(Go back one page to 3-Color compensation: examples,
or back to the introduction)

Unfortunately, the process of compensation introduces error into the measurement.
It does not introduce a systematic error, but simply increases the cv of
any measurement. This is because each compensated value is the convolution
of several measurements; therefore, the error in each measurement contributes
additively to the error in the compensated value.

A detailed discussion of the errors introduced by analog compensation (along
with a depiction) is given in informal discussion; click here
to go directly there (however, there is no direct way to navigate back to
this page from there).

The remainder of this discussion is about digital compensation (for instance,
in posthoc compensation analysis by software) and errors introduced in this
process. Digital compensation introduces significantly greater errors than
analog compensation, primarily because of the error introduced by "binning"
the data.

Consider a cell which is negative for a PE reagent but brightly fluorescent
for a FITC reagent. Assuming our (logarithmic) fluorescence scale ranges
from 0.1 to 1,000 (4 decades), then the "true" fluorescences of
this cell might be 0.5 for PE (i.e., negative except for some autofluorescence),
and 100 for FITC. Because of the 15% spillover of FITC to PE, the measured
PE fluorescence would be 15.5 (0.5 "true" + 0.15 x 100 "FITC
spillover"). Note that if the measurement were made exact, then the
true PE fluorescence could be determined. Using the first equation, PEtrue
= 15.5 - 0.15 x 100 = 0.5. But what would happen if there were a one channel
error in the measurement of fluorescence? In the PE channel (at this low
level of fluorescence), this is not a whole lot; one channels corresponds
to about 0.02 fluorescence units. But because of the logarithmic nature,
one channel error at 100 units (the fluorescein measurement) translates
into about 3.7 fluorescence units. If the machine were only one channels
low (out of 256), then the FITC might be measured at 96.3 units. Now the
"true" PE fluorescence is calculated as: 15.5 - 0.15 x 96.3 =
1.06. This is a shift of over 20 channels from the correct position: note
how much error has been introduced into the "true" PE fluorescence
value! A measurement that was ±1 channels is now ±20 channels.
(Note, of course, that this is because of the logarithmic amplification:
the error of the measurement is ±3.7 units; this results in an error
after compensation of 15% of this, or ±0.56 units. But 0.56 units at
the low end of the scale--negative cells--is much broader than 3.7 units
at the positive population.)

Another source of error will be the logarithmic amplifiers. "Log amps"
do not have a perfectly logarithmic response; they often vary from perfection
by a few percent at different ranges of the scale. Since digital compensation
assumes that the response of the log amps is perfect, a few percent error
in the apparent measurement can be introduced. The magnitude of this effect
can be as large (or larger) than the binning error discussed in the previous
paragraph.

In multi-color experiments (> 4), where there is a large number of compensations
to each channel being performed digitally, the effect can be significant.
In general, what happens is that the populations are significantly "smeared,"
resulting in a lower ability to discriminate between populations of varying
intensities.

Finish off.