If you did an ABX-test on the same song in 16-bit file and 24-bit file and heard the difference, then you have 2 different masters of that same song.
For example, if you compare a CD version with 24-bit-HDtracks version of the same song, there is a big chance you will hear significant difference in sound, because the files have been mastered in the different way.
Now take that same 24-bit-HDtracks-file you have and reduce it to 16-bit file (with Foobar2000, for example), then ABX those 2 files. You won't hear the difference between those 2.
* Unless you crank up your audio system above 160 dB — that's when 24-bit file benefits will kick in, but that sound level will almost instantly damage your hearing irreversibly, and eventually will make you deaf.