Variability of hominoid cranial capacities 



Material and methods. In Table 9 are cited data bearing on the 

 variability of each sample, namely the extreme range (or the difference be- 

 tween the maximum and minimum values of each sample), the estimated 

 standard deviation of the mean, and the estimated coefficient of variation 

 (V) of the sample. Similar parameters are given for pooled one-sex samples 

 and for combined-sex series. Some of the standard deviations are given by 

 the authors themselves, notably Randall (1943-1944), Ashton (1950), and 

 Ashton and Spence (1958): these S.D.s are marked with a superscript a 

 in Table 9. In some other published works the original raw data are 

 listed, as by Hagedoorn (1926), Schultz (1933), and Gaul (1933); whilst Dr. 

 Adolph Schultz generously sent me his unpublished raw data on his 95 male 

 and 85 female capacities of H. lar crania from the Chiengmai District 

 of northern Thailand. In these instances my research assistants, Miss 

 C. J. Orkin and C. Block, computed the S.D. directly from the original 

 data. Standard deviations obtained in this way are marked with an a in 

 Table 9. 



In most studies, however, the mean and the sample range are given 

 but not the S.D. or the raw data. To compute the S.D. of the series, as well 

 as of the pooled and combined-sex samples, we have resorted to the rela- 

 tionship for normally distributed variables between the sample frequency 

 (n), the mean observed range, and the standard deviation. These relation- 

 ships are tabulated, for example, by Simpson, Roe, and Lewontin (i960, 

 p. 141, Table 1) and by Lindley and Miller (1953, p. 7, Table 6). Briefly, 

 for a population that is normally distributed, the mean observed range 

 is 6 times <x when n = 442, and 6.48 times a when the sample is 1000. 

 For smaller samples, the observed range is, of course, less adequate as an 

 estimate of the population range: when n = 100, the mean observed range 

 is only 5.02 times a; when n = 50, the value is 4.50; when n = 20, it is 

 3.74; when n = 10, it is 3.08. Thus, while the observed range is not really an 

 adequate substitute for the S.D. in most instances, it can be used for a rough 

 estimation of a, where more accuracy is not required, or where no alternative 

 method of computing the S.D. is available, as when the raw data are not 

 given. Accordingly, where the S.D. has not been given in a publication, or 

 where the individual data are not listed, an estimate of the standard devia- 

 tion has been made by dividing the differences between the maximum and 

 minimum values (that is, the size of the extreme range) by the values given 



41 ^ 



