Enhancing Box-Cox Transformation with Simulation of the Normal Distribution: 2007--2010 What We Eat in America, National Health and Nutrition Examination Survey Flavonoids Data

• Activity Number: 262
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Theophile Murayi* and Joseph D. Goldman and Rhonda G. Sebastian and Alanna J. Moshfegh
• Companies: USDA/ARS and USDA/ARS and USDA/ARS and USDA/ARS
• Keywords: WWEIA/NHANES data ; Flavonoids dietary intakes ; Weibull distribution ; Data scaling ; Box-Cox transformation ; Monte Carlo simulation

Abstract

Objective: 2007-2010 What We Eat in America (WWEIA), National Health and Nutrition Examination Survey (NHANES) flavonoids data followed Weibull distribution. Data scaling before Box-Cox transformation and Monte Carlo simulation can restore normality to the data. Materials and Methods: Daily intake data of total flavonoids and six flavonoid classes (isoflavones, anthocyanidins, flavan-3-ols, flavanones, flavones, flavanols) were scaled by 0.01 to 6% of their data range before Box-Cox transformation. Sample mean and variance-covariance matrix subsets were iteratively inputted to the Monte Carlo normal distribution simulation algorithm to generate near-normal data distributions. Results: The sample mean to median ratios improved towards one and probability-probability plot (p-p plot) lines appeared more linear along the plot diagonal for total flavonoids and all flavonoid classes. However, the Kolmogorov-Smirnov test of normality remained significant (p< 0.01) for some flavonoid classes. Significance: Statistical inferences on WWEIA/NHANES flavonoids data can be greatly enhanced by Box-Cox transformation coupled with data scaling and Monte Carlo simulation of the normal distribution