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

Area of Science:

• Statistics
• Anthropometry
• Biostatistics

Background:

• Nutritional indicators like height/age, weight/age, and weight/height are crucial in anthropometry.
• Assessing deviations from reference distributions is vital for nutritional status evaluation.
• Existing methods may not adequately address skewed distributions common in nutritional indicators.

Purpose of the Study:

• To provide a statistical framework for the Area Between Curves (ABC) statistic.
• To refine and generalize the ABC statistic for non-parametric applications.
• To improve the assessment of sample distribution deviations from reference distributions in anthropometry.

Main Methods:

• Development of a statistical framework for the Area Between Curves (ABC) statistic.
• Derivation of formulae for normal distributions with common or different variances.
• Non-parametric generalization of the ABC statistic, linking it to the Kolmogorov-Smirnov statistic.

Main Results:

• The paper offers corrections to Mora's original ABC statistic formulation.
• Formulae are derived for partitioning ABC in normal distributions into malnourished and well-nourished groups.
• A non-parametric generalization of the ABC statistic is presented, suitable for skewed distributions.

Conclusions:

• The generalized ABC statistic offers a robust method for evaluating anthropometric nutritional indicators.
• The non-parametric approach enhances the applicability of the ABC statistic to real-world skewed data.
• This work provides improved statistical tools for nutritional assessment and anthropometric research.