What question did this study set out to answer?

The research aims to identify effective goodness-of-fit tests for determining the normality of geotechnical data based on sample size.

January 14, 2026Open Access

Optimising sample size for normality testing in geotechnical data using power analysis

Key Points

The research aims to identify effective goodness-of-fit tests for determining the normality of geotechnical data based on sample size.
Evaluated multiple goodness-of-fit tests including Shapiro–Wilk, Lilliefors, Anderson–Darling, Jarque–Bera, chi-square, Cramér–von Mises, and D’Agostino and Pearson tests.
Conducted a power analysis using Monte Carlo simulations to determine optimal sample sizes.
Assessed the performance and sensitivity of each test with varying sample and effect sizes.
Shapiro–Wilk test proved most effective in detecting normality, followed by Anderson–Darling and Jarque–Bera tests.
Minimum required sample sizes varied based on coefficient of variation, with specific numbers outlined for different CoV ranges.
Chi-square and Cramér–von Mises tests required substantially higher minimum sample sizes.

Abstract

Purpose This study aims to examine the performance of various goodness-of-fit (GoF) tests in assessing the normality of the data set, a crucial step in conducting probabilistic analyses in the geotechnical domain. The evaluation focuses on the efficacy of these tests when applied to small sample sizes and data sets with varying coefficient of variation (CoV). Identifying the most efficient GoF test based on the statistical characteristics of the data can enhance the reliability of results and minimise the risk of misleading conclusions. Design/methodology/approach Multiple GoF tests, including Shapiro–Wilk (S-W), Lilliefors (LL), Anderson–Darling (A-D), Jarque–Bera (J-B), chi-square (CSQ), Cramér–von Mises (CVM) and D’Agostino and Pearson Omnibus (DP) tests, were used for normality assessment. A computational power analysis was performed through Monte Carlo random sample simulation to determine the optimal sample size required to achieve the desired statistical power. Furthermore, the performance and sensitivity of each GoF test were assessed systematically by varying the sample size and effect size (d) to establish the relationship between the minimum required sample size and CoV. Findings Power analysis revealed that the S-W tests demonstrated higher effectiveness in detecting normality, followed by the A-D, J-B, LL and DP tests. The degree of skewness and CoV in the data sets plays a crucial role in optimising the sample size requirements. For S-W tests, the minimum required sample sizes varies with the CoV as follows: (a) CoV 10% requires at least 665 samples, (b) 10% ≤ CoV 30% requires 665–145 samples, (c) 30% ≤ CoV 50% requires 145–70, (d) 50%≤ CoV 100% requires 70–25 samples, and (e) CoV ≥ 100% requires at most 25 samples. In comparison, CSQ and CVM tests demand substantially larger minimum sample sizes, ranging approximately between 115 and 4,400. Originality/value This study presents a comparative analysis of GoF tests applied to geotechnical data, determining the required sample size through power analysis, with a target statistical power of 0.8 at a chosen significance level of 0.05. These findings provide practical guidance for selecting appropriate normality tests and the required minimum sample size for geotechnical data with varying CoV.

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