There are several studies. I know of two, but don't really have time to dig them out right at the moment.
Maybe someone knows the ones that I'm thinking of, though.
The more recent of the two suggested that the rate of occurence (which, please note is not the AMOUNT of ) cross contamination in UNLABELED products to be something around 2-5%, if memory serves (and maybe it doesn't), and that this wasn't that much higher than found among items labeled "may contain."