24 Life and Letters of Francis Galton
Galton, by means of seeking the slope of the regression line, found the regression of brother on brother to be 3 and this accordingly would be the fraternal correlation ; he then said : a nephew is the son of a brother, therefore his regression on his uncle =1 x 3 =1. Again I do not believe that regressions can be built up in this manner. It appears to be multiplying together probabilities that are not independent, but correlated; for all a regression provides is a probable deviation, and we cannot apply independent probabilities to a correlated triplet. Why may not a brother be considered as the son of a midparent and so have regression 3 x 3 =.- instead of Galton's observed value 3 ? Why might we not equally well argue that a nephew is the grandson of a midparentage, which gave rise to his uncle and thus the nephew-uncle regression be . x 3 x 3 = 2 instead of . -? Why should cousins* be considered the offspring of two brothers 3 X 3 x I rather than as the grandsons of one midparentage 3 x 3 x 3 x I? Even if we are always to take the "shortest way round," no argument is given in favour of it, and it could only be satisfactorily demonstrated by actual data.
Fig. 6. Galton's Filial and Fraternal Regression Lines.
I do not think Galton's method of deducing the degrees of resemblance between kinsmen of various degrees of blood relationship from the single datum of the regression of a filial array on its midparent will pass muster; it is extraordinarily suggestive-no one had thought before of giving a quantitative measurement to the various types of kinship. Galton indicated how it could be done by aid of correlation tables and gave at this time two such tables t, those for midparent with offspring and for brother with brother. These are both from his R. F. F. (Records of Family Faculties), but he also provided another correlation table giving the distribution for a special series of pairs of brothers. In Fig. 6 will be found his regression lines for offspring on midparents, and for brother on brother. His method of reduction was, however, very different from any we should adopt to-day. When he wanted a mean he determined a median, and he did this by roughly proportioning (graphically) the total in the cell in which it lies, he worked not with the
* The value s x 2 x I = 227 is given by Galton : Natural Inheritance, p. 133.
t If we include the earlier one for the seed-weights in mother and daughter plants for the case of sweet-peas (see our p. 4) we have here the four earliest correlation tables and regression
lines ever published.