I downloaded version 20 of PHPWebStat a week ago and noticed that there are too many accesses to my site from .us domains. So I added a few lines of code in pws.php to track the ones that looked like bots to me:

Code (PHP):

if ( $js_referer == "" && $country == "us") {
  $domain_name = trim(gethostbyaddr($ip_address));
  file_put_contents("bot.txt", date("H:i:s d/m/Y",$time_stamp)." * ".$ip_address." * ".$country." *".$js_referer."* $domain_name\n", FILE_APPEND);
  exit;
} 

The file was populated with entries with $domain_name containing the string:
Applebot
which I promptly added to:
Advance Setting > Exclude Bots (Searchengines)
solving the problem of the large number of accesses from the USA.
Surprisingly, the Apple bot does not appear in the list of bots.