Miscellanea 
417 
where a convenient method of finding p was by the formula 
P = l 
oragamby =\- ■ 
The problem has recently occurred of dealing with data where : 
(i) One variate is given quantitatively, the other variate is given by ranks. 
For example, place in school-class has to be considered in relation to marks in examination, 
or the rank in a teacher's general ajjpreciation has to be considered in relation to marks in 
examination. 
(ii) One variate is given by broad categories, the other by ranks. 
For example, five or six categories of general intelligence are given as the basis of the 
teacher's classification of intelligence, and this has to be considered with regard to rank in, 
say, class or examination, possibly with regard to a special subject. 
We require in both cases to deduce from the data the true variate correlation. 
Case (i). Let x be the character measured by its grade, y the character given quantitatively. 
Then with the notation above, if p' equal the correlation of grade and of variate, r the corre- 
lation of the two variates : 
where 
Integrating by parts after putting y = 0 and writing 
dz dh 
Integrating again by parts : 
= 0-1 I / p= — e <!\-zdxdy 
.r, r , r , , /2-r2 ,„ 2rx'i/' xi''^ \ 
= 1- 7- I - J dx' dy' 
V (1 
Hence cl^ ^ ± f p,,y \ ^ N ^ I 
dr dr\Na^crJ sVtt o-„ V 
Phil. Trans. A., Vol. 195, p. 25. 
