PART I - Different Encodings
The first file we used was given with the subject: natara.wav
We chose as second file one of my own music tracks. You can listen to it on my other web site.
Here is the link: DJ Yannix - On the Roof Tops (House Power Mix).
This file is an mp3 (the wav file is too large) but the quality is the same as for the wav file. For the compression and analysis, we used the wav file.
This is the conversion program we used: 'Switch Sound File Conversion Software'.
Subjectively, there isn't any loss of quality for either music file when converted to mp3, ogg or flac.
Nevertheless, we noticed a big quality loss when those files are reconverted to wav files. This loss is identical whichever conversion we did previously. You can check this out.
Here are the links to the natara wav files converted from different input files:
natara from cbr mp3
natara from vbr mp3
natara from cbr ogg
natara from vbr ogg
natara from flac
In the same way, here are the links to the other song:
On the Roof Tops from cbr mp3
On the Roof Tops from vbr mp3
On the Roof Tops from cbr ogg
On the Roof Tops from vbr ogg
On the Roof Tops from flac
Here are the experimental results we got using this matlab code: Matlab - PartI
The values represent the error (no unit needed)
For DJ Yannix - On the Roof Tops (House Power Mix):

For Natara:

We checked the file sizes and realized that all encoded files have the same size whichever conversion method was used. As a matter of fact, those results are useless for this study.