The correct way of testing if a user is logged in is to test whether $user->uid is 0:

global $user;
if ($user->uid) {
   $output = t('User is logged in!');
else {
   $output = t('User is an anonymous user.');
}

This approach is often used when defining a block that shows one thing to
logged-in users and something else to anonymous users:

<?php
   global $user;
   if ($user->uid) {
     return t('You are currently logged in!');
   }
   else {
     return t('You are not currently logged in.');
   }
?>