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.
Department of Epidemiology, Free University Berlin, Germany.
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Böhning
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Hempfling
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Schelp
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Schlattmann
D000704:Analysis of Variance; D000886:Anthropometry; D001827:Body Height; D002675:Child, Preschool; D006801:Humans; D007223:Infant; D008297:Male; D015233:Models, Statistical; D009752:Nutritional Status; D012016:Reference Values; D013223:Statistics as Topic