Posted by
dscho on
Mar 18, 2014; 7:19pm
URL: http://imagej.273.s1.nabble.com/Stanley-s-ICA-Intensity-Correlation-Analysis-ICQ-Intensity-Correlation-Quotient-tp5006977p5006978.html
Hi Dan,
On Mon, 17 Mar 2014, Daniel White wrote:
> >From: Johannes Schindelin <
[hidden email]>
>
> >On Sun, 16 Mar 2014, Jeremy Adler wrote:
> >
> >> So I suggest sticking with the Pearson and rank Spearman for
> >> correlation analysis, they have a long history. If you really want to
> >> go binary, try Kendall's tau.
>
> >For your interest: I am happy to report that Coloc 2 recently learnt to
> >calculate Kendall's Tau.
>
> I think I'm worried that most of our statistical assumptions are actually
> false in the case of using Pearsons etc. in coloc analysis of fluorescence
> images of biological systems.... why?
>
> Because the intensities distribution of the fluorescence signal are almost
> never anything close to being normally distributed: a Gaussian, bell
> curve.
It is true that already a Poisson distribution is a much better model for
fluorescence (because there is no negative fluorescence).
However, we cannot in general assume a Poisson distribution. There are
many challenges in typical images, such as offsets, noise, sometimes
signals which are non-linearly related to the underlying value we want to
measure.
That is why I implemented Kendall's Tau. It only assumes ranked values.
The only remaining problem with that is noise: Kendall's Tau is a
frequentist method that assumes that your data are exact, without flaw. I
guess it would not be too difficult to add a "grace difference" in which
values are considered equal as far as the Tau calculation is concerned
when the numerical values acutally differ. But that looks too ad-hoc to
me.
Ciao,
Johannes
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