Estimation of total water and fatness from weight and height: Inaccurate for lean women

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Abstract
Mellits and Cheek have provided a regression equation which predicts total water, and by extension, fat, from weight and height of women. The equation has been used by many researchers as a convenient means to estimate fat when more complicated body composition estimation techniques are not possible. It is an essential component of evidence provided by Frisch for the critical fat hypothesis. The equation has not been validated on another sample, however, and has a large standard error. I test the Mellits and Cheek equation on five samples of young women, two of which show a normal range of heights and weights. The other three are athletic samples composed of lean women. In the normal samples mean fat percent determined by density (from underwater weighing) is closely approximated by the weight and height equation but not in the lean samples. When measured fat is regressed on estimated fat, correlations are low, and standard errors are high, suggesting that the Mellits and Cheek equation predicts poorly the body fat percentage of individual females. In summary, the Mellits and Cheek equation is moderately useful for the prediction of group means for body composition on samples with normal ranges of height and weight. It does not produce acceptable results on groups selected for extreme leanness or obesity. It is not recommended for fat prediction of individuals.