Normality tests for transformed large measured data: a comprehensive analysis
Normality tests for transformed large measured data: a comprehensive analysis

Summary/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.

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