Normality tests for transformed large measured data: a comprehensive analysis

Abu Feyo Bantu; Andrzej Kozyra; Józef Wiora

doi:https://doi.org/10.59139/stattrans-2025-034

Normality tests for transformed large measured data: a comprehensive analysis

Abu Feyo Bantu Department of Measurements and Control Systems, Silesian University of Technology, Gliwice, Poland ORCID:https://orcid.org/0000-0001-6463-9864 , Andrzej Kozyra 2Department of Measurements and Control Systems, Silesian University of Technology, Gliwice, Poland ORCID:https://orcid.org/0000-0003-2645-3537 , Józef Wiora Department of Measurements and Control Systems, Silesian University of Technology, Gliwice, Poland ORCID:https://orcid.org/0000-0002-8450-8623 Statistics in Transition new series, vol. 26, 2025, 3, pages: 195-208 Published online: 5 September 2025 https://doi.org/10.59139/stattrans-2025-034 Citation: Bantu A.F., Kozyra A., Wiora J., 2025. Normality tests for transformed large measured data: a comprehensive analysis. Statistics in Transition new series, 26(3), pp. 195-208 https://doi.org/10.59139/stattrans-2025-034

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ABSTRACT

In statistical analysis, evaluating the normality of large datasets is crucial for validating parametric tests, particularly in areas such as Global Navigation Satellite System (GNSS) measurements, where data often exhibit non-normal characteristics resulting from their variability and errors. This research aims to transform the measured GNSS data and to assess the effectiveness of transformation methods in achieving normality. Techniques like logarithmic, quantile and rank-based Inverse Normal Transformation (INT) were evaluated using visual methods (histograms, Q-Q plots), descriptive statistics (skewness, kurtosis) and statistical tests, including Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Lilliefors (LF), D’Agostino K-squared (DA), Shapiro-Wilk (SW), Jarque-Bera (JB), Cramérvon Mises (CM), and Pearson Chi-square (Chi2) tests. The sensitivity of these tests to deviations from normality was assessed through the Receiver Operating Characteristic (ROC) analysis and the Area Under the Curve (AUC) values at a significance l evel o f 0 .1, using Monte Carlo (MC) simulations across the varying sample sizes. The results showed that untransformed latitude data consistently failed normality tests, while transformed data displayed normal characteristics. The rank-based INT showed superior effectiveness, influenced by the original distribution and characteristics of the dataset. The findings underscore the importance of tailored transformations in large-scale data applications, enhancing the accuracy and applicability of parametric statistical methods in geospatial and other industrial domains.

KEYWORDS

GNSS, ROC, normality test, statistical analysis.

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