I just installed JoomlaStats on my Joomla 1.5.9 site. The only thing I have done to make it work on Joomla 1.5 is to enable legacy mode.
The installation is very simple.
The only difficulty is probably the choose of what files to download because in the download site there are many links. For example I suggest to delete or put in an "old version" visitors by country module which has been replaced by mod_jstats_flags.

However, great work guys and many thanks making your work freely available to the community.