I calculate (with flow cytometry) pecentage of lymphocytes with a specific receptor (Lph*) as a ratio to general number of lymphocytes (Lph). Should I consider them (Lph*) as Poisson distributed?
(My data set is here.)
Poisson distribution makes sense from the general point of view of flow cytometry measurements: you "sit on your detector", and wait a random time for a/the next lymphocyte to come along. The same is true for lymphocytes expressing the receptor you're interested in. But you then ask for the proportion of two such Poisson distributions.
If you focus on the proportion, you can assume that a true underlying proportion $p$ (possibly depending on the treatment) of lymphocytes exists that does express the receptor. That would be more like a Bernoulli experiment (binomial distribution). You sit on your detector and look at whether the next lymphocyte coming along does express the receptor (it doesn't matter how long you have to wait for it), which happens with probability $p$.
Note that the binomial distribution is related to the beta distribution - you get beta distributions when estimating the true proportion $p$ of a binomial distribution from Bernoulli experiments.
If you look at large enough numbers of cells, you can use approximations (e.g. normal approximation of the binomial if the smaller of $np$ and $n(1-p)$ exceeds 5 or better 10.
Assuming you have 10⁵ lymphocytes per FACS run, that means that for 0.0001 $\leq p \leq$ 0.9999 you should be OK with the normal approximation. As the lowest proportion you report is 0.0015, you are on the safe side even if you add a bit more "safety margin" for the fact that you only have an observed $\hat p$, not the true proportion $p$ (unless your FACS run takes only a very small aliquote of the sample).
See Wikipedia on distributions related to the Poisson distribution and Wikipedia on distributions related to the binomial distribution for relationships and also rules of thumb about the approximations.
The short answer is probably not, since:
- the Poisson distribution is discrete, your data is continuous;
- the Poisson distributions has support on 0,1,2, ..., whereas (I think) your data has a range from 0 to 100.
Without seeing your data and knowing your problem, it's tricky to give you a suggestion. A good starting position would be to look at the statistical analysis section of publications that analyse data similar to your data.