The effect of small samples on crown-size interrelationships.

In a recent paper Lavelle ( Dent Res 56:541, 1977) reported both differing magnitudes and patterns of mesiodistal-buccolingual crown-size correlations in 3 human races and in samples of Pan, Pongo, and Gorilla, using 20 males in each case. Others have called attention to differences in crown-size correlations (r) and variances (a2) from similarly small archeological samples (SUAREZ, AmJ Phys Anthrop 41:411, 1977). While the sampling distributions of a single r are well known, such results are difficult to interpret in the context of correlated values of r derived from a single sample. Accordingly, we have taken a computer simulation approach, using successive independent samples from a larger population and calculating mesiodistal-buccolingual correlations (r) for each tooth. The data base consisted of 109 males and 99 females, described by MOYERS ET AL (Standards ofHuman Occlusal Development, 1976). A computer-based program was used to draw five completely random subsamples of 20 individuals of each sex (Fox and GUIRE, Documentation for Midas, 1976, p 82). In question was the extent to which mesiodistal-buccolingual correlations could vary in magnitude or in pattern from sample to sample. For the five random subsamples for each sex, restricted to individuals with complete and measurable dentitions, differences in mesiodistal-buccolingual correlations for each of 14 teeth ranged from as little as 0.12 to as much as 0.73. The largest range of MDBL r's for a single tooth extended from -0.45 to ± 0.28 in girls. In addition, there were wide subsample variations in the relative values of r for anterior and posterior teeth, as shown here for males (Figure). In all, 74% (31) of the mesiodistal -buccolingual correlations given by Lavelle for three races of man fell within the range established for males within a single base population. Moreover, 62% (26) of the MD-BL correlations given for Pan, Pongo, and Gorilla fell within these same subsample ranges. This