Uses and abuses of logarithmic axes - GraphPad Software
Uses and abuses of logarithmic axes - GraphPad Software
Uses and abuses of logarithmic axes - GraphPad Software
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ambiguity,considershowingthemedianinstead.Forthesedata,themeanis1541.3,thegeometricmeanis141.2,<strong>and</strong>themedianis116.3Displaying variability on a lognormal distributionsIntheexampleabove,thest<strong>and</strong>arddeviation(SD)is4930.TherangethatcoversameanplusorminusoneSD,therefore,extendsfrom1541–4930to1541+4930,whichisfrom‐3389to6741.Thisrangecannotbeplottedona<strong>logarithmic</strong>axis,becausesuchanaxiscannotincludenegativevaluesOnealternativeistocomputeageometric st<strong>and</strong>ard deviation,butthesearenot<strong>of</strong>tenused(muchlessthangeometricmeans)<strong>and</strong>aretrickytounderst<strong>and</strong>.Fordisplaypurposes,ifyouarenotgoingtographeveryindividualvalueasonthegraphsabove,abox‐<strong>and</strong>‐whiskersplotasshownbelowdoesagreatjob<strong>of</strong>showingvariation.Theboxextendsfromthe25 th to75 th percentiles,withalineatthemedian(50 th percentile).Thewhiskers,onthisgraph,godowntothesmallestvalue<strong>and</strong>uptothelargestvalue(alternativedefinitionsare<strong>of</strong>tenused).Again,thegraphiseasytounderst<strong>and</strong>whena<strong>logarithmic</strong>axisisused(right)butisnotveryhelpfulwithalinearaxis. 10
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