Has any one seen any numbers to support this actually works? What I mean is: Does using a two-step logout help users stay logged in? I would really want to see

Has any one seen any numbers to support this actually works? What I mean is: Does using a two-step logout help users stay logged in? I would really want to see some numbers around it. I don't think I really do understand if making the logout feature less apparent actually returns value to the site in any way. I mean thinking a bit further, this is really not pushing users to stay "logged in" and add value to the site right? Also I think the security issues of keeping users logged in just to keep them logged in is not really that encouraging. Now I understand the value of keeping the user logged in, I just don't see the value of having the logout feature hidden in a menu, other than simplifying the User Experience. If anyone has more information on this, please list them. I am interested in researching this further.