Comment 6 for bug 1252467

Either running the cron job as root or allowing www-data to read the apache log files are bad ideas. Instead you want to create a new user and add it to the www-data and adm groups and make the cron job execute as that user. I called mine "awstats":

useradd awstats && usermod -a -G www-data awstats && usermod -a -G adm awstats

Seems to work like a charm.