I don't think that dancer tells anything about whether you're "left brained" or "right brained". Rather, the way you see her spinning is dependant on whether you expect to be looking at her from slightly above her, or from slightly below. If you think you're slightly above her, looking down at her, then she will appear to spin clockwise. If you think you're slightly below her, looking up at her, then she will appear to spin counter-clockwise.

I have wasted enough time learning to control which way this particular bistable illusion spins that I can sometimes actually make her top half spin the opposite way her bottom half does, at the same time. O.o