Dennis Laffey had this to say about rolling in secret. 

John Laviolette responded with agreement.

I’m going have to agree with them both on this one. Particularly John on the point he makes that the mechanisms are for the game master to be concerned with. When players are thinking about the mechanisms of the game, they are thinking less about the conceptual situation their character is in.

The one thing I will vary a bit from these gentlemen is to say that there are certain circumstances when I will show certain rolls in the open and in other circumstances I keep them in the dark. This is more intuitive than anything else. If I’ve built up the consequences of the roll in the players mind and there is a clear high stakes result on the die roll, I’ll leave it out in the open because the release of emotion you get from that. I may then keep a similar roll behind the screen in the future because keeping the secret creates tension. When the tension gets to an appropriate level, I release it with a player facing die roll.