XVL.—NORMAL CORRELATION. ) 
each of the two variables may be regarded as the sum, or some 
slightly more complex function, of a large number of elementary 
component variables, the intensity of correlation depending on 
the proportion of the components common to the two variables. 
Stature is a highly compound character of this kind, and we 
have seen that, in one instance at least, the distribution of stature 
for a number of adults is given approximately by the normal 
curve. We can now utilise Table IIL., Chap. IX, p. 160, showing 
the correlation between stature of father and son, to test, as far 
as we can by elementary methods, whether the normal surface 
will fit the distribution of the same character in pairs of indi- 
viduals : we leave it to the student to test, as far as he can do so 
by simple graphical methods, the approximate normality of the 
total distributions for this table. The first important property 
of the normal distribution is the linearity of the regression. 
This was well illustrated in fig. 37, p. 174, and the closeness of 
the regression to linearity was confirmed by the values of 
the correlation-ratios (p. 206), viz, 0-52 in each case as com- 
pared with a correlation of 0-51. Subject to some investiga- 
tion as to the possibility of the deviations that do occur 
arising as fluctuations of simple sampling, when drawing 
samples from a record for which the regression is strictly 
linear, we may conclude that the regression is appreciably 
linear, 
9. The second important property of the normal distribution 
for two variables is the constancy of the standard-deviation for 
all parallel arrays. We gave in Chap. X. p. 204 the standard- 
deviations of ten of the columns of the present table, from the 
column headed 62:5-635 onwards ; these were— 
2:56 2:60 
2°11 2:26 
2-55 2-26 
2-24 245 
2:23 2:33 
the mean being 2:36. The standard-deviations again only fluctuate 
irregularly round their mean value. The mean of the first five 
is 2:34, of the second five 2-38, a difference of only 0:04: of the 
first group, two are greater and three are less than the mean, 
and the same is true of the second group. There does not seem 
to be any indication of a general tendency for the standard- 
deviation to increase or decrease as we pass from one end of the 
table to the other. We are not yet in a position to test how 
far the differences from the average standard deviation might 
arise in sampling from a record in which the distribution was 
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