Misapplication of statistics in scorpiology: a case study

A recent paper by Ait Hammou et al. (2026) studied morphometric differentiation among Androctonus aeneas C. L. Koch, 1839, A. liouvillei (Pallary, 1924), and putative hybrids from Algeria, based on 23 linear measurements from 12 females. The present article re-examines the statistical procedures applied therein through an independent reproduction of all reported analyses using the same data matrix. Six categories of issues are identified. (1) The 23 variables consist exclusively of raw absolute-size measurements and thus contain no shape information. The first principal component, which accounts for 71.6 % of the total variance, shows uniformly negative loadings across all 23 variables and thus represents a generalized size axis. (2) Two data anomalies (the carapace length of A. aeneas (Rechaiga) and the telson width of A. liouvillei (Arbouat bayadh) are statistically incompatible with the remainder of the dataset. The true carapace length of A. aeneas (Rechaiga) is reconstructed as 26.97 mm using two independent geometric methods. (3) The sample size (n = 12, distributed 7 : 3 : 2) invalidates the authors’ multivariate procedures in several mathematically distinct ways: degenerate within-group variance for A. aeneas, unreliable asymptotic approximation in the Kruskal-Wallis test, and a singular within-class scatter matrix preventing linear discriminant analysis from running under a standard implementation (R’s MASS::lda() returns the error “variables are collinear”). (4) No correction for multiple comparisons was applied to the 23 simultaneous univariate tests. None of the three variables reported as “significant” by the authors remains significant after either Bonferroni or Benjamini-Hochberg correction, even when exact rather than asymptotic p-values are used. (5) The authors’ verbal interpretations of their PCA, HCA, and LDA results contradict the corresponding figures, while PCA and HCA partition the 12 specimens in qualitatively different ways. (6) Re-analysis after Mosimann log-shape ratio transformation, which removes the dominant size component, places the three putative hybrids within the A. liouvillei point cloud rather than between the two parental species. In a DAPC of the size-corrected data with regularized dimensionality (n.pca = 2), the training-set classification accuracy decreases from 100% (the value implicitly obtained by the authors’ p > N−g LDA) to 67%. The hybrid status of the three specimens assigned a priori on the basis of collection from “contact zones” is therefore unsupported by any multivariate analysis once size is properly disentangled from shape.