I summarized most of the concepts in a plot that's on the lab web page:
http://nucleus.immunol.washington.edu/Research_facilities/Apps/logscale.html
I noted the formula for estimating (heavy emphasis on 'estimating) the relative
brightness of a given population for 8-bit (256 channel) data. The general
formula is as follows:
relative brightness = 10^(channel #/(resolution [# of bits])/# decades of
log amp)
And I agree with Derek that the chief benefit of doing a log transform of the
data is to increase the display range. Note on the graph in the web page above
that really "bright" signals on a log scale can be one tenth the detectable
brightness. That is, most of the immunofluorescence that you look at is really,
really dim.
Note also, that you can convert the fluorescence brightness into some sort of
biologically meaningful units as well. See the illustration at:
http://nucleus.immunol.washington.edu/Research_facilities/Apps/quant/quant_cytom
.html
Quantitative cytometry is where it's at, man.
Dave
----- Original Message -----
From: Derek Schulze <flow@post.queensu.ca>
To: cyto-inbox
Sent: Monday, April 02, 2001 1:08 PM
Subject: Re: Mean ratios - Log to Linear
>
> 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/
>
>
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