Boros István (szerk.): A Magyar Természettudományi Múzeum évkönyve 52. (Budapest 1960)

Thoma, A.: Anthropometric characters and selective survival

vais of 9 years, breaking up his material into age groups of 9 years. The oldest age group is open upward, and consists of a very small number of subjects, so this class shall be omitted from the calculations. At the time of the first survey the lowest age limit was 20 years, whereas at the second the highest was 73 vears. Only the males shall be considered. With each character the number of subjects varies slightly, and in the case of stature the individual survey covers 121 males. Since we have 5 age difference values, the degrees of freedom shall be 4. — As regards our problem, it would be most gratifying to be able to take from the same population also the data called for by the generalizing method. Here this is unfortunately impossible, as the material consists of such a small number of subjects that the fluctuations due to sampling errors may to a large extent conceal the effect of the factors under discussion. We therefore utilize the data of the Irish male series published by Hooton& Dupertius (2). The material comprises 11 age groups of 5 years each, ranging from 20 to 74 years, in the case of stature with data for 8848 males. The number of differences between the age means being 10, the degrees of freedom are 9. — Between the upper age limits there is a difference of 1 year : the Irish material ranges over an interval of 54, the Swiss material over one of onlv 53 vears. However, this difference is negligible, since one of these intervals is only 1.018 time s the other. The difference in size of the age groups, however, is already essential, because in this case the variance is the mean square of the age changes relative to the given periods. If these changes are directly proportional to time, we must reduce the variance of the individual observation / 5\

2 to j I = 0.31. However, the growing processes of the living organisms are not proportional to time, but rather to its logarithm. The correction factor with which we must multiply the variances obtained by the individual observation shall therefore be ^ | = — = 0,53. Thus the correction results smaller, I log 9 j 0.9542^ which incidentally means that as regards the aim of our research — the intensity of selection — we have only rendered the conditions more exacting. Where adjustments with mixed and negative selections are concerned, we apply the correction directly to the square deviations. — For technical reasons of calculation all the differences have been multiplied by 100. Our calculations are encumbered with errors of a twofold origin : the two different observers and the two different populations. It is easy to see that the former cannot influence the results, if only we give some thought to the nature of the „error of measurement". Let us in fact imagine a phantom who takes all the measurements conformably to the instructions of Rudolf Martin, with absolute accuracy. The measurements taken by all of us shall more or less differ from these values. The divergence between the measurements of the individual observer and those of the phantom represent the observer's error of measurement. However, whereas the error of the untrained anthropometrist proves erratic, that of a practised observer shall have a definite direction and value. In our case the skill of the two observers (B ü c h i and Dupertuis) and their pursuit of scientific accuracy are beyond all question. Since the absolute value of the measurements is in each case cumbered with a constant error, this does not influence the value of the differences found between the different age groups. Seeing that in our case we are interested only in the differences, and that these are individually reliable, the comparison may be made without more ado. — An