Yes, there are a ton of psych and neurological studies that back up this practice. It is one of those blind-spots in your brain. You peg on the $19 part of $19.99. If you stop to rationally consider things then $19.99 and $20 are effectively the same, but for most casual purchasing decisions you do not actually apply a significant amount of intellectual rigor. You may think that you consider $20 and $19.99 to be the same, but study after study shows that what you think that you are thinking about and what your brain is actually doing are not the same.
Interesting, I always feel like 19.99 = 20, but that is probably because of how my Dad taught me to add and multiply quickly by doing so rounding first then backing off from there.
