We have been conducting call-playback surveys at 20 different sites once a month for a few years. We want to see if owl presence is effected by illumination level (6 categories), or moon phase (7 categories). The data is strongly right-skewed (lots of zeros) and only 1 or 2 owls was typically detected if they were found, although occasionally 3 or 4 were found. The occurrence of surveys during the different categories was also unevenly distributed (ex. lots of nights with an illumination of 1, very few with illumination of 3).
Is Kruskall-Wallis an appropriate test to use in this situation? Is there a better test?