What is the AppArt process and why does it want to connect to application-stats.com?
Following @tubedogg's comment above, I think I've fixed this:


http://www.malwareurl.com/listing.php?domain=application-stats.com identifies the domain as Malware
Double-clicking the "AppStats" process in Activity Monitor and then clicking the "Open Files and Ports" tab reveals that something is running from /Users/jim/Library/Application Support/Spigot/AppStats
Searching "Spigot" then takes us here, which gives removal instructions: http://www.thesafemac.com/arg-spigot/
I didn't find any weird browser extensions in Firefox, Safari, or Chrome (the directory in Application Support included a file with a name that referenced a .xpi file, so I'm guessing the problem may have been something to do with an old Firefox extension) but I did remove the following directories and files: ~/Library/LaunchAgents/com.applicationstats.AppStats.plist, ~/Library/LaunchAgents/com.appart.AppArt.plist, ~/Library/Application Support/Spigot/