532 WRIGHT: CORRELATION IN SUBGROUPS OF POPULATION 



Experiments are described in which a thin blackened strip of 

 platinum or of gold-leaf is joined through a battery to an 

 audion amplifier. The variation in temperature and hence in 

 the resistance of and in the current through the strip, caused 

 by the fluctuation in intensity of the intermittent light, was 

 sufficient in magnitude to produce an audible sound in the 

 telephone receiver. 



GENETICS. — The average correlation within subgroups of a 

 population. Sewell Wright, Bureau of Animal Industry. 



In studying the relationship of characters it often happens 

 that the available data consist of a number of more or less dif- 

 ferentiated groups, each one of which is by itself rather small 

 for the calculation of a coefficient of correlation. Sufficiently 

 large numbers can be obtained by combining all into one table, 

 but if this is done the correlation due to differentiation of the 

 subgroups among themselves complicates the interpretation. 

 The coefficients for the whole population and for the means of 

 the subgroups are easily calculated, but the calculation of co- 

 efficients within the subgroups may be a very tedious task if 

 these are numerous. 



It seems desirable therefore to have a method by which the 

 average correlation for the subgroups can be derived directly 

 from the distribution surfaces of the whole population and that 

 of the means of the subgroups. The very simple formula dis- 

 cussed below has been useful to the writer and does not seem 

 to be well known. 



Assume that a population is composed of a number of sub- 

 groups which may be expected, within the limits of random 

 sampling, to show the same correlation between two variables 

 x and y and the same standard deviations. They may, however, 

 be of varying sizes and be differentiated from each other signifi- 

 cantly with respect to the mean values of x and y. 



Let o- X (g), o- y (g), r xy(g) be the average standard deviations and the 

 average correlation between x and y for the individuals within 

 a single subgroup. Let <r x(m ), ov (m) , r xy(m) be the correspond- 

 ing values for the means of the subgroups weighting each mean 



