normalization "loss"

As an experiment, I normalized a file, de-amplified it by the same amount, then did a mix-paste inverted with the original. The Average RMS difference was -101dB. This is working in 32 bit and using my normal 97% normalization.

Starting with the same source file, I normalized to 100%. The difference in this case was much higher: -93dB.

Using a 16 bit CD file, those differences, between 97% and 100%, were -92dB and -85dB.

I repeated the experiments to verify the results. My program is CoolEdit 2000.

Why is there so much difference between using 97% normalization and 100% normalization, especially in floating point math?

What values did you use for the de-amplification? Swapping between percentages and dBs may not give identical results.

Thinking about this a bit, the problem may merely be the fact that the only thing I have to rely on is Analyze/Statistics for the amount to reduce after normalizing. These values are only displayed to two decimal points. That may simply not be enough accuracy to get the same results between one normalization value and the next.