Re: Mean ratios - Log to Linear

From: Derek Schulze (flow@post.queensu.ca)
Date: Mon Apr 02 2001 - 15:08:35 EST


I hope the big guys don't mind my, hopefully not too ignorant, contribution
to this seemingly never ending discussion over log scale data.  Please
don't fry me on this one because I am really just trying to understand this
stuff.

Upon consulting the statistics section of my EPICS ELITE user manual I
discovered that all log data is converted to linear before any calculations
are performed.  This is accomplished by the following calculation:  Log to
Lin (N) = 1.024 x 10EXP (3 x N / 1024) where N is the channel
number.  Basically they are taking the anit-log (10EXP3) and correcting for
the extra few channels that a 10 bit AD converter gives (2EXP10).  Coulter
goes with an arithmetic mean after the conversion by summing the counts in
the corresponding linear channel numbers of the range of interest and then
dividing by the total number of counts in that same range.

Basically what I am getting at is that the data is no longer logarithmic as
far as the statistics is concerned BUT is displayed as logarithmic.

As far as taking a ratio is concerned you are dividing linear numbers NOT
logarithmic numbers so why not let the guy divide his means/medians for a
ratio (recognizing that the argument for subtraction is more convincing for
most applications).

Log amps give us the ability to see both dim (like myself) and bright (like
Howard) events on the same scale (and get pretty peaks) BUT they do so with
a sacrifice.  My interpretation of that sacrifice is, for lack of a better
word coming to my mind, resolution.  With a linear scale the signal goes
straight to the AD converter through a user selected amplification (1 -
100) which gives 1024 (with 10bits) channels or levels of intensity (single
parameter histogram).  With log data the events bypass the linear amp and
go to a log amp, which to put it crudely is an amplifier with a nonlinear
response where it would appear to be most sensitive to faint signals and
least sensitive to bright signals.

What you end up with after transforming the log output to linear is a wider
range of sensitivity with the same number of channels to represent it with
as the linear amplifier.  Essentially your ability to resolve minor shifts
in data is diminished (try detecting aneuploids on a log amp).

Most people must be at least subconsciously aware of the fact that their
"log" data is linear when they discuss the "linearity" of their log amps.

I have really stuck my neck out on this one.  I do welcome any criticism so
I can clear the murky waters in my head.


Derek Schulze

Cancer Research Labs
Queen's University
353 Botterell Hall
Kingston, ON, K7L 3N6
(613) 533-6635

http://meds.queensu.ca/medicine/crl/



This archive was generated by hypermail 2b29 : Sun Jan 05 2003 - 19:01:14 EST