmicaxis.Doyoumeanthemeanoftheactualvalues,orthemeanofthelogarithms(thegeometricmean)?Becauseofthis 9
Page 1 and 2: The Use and Abuse of Logarithmic Ax
Page 3 and 4: GraphPadPrismcanplotlog2axes.Choose
Page 5 and 6: Sincezerocan’tbeshownonalogaxis,t
Page 7: axis,thevalueplottedontheYaxisequal
Page 11 and 12: Distinguish using a logarithmic axi
Page 13: ange(0to5).Thefirstaxishasdecimalnu

Uses and abuses of logarithmic axes - GraphPad Software

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