My answer is............I have no idea and have judged my results purely on what my eyes have told me for the past 30 years.
It's been good enough to get repeats and referrals and I've never felt the urge to justify the service provided.
I have, however read a lot of claims over the years from manufacturers or suppliers of cleaning equipment and I've no doubt that similar sections of carpet taken from a concentrated foot fall area, weighed, beaten, vacuumed and subjected to a number of different systems of cleaning might have surprising results.
This, however is of no interest to the purchaser of carpet cleaning services who will believe what their senses tell them, particularly their sight, touch and smell.
Derek posted while I was typing and typed what I'd expect a T/M user to type which is fair enough ..............but it's worth finding out from ANY recognised expert in their field what their views are and the tests / comparisons they've allowed their products to take part in.
The cleaning method that astonished me when I first tried it was Texatherm which I was using in a retail environment with very high traffic areas.