CV question

Eric Van Buren aa9080 at
Tue Sep 19 12:40:37 EST 2000

>> There is an effect that has been observed regarding the CV of 2.5 micron
>> calibration beads using on a flow cytometer. When the peak channel is
>located at
>> lower channel numbers the CV is increased. i.e. the CV of a population is
>> at mean channel 100 ( 2.41)  than at mean channel 800 ( 1.25). What is the
>> statistical explanation for this phenomenon.
>Hello Robert,
>Statistics for a histogram are calculated as follows:
>CV = (SD/Mean) x 100
>where Mean = [SUM(channel number x count in the channel)]/total number of
>cells in the region.
>So higher channel numbers give higher Mean and - finally - lower CV. I think
>it works for any kind of particles.
>I hope this helps you.
>Best regards,
>Michal Bochenek, PhD.

If the mean increases, so too should the standard deviation (SD). Let's look
at an example. Suppose we measure the volume of 3 samples, first in liters
and then in milliliters. The samples are measured and found to be 99 L, 100 L,
and 101 L. This gives a mean of 100 L, a sample SD of 1 L, and a coefficient
of variation (CV) of 1%. The same samples are 99000 mL, 100000 mL, and
101000 mL, with a mean of 100000 mL, sample SD of 1000 mL, and CV of 1%.
Notice that the CV does not change.

On the flow cytometer, however, we see that the CV can change, by changing
nothing more than the mean of the population. The explanation is not
statistical; rather it is an artifact of the flow cytometer's analog-to-
digital converters.

Let's look at the situation above, when the mean is near channel 100 or 800.
Suppose that in the case where the mean is near 100 that 3 beads with "analog"
values of 99.875, 100, and 100.125 are to be measured; after digitization, the
beads fall in channels 99, 100, and 100, respectively, leading to a mean of
99.67 and CV of 0.58%. However, the same 3 beads will fall in channels 799,
800, and 801 in the case where the mean is near 800, resulting in a mean of
800.00 and CV of 0.13%. The CV decreases in this second case because the
cytometer can more accurately record small differences in signal (0.125%,
versus 1% in the first case). Or put another way, the effective digital
resolution has increased 8-fold (there are 8 channels per 1% signal change
versus 1 channel per 1% signal change). [Using logarithmic amplification
changes everything; now there is a constant 0.9% per channel resolution (on
a 1024 channel histogram with a 4 decade log amp).]

Of course, other factors can contribute, like PMT response at different HV
settings, amplifier noise at different amplifier settings, linearity of the
amplifier, etc.

The same effect can be seen by collecting the same data on a 256-channel scale
and a 1024-channel scale, without changing any other settings. But this is a
whole different can of worms, fraught with noise versus resolution and
increasing cell number per sample, among other things. :)


/\/\/\_ Eric Van Buren, aa9080 at
\ \ \   Karmanos Cancer Institute and Immunology & Microbiology
 \_^_/  Wayne State University, Detroit, Michigan, USA

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