This whole thing gets more complex as you look deeper into it.
I use Adobe Audition 2.0 and other versions may offer other features. When you normalize an audio file and specify a value, it looks for PEAK values, not RMS values. Thus, specifying a PEAK value of 0 dBfs or -0.3 dBfs, clipping does not occur, and distortion does not occur. And I can normalize to the peak value of my choice: 0, -1.0, -3.0, -10.0, -25 if you like. (does not have to be round number. I typically take work that I am finished editing and normalize to -0.667.... fractional amounts are accepted. Or at the click of a check-box I can specify values in percentages: 100, 93, 80% etc.
Then under WINDOW > AMPLITUDE STATISTICS I can see the values of the area I have selected:
Minimum RMS peak values,
Maximum RMS peak values,
Average RMS values
Total RMS values
and Emmett nailed it: you can normalize your audio to 0 or -3 PEAK values and go to statistics and find that your AVERAGE RMS value is in the -20 dBfs range. Head-banging rock music normalized to 0 will have a considerably high AVERAGE RMS than a lecture by a seminary professor using medium paced to slow conversational style speech. (-23 to -26 Average RMS value)
Thank you for bringing up this topic. Here is what I got busy and discovered about Audition today. They have a feature that I had never opened up and explored. It is designed for people getting ready to move some audio to a CD. Would work well also for people putting recordings onto a hard drive for a station automation system. It's called "Group Waveform Normalization". Open up multiple files. Select all the files in Group Waveform Normalization and ANALYZE. The little statistics table will tell you what the Average RMS value of each file is. BUT WAIT, THERE'S MORE! The feature will analyze the critical mid-range frequencies that affect listen-ability and also calculate: LOUDNESS Average RMS. When you push the button and execute a Group Normalize you end up with all the tracks appearing to be of EQUAL LOUDNESS. When you look at the resulting wave forms on screen some fill the screen vertically with a lot of white space in the horizontal space. Others will only partially fill the vertical space but the wave form will be almost solid black. (Head banging rock and roll?) ;D
And Emmett: A wave form does not have to be a pure Sine Wave to have an RMS value. Complex voice waves also have an RMS value as to SQUARE WAVES.
I think this topic may be more complex than many of us are ready to think. I'm going to play with this GROUP Waveform Normalization some. I have some uses for that!