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I understand what you are saying CharlesWayneCT, but you are misreading the study. Your example shows that people can move among which “quintile” they are in. The study specifically removes that possibility by tracking the families from the quintile they were in when the data was first collected. In your example, the study would show the quintiles, after the 100% increase for the middle class, as 1,4,6,8,5. It would correctly show all 3 middle quintiles getting a 100% increase.

I didn't see that from the study. The preface mentions tracking particular families over a "3-year" period, but that doesn't cover the 15 years of the study. The article doesn't mention it at all.

The 35% increase cited seems specifically based on a comparison of the 1st-Q numbers from the first and last years, NOT a comparison of the earnings of the 1st-Q group from the 1st year at the last year.

In fact, this paragraph from the summary tells the scope of the study in regard to tracking individual families:

The 35 percent real income growth between 1991 and 2005 for low-income households with children—considered as a group—does not describe changes for individual households over time. Surveying such households at a specific point (in this case, 2001) and following them over the next two years provides a different perspective.
The average income for those households increased by nearly 45 percent from 2001 to 2003. (By contrast, average income for low-income households with children— that is, the households constituting the group as a whole—fell over that same three-year period.) Six in 10 of the surveyed households experienced a substantial increase in income, while 1 in 4 experienced a substantial decline.

Realise that tracking the same people over time is ALSO has it's problems. An individual is expected to increase their salary over time, as they become more experienced in their job and older and more mature and therefore more trusted with more important jobs. So individuals will tend to move up the quintiles over their lifetime, with the highest number of people in the higher quintiles near the age of retirement.

Worse, when you survey individual households, such that they know they are being measured, that knowledge effects the measurements. Especially in an area of "pride" like income. Those who know they are being tracked for "improvement" will work harder, try harder, and make more effort to get increases that make them "look good". So I don't trust that the 45% number is a valid one.