We have to set some things straight. Privacy, anonymity and security although close connected is not the same.
Privacy:
As previously stated privacy does not exist on an open forum. Data is sent back and forth, what you write is stored in clear text in the database and is tied up with your handle and all the other actions you are doing. Even though this privacy is only in connection with your handle in here, it's still lacking completely when the forum is open to everybody.
Anonymity:
You are on an open forum. Again you represent yourself with a the same handle when you write. Even if your real life privacy is not published in here, you still have certain clues as to who and what you are just based on your way of writing, how you interpret things and so forth.
Funny question: do you some time admit not knowing something, that you actually do know (not the other way around, everybody does that.. It's the internet!)? Do you some times make gramma mistakes you would not normally do? Fight for opinions that is not actually yours or you don't really believe in?
All your actions can be used to compromise your anonymity and privacy, not just logs, ips and browser data.