EFFECT OF SILICA CONTENT ON HABIT OF CORETHRON 325 



vations available from forty-five stations in the Northern Region within the one season 

 1938-9, covered by the repeated cruises between o and 20° E. It was thought that by 

 limiting period and locality in this way a fairer comparison would be obtained than by 

 using more widely dispersed data. I am largely ignorant of mathematics myself, but 

 Mr G. M. Spooner, of the Plymouth Laboratory, has very kindly checked my use of 

 the methods, taken from Fisher (1930), and informs me that they are applicable to the 

 work in hand. 



The first step was to determine the degree of direct correlation assuming a linear 

 regression, between percentage of Corethron in spineless phase and silica content, 

 percentage spineless and temperature, and between silica content and temperature, 



according to the well-known formula 



,_S{xy) ^ 

 n.axay' 



This yielded the correlation coefficients tabulated below. In testing their significance 

 I have used the formula 



which Fisher recommends for small samples in preference to use of the standard error, 

 which tends to exaggerate the significance of the correlations obtained, but standard 

 error has also been given: 



r a, t :. P = 



% spineless/silica -0'5739 ±o-ioii 4595 less than 001 

 % spineless/ r° C. +0-5365 +0-1074 4-169 less than 0-0 1 



Silica/r° C. —0-7700 ±0-0614 7-913 less than 001 



Next applying the formula r^^ 3= /r/ ^'^^'^"/"^ -= to get the partial correlation 



between percentage spineless and siUca content, eliminating the effect of temperature, 



we get 



r= —0-3007, ar= ±0-1363, /=2-o43, with P between 0-02 and 0-05. 



But applying the same formula for the partial correlation between percentage spine- 

 less and temperature, eliminating the effect of silica content, we get 



r= +0-1811, (7?-= ±0-1458, ^=1-193, whence P lies between 0-2 and 0-3. 



This means that this second partial correlation is much less significant in itself, but 

 the main point is to determine how far the diff"erence between the two partial corre- 

 lations is significant in order to see what justification there is for the view that silica 

 content is the more important of the two factors. From the initial direct correlations 

 it is already probable that both act together to a large extent. 



To test the significance of the difference between the two partial correlations the 



method given by Fisher (1930, p. 168) involving the 2 transformation has been used, 



with the following result: 



r z "' — 4 Reciprocal 



I St partial correlation -0-3007 -0-3103 41 0-02439 



2nd partial correlation +0-1811 +0-1813 41 002439 



Difference 0-4934 ± 0-2209. ^um 0-04878. 



