If your Plesk control panel is anything like mine, then you will find that there are no visitor stats for any of the domains on there, but fear not, the stats are/have been collected (usually by default they're pre-collected by 3 months - well that's what mine were set to).
First of all check that your domain(s) have got webstats enabled. To do this you'll just need to log in to your Plesk control panel, then on the right hand side select your domain from the "My Webspaces" section.
Then select the "Websites & Domains" tab, scroll down and click on the domain name in question.
The page that loads will be the "Hosting Settings for" page. Scroll down and right near the end in the "Web Scripting and Statistics" section, there'll be a dropdown menu "Web statistics". Make sure you've got AwStats selected and the "(accessible via password-protected directory '/plesk-stat/webstat/')" section ticked aswell. If these options are already selected, just click "Cancel", if not then click "OK".
That's this bit sorted - so we now know that Plesk will be collecting the stats.
Now we need to be able to access them. To view your stats you will need to visit (replacing YOURDOMAIN with your domain):
You will need to login where the Username and Password is what you have specified for the domain when you set it up in Plesk. When correct, you should see this placeholder screen.
For stats to be accessible this way, you will need to run them. To do this you can either use the Secure Shell Terminal (SSH) built-in to Plesk, however with the latest update of JAVA, it will no longer allow you to run it (even when you have your JAVA security settings switched to the lowest setting possible, which in my opinion is absolutely bloody retarded). So we will need to use a SSH Terminal on our own computer to connect, which the best one I know that's small, simple and free (works on Windows) is called PuTTY.
Once you've downloaded PuTTY, run it and you'll be prompted with a box where you have to enter a "Host Name (or IP Address)" (for this you will just enter your main servers IP address) and keep the Port number as the default (22) and "Connection type" as "SSH", then click "Open".
When it loads it will look just like a "Command"/"DOS" style window and it should show this:
At this point, you will need to enter the login details for your "root" account (should be in your welcome emails from your host). It'll have the username as "root" and then a password (so NOT the one that has the username "admin" or similar). Hit [ENTER] and it'll say:
Enter your password (it will not show on the screen though), once you've wrote it press [ENTER] and you should get something similar to this:
At this point you will now need to simply type in this (replace "YOURDOMAIN.com" with your domain):
/usr/local/psa/admin/sbin/statistics --calculate-one --domain-name=YOURDOMAIN.com
Press [ENTER] and wait a while - it might not look like anything is happening, but after a few minutes it'll complete its task. Once complete, just close the SSH Terminal window and head back to your "/plesk-stat/webstat/" page and login.
You should now see your stats! :D
I do hope this enables webstats in Plesk for you like it has for me. (I have noticed it mentioned on quite a fair few forums too).