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Sensitivity and specificity of normality tests and consequences on reference interval accuracy at small sample size: a computer‐simulation study
Author(s) -
Le Boedec Kevin
Publication year - 2016
Publication title -
veterinary clinical pathology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.537
H-Index - 51
eISSN - 1939-165X
pISSN - 0275-6382
DOI - 10.1111/vcp.12390
Subject(s) - sample size determination , normality , statistics , normality test , parametric statistics , population , nonparametric statistics , mathematics , normal distribution , log normal distribution , sample (material) , gaussian , univariate , statistical hypothesis testing , medicine , multivariate statistics , chemistry , environmental health , computational chemistry , chromatography
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. Objectives 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 .

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