Apparently I am right brained (turning clockwise for me) unlike most people. I'm also left handed; I'm wondering if there's a connection.
I'm left-handed as well, and yes, the opposite side of the brain does control it. I have a quote that reads "If the right side of the brain controls the left side of the body, then only left-handed people are in their right mind". 
I'm very confused though. When I first went to it, it was turning clockwise. I read the descriptions of the characteristics and looked again, and it was turning counter clockwise. I sat and stared for a while, and it would change periodically. Sometimes, there would be a pause and then it would change direction - other times, it would just suddenly change. At this point, I don't know if my mind is doing that, or whether this is one of those things that attempts to fool you by changing periodically. I want you all to go back and watch it for a bit and tell me if it happens to you!
Hmm, yes. Apparently there is a
slight connection: I've seen some right-handed people with their right brain dominating.
As for the animation, I believe it is not an attempt to fool anyone: first and foremost I seriously doubt the
Daily Telegraph pull pranks on people

, and secondly, people who have analyzed the animation found out it's strictly moving clockwise, so we
ARE right, sari

Pardon the pun(s).
Yeah, sometimes it changes for me too. You can try looking at her heels or staring at the right side of the screen; it seems to help changing the direction sometimes. However, it's clockwise most of the time. My mother tried this out and she found out the dancer switches directions; I'm wondering if it actually states how
much right brained you are.
Anyway, to test the validity of this test, I went to 2 more online tests featuring questions that you have to answer, and on both of these, I am a right brainer. So I guess this is really true!