PROFESSOR PEARSON ON THE DISTRIBUTION OF FERTILITY.
In a note concerning the question of the birth rate in the April number of the Monthly, you quote Professor Karl Pearson's distributions of fertility and also refer to his measurements of the resemblance between mother and daughter in fertility. The skewness of the distribution of fertility in the case of the Quaker families probably represents no real condition, but is due to a statistical procedure, namely, to the combination in one distribution of groups of individuals of a number of different generations. As I show in an article in this number of the Monthly, the distribution of natural fertility in any one decade is approximately 
normal, there being no pronounced skewness save that due in late decades to the undistributed zeros. But if I combine all my results from Middlebury College, using thus families of men born from 1780 to 1850, I get a curve, as shown in the diagram, like Professor Pearson's in its pronounced positive skewness. If we suppose, as I am sure we must, that in Professor Pearson's Quaker families, the families are of larger and larger size as we go back in time and that also the number of families examined is fewer and fewer as we go back in time, we must conclude that even if the distribution were perfectly normal at any one period the total score would give just such skewness as he found. The abnormality of his distribution is thus a sign of the statistical mixture of species, not of any essential physiological characteristic. Of the Copenhagen records I can not speak assuredly as I do not know how the individuals were distributed in time. The occurrence in Professor Pearson's records of families of 13-22, higher that is than any that I have found in over 2,000 families of the last century, would seem to show that the beginning of the decadence of the American stock dates back beyond the nineteenth century.
It is possible too that the resemblance in fertility between mother and daughter which Professor Pearson has measured, and naturally enough attributed to heredity, may be really due to the necessary nearness in time of a mother and her daughter. If, for instance, in five generations fertility dropped steadily from 10 to 2, and we calculated a coefficient of filial correlation for a group of mother-daughter pairs distributed throughout the five generations, we should have a result showing marked mother-daughter resemblance, although heredity, as measured by the comparison of measures taken relatively to the average fertility at the time the individual lived, might amount to nil.
| Edward L. Thorndike. |
| Teachers College, New York. |
