Then, phase inverting one of the stereo files and lining it up (as best as possible) with the other file. It's only lined up within a .008 second tolerance because the software won't let me view waveforms from multiple files at less than a 1:1 ratio. But, it's pretty close.
The artifact sample allows you to hear what's left over. A perfectly matched set of phase inverted files would yield no sound at all.
This comparsion doesn't really say that much if you want to measure the perceived quality of the MP3 file. The compression algorithms used in the MP3 format are (as in most other lossy codecs) based on psycho-acoustics. It means that the codec tries to save space by excluding those parts of the sound which are not likely to be perceived by the human ear. The differences you get by comparing waveforms this way are not representative for the audible differences (although there may of course be audible differences, too).