# [R] Confidence interval around a mean count (poisson based?)

JiHO jo.lists at gmail.com
Wed May 5 21:27:24 CEST 2010

```Hello all,

I am observing animals in a behavioural arena and recording their
distance from a specific point at regular time intervals (large enough
so that I can assume two successive positions are independent from
each other). Each animal provides a complete histogram of distances
which reflects its trajectory in the arena. I repeat those
observations with several animals in two scenari and I want to
describe the distribution of distances in each treatment.

I computed the mean histogram per treatment: per bin, I count the
number of distances falling in the bin for each animal and then
average this count over all animals, within treatment. Now I want to
represent the variability around this average count and compute a
confidence interval.

The data is counts so, unsurprisingly, it is not normal. I have less
than 30 animals in each treatment so I cannot assume that the mean
would be normally distributed. The means indeed look
Poisson-distributed, as the counts are. I tried to find ways to
compute confidence intervals for Poisson processes but everything I
come up with in R (poi.ci in NCStats, exactci in the package of the
same name) requires integers. This makes sense for raw counts but
makes me wonder if what I am trying to do is really "right" with those
means (which are floats).

I understand that this is more a statistics question than a R question
but I am a bit stumped and would appreciate any help I can get from
the experts on this list. Thank you very much in advance.

PS: what I did so far was just compute mean +/- SD. The result is here:
http://dl.dropbox.com/u/1047321/hist_mean-SD.pdf
Maybe the SD is already so large that it is not even worth trying to
pursue my goal above...

Sincerely,

JiHO
---
http://maururu.net

```