An evaluation of the M-statistic in human odontomorphometric distance analyses

The usefulness of the M-statistic in odontomorphometric distance analyses was evaluated against a battery of more traditional metrics, which included Mahalanobis' D 2 , Penrose's shape metric, the Manhattan distance and Delta. Odontometric data used for the analyses were derived from 202 Paraguayan Lengua Indians and 125 contemporary caucasoids. Efron's Bootstrap procedure was used to evaluate the statistical accuracy of the different metrics, when each was applied to the same populations. Additionally, metric stability in the face of reduced sample size, statistical bias resulting from over- and underestimation, and the effects of standardization, were investigated. Our results indicated that Penrose's shape metric rather that the recently introduced M-statistic was the most reliable metric evaluated. Penrose's shape remained the most reliable when sample size was artificially reduced and when raw data were used. Interestingly, Mahalanobis' generalized distance emerged as the least reliable statistics, especially when used on small sample sizes.