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The human remains from the Late Pleistocene Mousterian sites in modern day Israel raised the issue of variation for the first time in the history of paleoanthropology. Their current interpretation is both problematic, in that the sources of their variation still remain unresolved, and historic, in that attempts at resolution reflect the currently accepted philosophy of the paleoanthropologists as strongly as they reflect the nature of the data. Today this philosophy can be seen in the penchant of some paleoanthropologists to define species taxa on the basis of consistent differences, no matter how minute. Here, we examine the question of whether the observed variation in the cranial remains from Amud, Qafzeh, Skhul, and Tabun reflects species differences. We try to refute a hypothesis of no difference, and suggest new approaches for examining this phylogenetic question. We report on the distribution of a testing statistic based on the standard error of the slope of regressions relating the measurements common to pairs of specimens. We show that this standard error test of the null hypothesis (STET) has the power to reject a null hypothesis for significant hominid taxonomic differences but does not reject the null hypothesis for the Israeli remains.