The distribution of fatty dimensions

W table

Most anthropometry datasets assume that small people are smaller than the average by the same amount as big people are bigger - this is called a 'symmetrical distribution'. This assumption is true for bony dimensions, but not true for dimensions that are affected by fat. Because we can get fatter than we can get thin, a heavy person is disproportionately heavier than a light person, compared to the average. For example, a heavy US Male (97.5th percentile) is 50 kg heavier than average, but a light US Male (2.5th percentile) is only 30 kg lighter than average.

The normal way of calculating the various percentile values is to use a statistic called the Standard Deviation, which is a measure of dispersion. It is calculated using a table of coefficients called the Z table, which defines the characteristic 'normal distribution' of human dimensions. The Z table describes arithmetically the way that most people are near the average, and that extreme dimensions are progressively rarer. However Z table is symmetrical, and so is a source of error if applied to fatty dimensions.

The PeopleSize dataset uses both the Z table and a developed variant of it, that we have called W table - because it describes the distribution of Weight. W table was generated using the NHANES 2005 adult dataset. Weight was chosen because it is the one fatty dimension that is sufficiently common among all the various survey datasets.

W table was derived by this method:

Separately for males and females, the real percentile values of weight were calculated in a large raw dataset (the value below which each given percentage of values fell). The mean was subtracted from each value, and the remainder was divided by the Standard Deviation for weight. The result in each case was a coefficient that would have been the Z value in a perfectly symmetrical Normal Distribution, but in fact was smaller below the mean and larger above it. The differences were greater among women than among men, so a separate W table was created for each.

For each dimension, the extent to which it uses Z table and W table is determined by wtcv.coef (the coefficient derived from the correlation with weight factored by the ratio of the dimension CV with weight CV )- so that if wtcv.coef is 1 only W table is used, if 0.5 a 50/50 average is used, and so on. This process creates a realistic distribution for dimensions that are highly correlated with weight, although you should be aware that the estimate is necessarily an approximation.

You should also be aware that 50th percentile weight (or any fatty dimension) is smaller than the average for that dimension, and PeopleSize correctly gives the 50th percentile when that is specified and not the average.

Wtable is used in both Pro and Easy versions of PeopleSize.

See also:

Estimation methods

Adjusting for weight


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