The user’s guide for your software should have a brief description of each of the equation sets, and why it was created. (It may be in the FAQ section in the back.)
In general, most people tend to use the “NHANES-III” equation set. The equations for Fat and Fat-Free Mass, and Total Body Water were developed as part of the Fels Longitudinal Study, which collected information about a large cross-section of the American population. A second study was done which showed how the equations performed on data collected in the NHANES-III survey, which also included a large cross-section of the American population. As a result, it tends to provide good estimates for body composition for individuals with relatively nondescript body types — that is, they resemble a “typical American of their sex and (approximate) age.”
However, for people who do not resemble the general population, the accuracy of these equations will tend to degrade. For example:
For people who are very thin or very skinny or who, when you look at them, you can say “Just by looking at you, I can tell that you work out on a very regular basis,” the NHANES-III set will tend to over-estimate body fat. That is, they may estimate body fat too high. For these people, we generally recommend the “Athletic” equation set.
On the other end of the spectrum, for people who are very obese, the NHANES-III equations will tend to under-estimate fat. For these people, the “Obese” equation set will likely provide a more accurate estimate.