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In response to Goeff's message...
LYSYS II, version 1.1 and PC-LYSYS give the user the ability to generate
the mean on log data by selecting one of four different methods:
Method 1. Geometric mean expressed as a channel value:
Data in channel values --> calculate mean --> report result
Method 2. Geometric mean expressed as a linear values:
Data in channel values --> calculate mean --> convert
mean to linear value--> report result
Method 3. Arithmetic mean expressed as a linear value:
Data in channel values --> convert data to linear values
--> calculate mean --> report result
Method 4. Arithmetic mean expressed as a channel value:
Data in channel values --> convert data to linear values
--> calculate mean --> convert mean to a channel value -->
report result
Each method will give a different result, and for the most part,
arithmetic means will have a larger value than geometric means
since the arithmetic method tends to be biased by high values in
the data.
Since it represents the population's average signal intensity, the
arithmetic mean is useful for comparing flow cytometric results
with those obtained on the same sample using a spectrofluorimeter.
For data distributions where logarithmic presentation is appropriate,
the geometric mean represents the typical signal level better than
the arithmetic mean because it is less influenced by high outliers.
For example, "loose" gating with the inclusion of one bright
contaminant within the gate could significantly alter the arithmetic
mean.
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Excerpts from an unpublished BDIS Research Note: STATISTICAL
CALCULATIONS IN BECTON DICKINSON SOFTWARE ON LOGARITHMICALLY
AMPLIFIED DATA, by D. Gandour, et. al.
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