title: Is Middle-Upper Arm Circumference "normally" distributed? Secondary data analysis of 852 nutrition surveys.
abstract: BACKGROUND
  Wasting is a major public health issue throughout the developing world. Out of the 6.9 million estimated deaths among children under five annually, over 800,000 deaths (11.6 %) are attributed to wasting. Wasting is quantified as low Weight-For-Height (WFH) and/or low Mid-Upper Arm Circumference (MUAC) (since 2005). Many statistical procedures are based on the assumption that the data used are normally distributed. Analyses have been conducted on the distribution of WFH but there are no equivalent studies on the distribution of MUAC.
  
  
  METHODS
  This secondary data analysis assesses the normality of the MUAC distributions of 852 nutrition cross-sectional survey datasets of children from 6 to 59 months old and examines different approaches to normalise "non-normal" distributions.
  
  
  RESULTS
  The distribution of MUAC showed no departure from a normal distribution in 319 (37.7 %) distributions using the Shapiro-Wilk test. Out of the 533 surveys showing departure from a normal distribution, 183 (34.3 %) were skewed (D'Agostino test) and 196 (36.8 %) had a kurtosis different to the one observed in the normal distribution (Anscombe-Glynn test). Testing for normality can be sensitive to data quality, design effect and sample size. Out of the 533 surveys showing departure from a normal distribution, 294 (55.2 %) showed high digit preference, 164 (30.8 %) had a large design effect, and 204 (38.3 %) a large sample size. Spline and LOESS smoothing techniques were explored and both techniques work well. After Spline smoothing, 56.7 % of the MUAC distributions showing departure from normality were "normalised" and 59.7 % after LOESS. Box-Cox power transformation had similar results on distributions showing departure from normality with 57 % of distributions approximating "normal" after transformation. Applying Box-Cox transformation after Spline or Loess smoothing techniques increased that proportion to 82.4 and 82.7 % respectively.
  
  
  CONCLUSIONS
  This suggests that statistical approaches relying on the normal distribution assumption can be successfully applied to MUAC. In light of this promising finding, further research is ongoing to evaluate the performance of a normal distribution based approach to estimating the prevalence of wasting using MUAC.
authors.affiliation: Department of Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT UK.
authors.forename: Severine
authors.initials: S
authors.lastname: Frison
authors.affiliation: Faculty of Public Health and Policy, LSHTM and Humanitarian Technical Unit, Save the Children, 207 Old Street, London, EC1V 9NR UK.
authors.forename: Francesco
authors.initials: F
authors.lastname: Checchi
authors.affiliation: Department of Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT UK.
authors.forename: Marko
authors.initials: M
authors.lastname: Kerac
authors.affiliation: Department of Medical Statistics, London School of Hygiene and Tropical Medicine, Keppel Street, London, WC1E 7HT UK.
authors.forename: Jennifer
authors.initials: J
authors.lastname: Nicholas
keywords: Child malnutrition; Middle-Upper Arm Circumference; Normal distribution; Probit; Wasting