The area between curves (ABC)—measure in nutritional anthropometry

This paper considers a statistic — recently suggested by Mora — for the deviation of a sample distribution from a reference distribution which typically arises in anthropometry when using the nutritional indicators height/age, weight/age or weight/height. The statistic measures the area between curves (ABC) and stands for the mass of the sample distribution which is not covered by the reference distribution. The paper provides a statistical framework for the ABC and includes some minor corrections of Mora's original paper. For the normal distribution situation with common or different variances, formulae are derived which include a partition of ABC into parts corresponding to malnourished and well‐nourished groups. However, the main result is a non‐parametric generalization of the ABC, motivated by the fact that the nutritional indicators often have skewed distributions with heavier left tails. Non‐parametric statistical inference is provided by linking the ABC to the Kolmogorov‐Smirnov statistic.