Thank you very much for your answer, Lauren. It is right, that I have a very complicated study area, because it is the polygon of the whole island, so that explains the problems with the confidence envelope! That´s good to know. The points reflect bird sightings. As you suggested, it might be the reason why Ripley´s K shows strange results?! I used the Spatial Autocorrelation tool also to analyse the clustered areas. The results from this tool where right, I suppose, but the Ripleys K-Function showed completely different results. So I used Spatial Autocorrelation in my report in the end. I think I first had some problems with the projection/transformation because I had two coordinate systems in the ArcMap Document, ISN1993 and ISN2004.
Thanks for your help,
Mareike