ON THE PAKTIAL CORKELATION-KATIO 
PAKT II. NUMERICAL 
Being Part II of a Thesis for the degree of D.Sc. in the University of London 
By L. ISSERLIS, B.A. 
1. The object of the present paper is to provide numerical illustrations of 
some of the results in the first part*. Suitable material is not easily obtained, 
as many tables dealing with three variable characters are artificially curtailed as 
regards one or more of them. I am indebted to Miss Ethel M. Elderton for having 
kindly placed at my disposal manuscript tables of the heights to the nearest inch 
and weights to the nearest pound of the boys in group A (comprising schools in 
the poorest parts of the city) of her investigations into the heights and weights 
of school children in Glasgow f. 
I have arranged the material in tables which differ from Tables I-IX of Miss 
Elderton's paper in the following respects : 
(i) A uniform grouping of 5 lb. intervals for weight and 3 inch intervals for 
height is adopted at all ages; 
(ii) 384 boys of central age 5 (i.e. ages 4-5 to 5-5 years), omitted in 
Miss Elderton's tables, are here included, and two boys (age 6-5 to 7-5 years) 
whose height was below 21-5 inches, included in her tables, are omitted here. 
These tables are cut off artificially by the regulations of the School Board with 
regard to school leaving age and the admission age of infants. 
Tables I-X contain the data, the frequency distributions of height and weight 
being given for each of the ages from 5 to 14 of the 11,382 boys. 
* "On the Partial Correlation Ratio," Part I, Theoretical, by L. Isserlis. Biometrika, Vol. x, 1914, 
pp. 391-411. (The title of the first part was badly chosen, the generalized H there introduced is a 
multiple one, providing a measure of the dependence of one variable on two or more other variables. 
An example of a partial 57 would be x'Oz-ii' bemg the correlation ratio of z on y for a given value of x. 
Pearson has recently published very simple formulae connecting the partial correlation ratio with the 
multiple correlation ratio: see R. 8. Proc: Vol. 91, A, pp. 492-8. They suffice to show, that a 
knowledge of the multiple correlation ratios leads at once to the partial correlation ratios, and to that 
extent justify my title.) 
•j- "Height and Weight of Schoolchildren in Glasgow," by Ethel M. Elderton. Biometrika, Vol. x, 
1914, pp. 288-339. 
