From: Ray Hicks (rh208@cus.cam.ac.uk)
Date: Wed Feb 11 1998 - 08:40:23 EST
Hi Darren,
>Here's my question from actual data. I run a sample and get mean 2000 on
>FL3, and mean 50 on FL1. After treatment, I get mean 200 on FL3 and mean
>1000 on FL1. This is all visualized on the "log" axes. If I divide the
>numerical values given for the means, I get ratios of 0.025 pre and 5.0
>post, for a fold change in ratio of 200.
>
>First question: do I invoke the mathematics of dividing log values when
>what I'm really dividing are "linear" values presented on a log scale? Is
>the above division appropriate?
Those are linear values, so you're right to divide one by the other. As
long as the mean is valid. However, it's not the same answer as you'd get
if you took the mean of ratio for each event - Imagine the following three
cells:
FL1-H FL3-H Ratio
1000 200 5
1500 200 7.5
1250 140 8.93
mean 1250 180 7.14
the mean ratio is 7.14 but the ratio of means is 6.94. If you add a
non-responder to your data set:
FL1-H FL3-H Ratio
1000 200 5
1500 200 7.5
1250 140 8.93
50 2000 0.025
950 635 5.37
The effect of the outlier is to drop the mean ratio to 5.37, but the ratio
of means has plummetted to 1.496. Which one best represents the
"population" ? Means are best at describing normal distributions, which
you're unlikely to have in a calcium experiment, and it's probably best to
put off averaging of any sort until you have to do it. I'll send you a
copy of FCS Assistant that will ratio log values later this week, so that
you can ratio on an event by event basis, but I still think you'd be better
off if you tried modifying your loading so that you could acquire in
linear...
>Second question: The above plots show a tight, homogenous population
>moving >from lower right to upper left on the FL1(Y) v FL3(X) plot. The
>same data >acquired on the evenly spaced 1024 channel scale would have a
>population >scattered all over the place rather than a tight population,
>and the movement >would be a smear rather than a precise relocation of the
>distinct population.
>?Furthermore, some particles would be off scale to one end of the spectrum
>>pre-tx, and then off scale on the opposite side post treatment. I guess
>the >question is, are the events really any "closer" together if the
>population is >scattered all over the non-compressed axis (as many as 1000
>channels apart), as >opposed to the log axis, where the data may be
>numerically further apart, but >much more visually concise? Furthermore,
>even if greater numerical spacing >occurs, is that a real problem
>considering the number of events that will be >squashed against the axes,
>giving false replication of 0's (or 1's?) and >1024's?
The effect of "logging" your data is to make peaks with the same cv look
the same width anywhere on the axis, and that is indeed visually pleasing.
If you antilog your data (remember, that's what you do to get the numbers)
you'd find that it would have a similar form to that acquired in linear,
but there would be gaps between data points of increasing size. As an
oversimplification, imagine that you've got a population with a mean of 10,
and a spread of values from 5 to 15. If you turn your gain up so that the
population has a mean of 100, the spread of values goes from 50 to 150 and
is a lot wider on a linear scale (a spread of one hundred rather than a
spread of ten). If you log (base ten) the values you get 0.69, 1.176,1.69
and 2.176 for 5,15,50 and 150. If you look at the values you see that the
separation between log 5 and log 15 is the same as that between log 50 and
log 150 (it's log 3 - substracting one log from another gives you the log
of the ratio between their antilogs), so if you plot the log values you get
peaks with a (narrow) spread of 0.486 anywhere on the axis EVEN THOUGH the
data are exactly the same ones that have increasing spread when plotted on
a linear scale.
Try exporting some data from a log histogram and plotting it in excel (you
can use FCS Assistant to do that), next try antilogging the data and
plotting it [use =10^(ch/256) in excel to do the antilogging], try the
reverse process with some linear data. While you're at it try that equation
on all numbers in the range 0-1023 to see the entire gamut of linear values
that are available in your data sets. You should end up with a better feel
for what's going on. You could also take a look at Dave Coder's log amp
page.
http://nucleus.immunol.washington.edu/Research_facilities/Apps/logscale.htm
Ray
ps A log ratio-ing version of FCS Assistant will be winging its way to you
in the next day or so, and will be on my server soon after.
Ray Hicks
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