Statistical Normalization of Mechanical Properties of Natural Date Palm Biofibers Using the Box-Cox Transformation

Abstract

Characterizing the mechanical behavior of natural fibers presents unique statistical challenges. In our study, 82% of the initial datasets (n = 35) exhibited non-normality (Shapiro-Wilk p < .05). Tensile tests using an Instron 5969 machine provided stress (120–450 MPa), strain (5–25%), and modulus (3–28 GPa) data requiring careful transformation. We evaluated four methods – logarithmic, square root, Box-Cox (optimal λ = 0.32), and Johnson – with Box-Cox showing the best performance for modulus (89% normality). Overall, 68% of datasets achieved acceptable normality (p > .05), though extreme λ values (−1 or 2) reduced physical interpretability. Skewness also had to remain below 0.5 to ensure valid microstructure correlations. The novelty of this work lies in the creation of a tailored statistical protocol that balances transformation efficiency with material relevance. By integrating multiple validation tests (Q-Q plots, Shapiro-Wilk, Kolmogorov-Smirnov) and ensuring a coefficient of variation below 15%, we provide a robust, reproducible method for natural fiber analysis. This approach enhances both the statistical reliability and practical usability of mechanical data in sustainable materials research.