And indeed, the flow data that I have examined (cell surface immunfluorescence collected on a linear scale) are highly skewed to the right. That is, they are not normally distributed (in the statistical sense). A log transform of the distribution of CD3 on human PBL's gave a distribution that was not normally distributed (the distribution was left-skewed), but a square root transform (channel number to the 0.5 power) produced normally distributed data; CD4 and CD8 gave normally distributed data with larger exponents--0.6 and 0.8 respectively (Cytometry. 1994 Jun 15;18(2):75-8). I have yet to see any flow cytometry fluorescence distribution data that are in fact, normally distributed following a log transform. This might always be the case for the distribution of fluorescently labeled cell surface proteins. DNA contents of 2C and 4C cells (untransformed data) are assumed to be normally distributed and modeled as such. I don't know anything about the distribution of other fluorescently labeled intracellular constituents. So cast off your log amps! Find high resolution ADCs! Compute the transformation of your data until they are not longer skewed, and sin no more! Ite, missa est finita. (There's a song in there somewhere, Howard.) Dave (who's certainly not a statistician, but has good friends who are) ----- Original Message ----- From: MATTHEW ROSINSKI <mrosinski@cheque.uq.edu.au> To: cyto-inbox Sent: Wednesday, March 28, 2001 4:38 PM Subject: Mean ratios; complete with a bottom line! > > I agree with Mario and disagree > > Mario Roederer wrote: > > >Much better would be to calculate the > >10th, 25th, 50th (median), 75th, and 90th percentiles of a complex > >distribution: at least now you have 5 parameters to the distribution and > >therefore a much better chance of accurately describing it (and possibly > >discovering underlying phenomena hidden by using only a single value). > > Using 2 numbers a distribution can however, be completely defined if the > underlying distribution is log normal. Particulate systems often have > distributions which obey the log-normal distribution. Thus when the > distribution is replotted using the logarithm of the parameter, > asymmetrical or skewed curves are transformed into a symmetrical > "bell shaped curve". In the log normal distribution the mean, > median and mode coincide and have identical values. The geometric median > and geometric standard deviation completely define the distribution. > This is important because you can then apply the statistics derived > for the normal or Gaussian distribution to the data. > The 10th, 25th etc percentiles give you no extra information IFF the real > distribution is lognormally distributed. Incidentally, to put the cat among the > pigeons the geometric standard deviation is equal to the 84.1% value divided > by the 50% value (which in logs is logX(0.841) - logX(0.5)) > > These are not my ideas but those of: > Stockman, J.D. 1978. What is particles size: The relationship among > statistical diameters. In Particle Size Analysis. J.D. Stockman and > E.G. Fochtman, editors. Ann Arbor Science, Ann Arbor. > > If the linear data can not be described by a log normal distribution however > then Mario's advice on using the percentiles is certainly useful. > > Matt Rosinski > > > _______________________________________________________ > > Matthew Rosinski > The University of Queensland > Department of Chemical Engineering > College Rd > St Lucia Q 4072 > Australia > Ph: (07) 3365 8392/4352 > > _____________________________________________________ > >
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