TABLE 2 in Detecting morphological gaps in tooth outlines of a Pachyrukhinae (Hegetotheriidae, Notoungulata) lineage: systematic and palaeobiogeographical significance of the records from Northwestern Argentina

TABLE 2. — Clusters and morphological gaps of the upper dentition. Principal components scores (resulting from EFA and PCA) retained for statistical procedures, clustering algorithms used to determine the optimal number of groups under gap statistic methods (K-means, Ward, and centroid indices), Shapiro-Wilk test values for each cluster (α = 0.05), and tolerance regions (γ = 0.05; β = 0.1). Note that the overlap is calculated using the upper limit of Cluster A and the lower limit of Cluster B on their probability distributions along the canonical axis resulting from the LDA. Groups without overlap are highlighted in bold font, providing statistical evidence for the existence of a morphological gap (Fig. 5). Morphological gaps dataM1M2M3UMMP2P3P4UPMPC scoresPC1-8PC1-8PC1-8PC1-9PC1-7PC1-8PC1-7PC1-8K-means index (N clusters)–0.55 (2)–0.37 (2)–0.87 (2)–0.51 (2)–0.56 (2)–0.61 (2)–0.47 (2)–0.56 (2)Ward index (N clusters)–0.60 (2)–0.25 (2)–0.86 (2)–0.49 (2)–0.47 (2)–0.18 (2)–0.49 (2)–0.46 (2)Centroid index (N clusters)–0.86 (2)–0.68 (2)–1.16 (2)–0.58 (2)–0.69 (2)–1.06 (2)–1.07 (2)–0.54 (2)Cluster A (W / p-value)0.96 / 0.820.94 / 0.370.88 / 0.020.89 / 0.060.94 / 0.360.97 / 0.890.91 / 0.100.94 / 0.39Cluster B (W / p-value)0.95 / 0.350.93 / 0.200.94 / 0.550.95 / 0.620.95 / 0.660.95 / 0.530.94 / 0.280.95 / 0.71Upper limit (Cluster A)0.370.32–0.25–0.400.080.23–1.14Lower limit (Cluster B)–0.18–0.21––0.54–0.760.040.36–0.22