## Introduction

Despite criticisms on various grounds (1), both BMI (body mass (BM).height (Ht)^{−2}) and percent body fat (%BF, the ratio of fat mass (FM) to BM expressed as a percentage) remain commonly used measures of adiposity both clinically and in scientific studies.

Underlying the use of BMI is the assumption that BM is directly proportional to Ht^{2}, deviations from this proportionality indicating higher or lower relative mass than expected. Such direct proportionality would preclude any relationship between BMI and Ht. In accordance with the work of Benn (2), Cole (3) explored the value of *p* for which BM. Ht^{−p} was unrelated to Ht. In effect, he found the value of *p* which gave the “best” linear regression relationship between LnBM and p.LnHt. He concluded that *p* was ∼2 in preschool years, increasing to 3 by 10–11 years old, decreasing back to 2 after puberty. Cole added that BM. Ht^{−2} is appropriate for preschool children and adults, but in between it tends to assess tall children as being overweight, a bias that could be avoided by introducing a more precise power of Ht according to the child's age. Other authors have since supported this strategy, indicating that *p* increases steadily between the age of 3 and 7–9 years, varying around puberty (4); and cautioning against using BMI as an indicator of adiposity, proposing *P* > 2.0 before the age of 15 years (5); or proposing *P* = 3 for children aged 3–12 years (6).

There is also evidence that %BF is positively related to Ht in children (7,8). However, underlying the above-cited work with BMI is the assumption that Ht should be unrelated to any measure of adiposity. This position is taken by Wells and colleagues (9) as they investigated the use of FM in relation to Ht as a measure of adiposity in 8-year-olds. In the current study, based on the absence of any sound rationale to expect taller 8-year-old boys and girls to be generally fatter than their shorter counterparts or shorter children to be generally leaner, we assume that Ht is not related to adiposity in this age group. Our position then is that BMI and %BF will systematically misrepresent adiposity in 8-year-olds and so contribute to both clinical and experimental errors in body composition assessment.

The purpose of the current study was to find replacements for BMI and %BF, which indicate relative weight and fat, respectively, using the same primary variables but where the values of *p* and *q* are such that BM. Ht^{−p} and FM.BM^{−q} are unrelated to Ht. To do this, we studied the underlying relationships between the three primary variables BM, Ht, and FM. Given that relationships between FM, BM, and Ht vary with age and maturation (10), we chose to investigate relationships between these variables in a group of children all close to 8-years-old, thereby minimizing any influence of age and maturation. Our work is distinct from, but complements that of Wells *et al.* (9), who investigated indicators of adiposity in terms of FM and Ht determining that the function FM.Ht^{−6} was unrelated to Ht in 8-year-olds.