[Cytometry] MFI or Geometric Mean

David Novo david.novo at denovosoftware.com
Fri Jan 4 13:40:57 EST 2019

While the definition of Geometric Mean may have been shortsighted when it was defined hundreds of year ago nevertheless it is what it is. It is not simply an implementation detail that precludes calculation of Geo Mean on datasets with zero or negative values but the very definition of the statistic itself (although, technically you can have negative values as long as there are an even number of them). Any measure of central tendency that can be calculated on a data set with a value of zero may indeed be a useful measure of central tendency, but that statistic is NOT the geometric mean. Whatever new statistic a software package uses should clearly define what algorithm it is using to calculate this new central tendency and give this statistic a different name from Geometric Mean. Maybe the Geodesic Mean, the "my mother told me not to be Mean" or any other number of Mean related puns that I am sure Howard can think of far better than I 😊


David Novo


De Novo Software

213-814-1240 xt 802

-----Original Message-----
From: cytometry-bounces at lists.purdue.edu <cytometry-bounces at lists.purdue.edu> On Behalf Of Mario Roederer
Sent: Friday, January 4, 2019 6:05 AM
To: Cytometry Mailing List <cytometry at lists.purdue.edu>
Subject: Re: [Cytometry] MFI or Geometric Mean

The formal definition of Geometric Mean is the anti-log of the mean of the log of the values.  By this algorithm, Will is correct the GM cannot be computed on any series of values that includes non-positive values.  However, this turns out to be a short-sighted implementation of this statistic that should no longer be implemented in FACS software.  By its name, “Geometric” mean would indicate that it should represent a central tendency on data displayed graphically (i.e., originally on a pure log scale).  In other words, if you were to graph a histogram on a log scale on paper, and cut it out, then the geometric mean would be that position where the balance point was.  (This is what the mean is, with data graphed on a linear scale).  About 15 years ago, when Dave Parks, Wayne Moore, and I introduced the “Logicle” scaling (log + linear + negative log to display data in a more interpretable way), FlowJo implemented a version of Geometric Mean which also computes to the central tendency in any scaled data — i.e., it represents the central tendency of the data even if there are negative or zero values.  Think of it as a “graphical” mean.  It works very well.

Back to Kathik’s original question, there is NO “validated” method for documenting Ag expression.  I’m not even sure what “validated” means in this sense.  Like any quantification, any algorithm has its pros and cons.  Mean, Median, and GeoMean are all attempts to reduce a distribution to a single number.  Is that accurate?  Are you sure there is no heterogeneity in your sample?  Should you use multiple measures?  (e.g., medians and quartiles, means and SDs, etc.)?  How reproducible is your measurement?  How subject is it to outliers?  Or background (instrument, biological, experimental)?  Is a single value truly appropriate?  For those who advocate median (50th percentile), I ask, why not 75th? or 90th? or 45th?  What’s so special in your biological system that the 50th percentile is the one you should use?  There are multiple papers and discussions on this ListServ previously on this topic. Probably even a Cyto Workshop or two.

Like anything in science, try multiple methods and evaluate them for reproducibility, robustness, and then informativeness. Document what you find, and include it in your Materials and Methods to justify it.


PS:  Yes, Apple's spell checker just confirmed that “informativeness" is, much to my surprise, a real word….

PPS:  See this paper, published 23 years ago, when to my recollection I was still in high school, which uses many different percentiles:  Roederer, Herzenberg, and Herzenberg, 1996, Intl Immunol., "Changes in antigen densities on leukocyte subsets correlate with progression of HIV disease."  <https://www.ncbi.nlm.nih.gov/pubmed/8671584>

> On Jan 3, 2019, at 10:41 AM, Will Schott <Will.Schott at jax.org<mailto:Will.Schott at jax.org>> wrote:


> Geometric Mean will not work with even a single zero in the data. It worked in the analog FCS2 data days, not so much any since you can have a zero value for various reasons including overly aggressive baseline correction, or most commonly after compensation. Most folk will advise using the median as it is not effected as much by a few outliers.




> William Schott

> Manager, Flow Cytometry Service

> The Jackson Laboratory

> Bar Harbor, ME | Farmington, CT

> Phone:  (207) 288-6192

> iPhone: (207) 557-1449


> Internal Website


> From: <cytometry-bounces at lists.purdue.edu<mailto:cytometry-bounces at lists.purdue.edu>> on behalf of karthik bommannan <bkkb87 at gmail.com<mailto:bkkb87 at gmail.com>>

> Date: Thursday, January 3, 2019 at 7:18 AM

> To: Cytometry Mailing List <cytometry at lists.purdue.edu<mailto:cytometry at lists.purdue.edu>>

> Subject: [Cytometry] MFI or Geometric Mean


> Dear Flow cytometry community,


> Happy new year to all.

> Between geometric mean and MFI, I would like to know which is the validated way to document the intensity of antigen expression.

> Literature search shows that there is only a minor difference, and of late many publications are using Geometric mean to express antigen intensity.



> With Regards


> Dr.karthik Bommannan B.K., D.M,

> Assiatant Professor,

> Department of Oncopathology,

> Cancer Institute (W.I.A.),

> Adyar, Chennai, India.

> Phone: +91 8872896711

> ---


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