Dear Ulrik,
Thanks for that post, which, I for one, think is eminently sensible!
The variation of means of the same sample re-run on the cytometer is
something that few people seem to take into account and seems to me
that, especially if you are looking for small fluorescence shift, that
this is an important measurement.
I often have users who want to claim a significant difference between the
cumulative distributions of the control and test samples on the basis of a
small shift in mean channel value in one experiment. I always say that
they need to repeat to verify that but that they also need to be aware
that there will be a variation in fluorescence level even between
negatives run at different times. At some point, a muliple run of the same
sample must be done so that the variation can be quantified. If this is
then smaller than the variation between the control and the test samples,
then a further statistical test can be performed to determine the level of
significance. Let us also not forget that the change of a continuous
distribution into a dicrete channelised distribution will also involve
loss of resolution so I am always wary of small changes in any one
experimental run.
As for KS statistics, as they always seem to indicate a significant
difference (for the reasons stated by previous repsondents) I have never
encouraged their use.
{Apologies for quoting the whole of the previous text, but I think it
needs it!}
Derek
On Tue, 12 Oct 1999, Ulrik Sprogøe-Jakobsen wrote:
> The use of K-S or other appropriate statistics to the comparison of two
> histograms (e.g. sample A versus sample B) will reveal the true
> statistical difference (i.e. either a p-value or a confidence interval).
> Given the high number of events (typically 5 - 10,000 or more), the
> uncertainty of the mean (aka. standard error of the mean) is very very
> small, even though the distribution of each histogram is broad and
> overlapping. Consequently, even the smallest difference in mean
> arbitrary fluorescence of sample A versus sample B, is perceived as
> statistically significant. Therefore, as reported to this list, running
> the same sample twice, will often lead to statistical significance when
> comparing results of the two runs by the K-S test.
>
> However, this is not what we really want to know !!!
>
> What we want to know is: as evaluated by measurement of fluorescence, does
> sample A belong to population of cells (or individuals) different from
> that of sample B ?
>
> To answer this question we have to know the variation in mean (geometric
> mean or median) fluorescence when running the same sample multiple times
> on the flow cytometer. Next, to compare the difference of mean
> fluorescence of sample A and sample B with this uncertainty of the mean.
> If the former is bigger than the latter, it may be concluded that sample
> A and sample B belong to two different populations of cells. Formally,
> this may be expressed as:
>
> Mean fluoresc. sample A - mean fluoresc. sample B > SQRoot 2 x standard error
> of the mean (of fluorescence measurement)
>
> To conclude, the relevant comparison is not that of 2 means from 2
> distributions of events (each from a single run), but the comparison of
> 2 means from 2 distributions of means (from multiple runs). In the
> latter case, knowledge of a general uncertainty of measurement of mean
> fluorescence (CV% or standard deviation), may substitute for the repeat
> measuring of the 2 samples, according to the abovementioned formula.
>
> Please note: The above does not take into account the variations introduced
> by staining, lysing, washing, etc, only the crude variation in
> fluorescence measurement by the flow cytometer.
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Derek Davies Voice: (44) 0171 269 3394
FACS Laboratory, FAX: (44) 0171 269 3100
Imperial Cancer Research Fund, e_mail: derek.davies@icrf.icnet.uk
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Web Page: http://www.icnet.uk/axp/facs/davies/index.html
In tenebris lux
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