title: Sensitivity and specificity of normality tests and consequences on reference interval accuracy at small sample size: a computer-simulation study.
abstract: BACKGROUND
  According to international guidelines, parametric methods must be chosen for RI construction when the sample size is small and the distribution is Gaussian. However, normality tests may not be accurate at small sample size.
  
  
  OBJECTIVE
  The purpose of the study was to evaluate normality test performance to properly identify samples extracted from a Gaussian population at small sample sizes, and assess the consequences on RI accuracy of applying parametric methods to samples that falsely identified the parent population as Gaussian.
  
  
  METHODS
  Samples of n = 60 and n = 30 values were randomly selected 100 times from simulated Gaussian, lognormal, and asymmetric populations of 10,000 values. The sensitivity and specificity of 4 normality tests were compared. Reference intervals were calculated using 6 different statistical methods from samples that falsely identified the parent population as Gaussian, and their accuracy was compared.
  
  
  RESULTS
  Shapiro-Wilk and D'Agostino-Pearson tests were the best performing normality tests. However, their specificity was poor at sample size n = 30 (specificity for P < .05: .51 and .50, respectively). The best significance levels identified when n = 30 were 0.19 for Shapiro-Wilk test and 0.18 for D'Agostino-Pearson test. Using parametric methods on samples extracted from a lognormal population but falsely identified as Gaussian led to clinically relevant inaccuracies.
  
  
  CONCLUSIONS
  At small sample size, normality tests may lead to erroneous use of parametric methods to build RI. Using nonparametric methods (or alternatively Box-Cox transformation) on all samples regardless of their distribution or adjusting, the significance level of normality tests depending on sample size would limit the risk of constructing inaccurate RI.
authors.affiliation: College of Veterinary Medicine, University of Illinois, Urbana, IL, USA.
authors.forename: Kevin
authors.initials: K
authors.lastname: Le Boedec
mesh_terms: D000818:Animals; D003198:Computer Simulation; D000068598:Data Accuracy; D016011:Normal Distribution; D012016:Reference Values; D018401:Sample Size; D012680:Sensitivity and Specificity
keywords: Gaussian distribution; Shapiro-Wilk test; nonparametric method; parametric method