means
Paul.M.Guyre@Dartmouth.EDU
14 Jul 92 20:08:00 EDT
This is a somewhat simplistic explanation of geometric vs arithmetic means
that I wrote for an in-house flow lab newsletter. It explains the difference
in the two types of statistics -- I assume that the BD software uses the
relative fluorescence intensity (i.e. 1-10,000 for a 4-log-decade amplifier
OR 1-1024 for a linear amplifier) to calculate these values, but I haven't
checked the calculations myself. This may just be telling you what you
already know....
"The third value that can be used to describe a histogram distribution is the
mean. The mean is the conventional "average" -- that is, you add up
everybody's weight, divide by the total number of kids in the fifth grade,
and end up with the average weight of a fifth grader. The main (and serious)
complication is that statisticians talk about two kinds of means -- depending
on whether they are considering geometrically or arithmetically distributed
normal distributions (does the distribution look symmetrical when plotted on
linear graph paper or when plotted on log graph paper?). To calculate an
arithmetic mean you add up all the values and divide by the total number of
individuals. To calculate the geometric mean, you multiply together all the
values and then get the nth root of the total product. Which value is
appropriate depends on whether or not you want to weight the bright cells
according to their true (high) brightness. By way of an example, if you
have a population of five cells, with fluorescence intensities of 1, 100,
100, 100, and 10,000, then their arithemetic mean intensity will calculate to
be 2060; their geometric mean will be 100. (Their mode will be 100, and the
median value will also be 100). It is the arithmetic mean which gives the
cell at 10,000 its "real" weight -- in much the way that one very large kid
in the fifth grade can seriously affect the calculated weight of an "average"
fifth grader. The geometric mean sees that the cell at 10,000 is 100 times
brighter than the cells at 100; and the cell at 1 is one hundredth as bright
as the cells at 100 (i.e. the cells show a log-normal distribution -- they
look symmetrical when plotted on log graph paper). Therefore the cell at
10,000 is given equal weight to the cell at 1 in the calculation of the
geometric mean. "
Which mean you use is, I would think, a matter of taste. My own opinion is
that the median is a far better flow cytometric parameter -- partly because
it avoids the problem of deciding which type of mean is relevant (it also
avoids the problem of correctly evaluating "off scale" events.
Hope this helps a bit.
Alice Givan
Dartmouth Medical School
Lebanon, NH
E-Mail c/o Paul M Guyre@dartmouth.edu
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