4 
MISCELLANEA. 
I. On Spurious Values of Intra-class Correlation Coefficients arising 
from Disorderly Differentiation within the Classes. 
By J. ARTHUR HARRIS, Ph.D. Carnegie iDwtitutiou of Washington, U.S.A. 
When the constants of the and y chaiucters of the population in r^^ are quite indistinguish- 
able symmetrical tables* may be used, but not otherwise. 
Primarily and for the most part, however, the use of symmetrical tables has been restricted 
to cases in which the degree of interdependence between the measures of all possible pairs t drawn 
from a considerable series of associated individuals — in short to intra-class correlations! — is 
sought. 
The dangers of spurious correlation due to the artificial symmetry of the surface is then much 
greater §. Pearson || long ago pi)inted (.)ut that when intra-class differentiation exists, for example, 
because of age in the case of characters determined upon the members of a fraternity, or of posi- 
tion on the axis in the case of serial organs, the values of r may be to some extent spurious. 
In the cases considered by Pearson differentiation is an orderly phenomenon, i.e. the magni- 
tudes under consideration increase or decrease with age, position on the axis, or some other 
extrinsic characteristic with such regularity that the relationship can be expressed by an 
equation which may be used in correcting the raw values of r. 
In other cases, the problem is not so simple. Differentiation within the class may exist, but 
it may be difficult or impossible to arrange the individual measurements by any character outside 
of themselves to obtain the constants necessary for determining the true correlations from the 
spurious values deduced from the tables. 
Illustration I. The correlation between yields of wheat in variety, testing. 
In variety testing, the experimenter seeks (or should seek), among other things, to determine 
the correlation between yields of varieties in different years. If this correlation be 0 (and regres- 
sion be linear) it is clear that the yield of a variety in one year furnishes no basis for prediction 
* R. Pearl, Biometrika, Vol. v. pp. 249—297, 1907; H. S. Jennings, Journ. Exp. Zool. Vol. xi. 
pp. 1—134, 1911 ; J. Arthur Harris, Biometrika, Vol. vii. pp. 325—328, 1910. 
t K. Pearson and others, Phil. Trans., A, Vol. cxcvn. pp. 285 — 379, 1901; K. Pearson and 
A. Barrington, Eugenics Lahoratorij Memoirs, No. V, 1909. 
t Biometrika, Vol. ix. pp. 446—472, 1913. 
§ With only one pair of measures the probability of spurious correlation is, in cautious work, very 
slight, for the possibility of differentiation can be easily tested by the critical comparison of the physical 
constants. 
II Pearson, K., "On Homotyposis in Homologous but Differentiated Organs." Boy. Soc. Proc. 
Vol. Lxxi. pp. 288—313, 1903. 
