Dear Imen,

Your question is put nicely but I think something is missing. First, I wonder if a simple statistical analysis can tell if and when a fish is attracted by a prey. You may need for instance a behavioural marker ? A fish is attracted by a prey only if the fish attacks it or at least follows it ?

So, is your question rather: when I know that a fish was interested by a prey because he attacked it, how can I retrospectively identify the time at which his interest for its prey began ? And then, can we really identify this moment only by evaluating a distance ? Isn't that easier to study the behaviour ? Unless you deal with fish larvae ?

Indeed, we already knew that an attack was made on the prey and we are investigating if we can identify the time at which this interest began by evaluating the distance's decrease between fish and its prey.

That is why we made this analysis on video. It is a part of behavioral analysis.

As graphically we can really see this difference between target prey and the others, we are looking for a statistical method to prove it.

To attack or not to attack, that is the question :)

Sounds like if you use prey distance each as an independent factor, and the binary factor attacked or didn't attack as the dependent, then you have a logistic regression analysis.  It takes time out of the picture entirely, but gives you the probability of attack for a given prey distance.  

Dear Imen Ben Ammar,

To my understanding - your question - seems for me rather theoretical and it is "over-sophisticated". For determination of prey selectivity preference I would like to suggest simply to count and individually measure of each prey individuals at stocking and at the time of  further sampling.  The difference between in the number of stocked and harvested prey fishes could be informative in this respect ( and also could give some information on the preferred prey  size).

Sincerely yours:

András

P.S. Of course my above suggestion could be applied only in controlled conditions.

We already knew which fish attacked but we wanted to determine at which time the fish shifted its behavior into an attack. The result is known bu we wanted to see if the action of attack is initiated around a specific time/distance in our fish specie or if it is random.

Dear Imen,

I think you should first determine what your H0 hypothesis is. As a reminder, the H0 hypothesis is the hypothesis where you consider that two or more statistical datasets are not different from each other. These datasets should be built so as to check whether a scientific assumption is most probably true or not. It is important to precisely define this scientific assumption and be able able to write it down, so that it is a yes/no assumption. Then, you can choose the appropriate statistical test to check if it is probably true or not. There is no statistical test which will emits the scientific assumption and conclusion by itself.

In your case, it is unclear what the scientific assumption is and what these datasets are. From what you explained, I could propose many scientific assumptions to look for. But I think you already have your own idea. So, as Andreas said,  I think it looks like you're trying something over-sophisticated because you did not provide the scientific assumption and what the corresponding datasets exactly are.

If you're looking for discussions  about ideas of scientific assumptions to be tested, this is another story and I would be glad to discuss it, although I'm no expert at all in fish behaviour. So, you may not learn much from me and I would probably learn much from you.

Best regards,

Neil