276 Ori the Probable Error of Dr Spearman's Correlation Coefficients 
TABLE VIII. 
Certain Gonstavts of the Frequency Difstrihations of Various Correlation 
Goejficients derived from 375 Santples of 8. 
(1) r calculated from co 
operati\'e paper 
(2) r actual using She])-^ 
pard's corrections \ 
(3) r actual using no cor-| 
rection for grouping \ 
(4) Tp actual 
(5) »■« „ 
(6) P „ 
(7) R „ 
Mean 
S.D. 
Coefficient 
of 
Variation 
Number of samples 
required to give as 
great accuracy as 
100 samples of (1) 
Number of samples 
required to give as 
great accuracy as 
100 samples of (2) 
•631 
•250 
39^6 
100 
•624 ± -010 
•274 ± •OO? 
43^9 ±r3 
120±5^9 
100 
•614±^010 
•271 ± ^007 
44^1 ±r3 
117±5^8 
. 98 
•586+ -010 
■291 + •OO? 
49^7 ±1^5 
135 + 6^7 
113 
•566+ •Oil 
■309 + ■OOS 
54-6 + 1^7 
153 ±7^5 
127 
•580 ± •Ol 1 
■289 + ^007 
49^8 + l-5 
•407 ± •OOS 
•237 ^- ^006 
58^2+ 1-9 
TABLE IX. 
Certain Constants of the Frequency Distributions of Various Correlation 
Coefficients derived from 100 Samples of SO. 
Mean 
S.D. 
Coefficient 
of 
Number of samples 
required to give as 
Numberof samples 
required to give as 
Variation 
great accuracy as 
great accuracy as 
100 samples of (1) 
100 samples of (2) 
(1) r calculated from co-} 
operative paper j 
■653 
•109 
16^7 
100 
(2) r actual using Shep-/ 
pard's corrections ( 
■661 ± -007 
•101± ^005 
15^3 ± -7 
86 ± 8-2 
100 
(3) Vp actual 
(4) r„ „ 
(5) r actual from median | 
■639 + -008 
•113+^005 
17-7+ ^9 
108 + 10^3 
125 
■638 ± ^008 
■i22± •ooe 
19^1 ± -9 
125±ll-9 
146 
4-fold division = cos ~--r ( 
•609+ ■Ol 2 
■i83± ■oog 
30^1 ±V6 
282 ±25-1 
328 
A + B) 
(6) p actual 
■624+ ^008 
■116+ -006 
18 ■6.+ -9 
(7) R , 
•428 + -007 
■100± -005 
23^4± r2 
Tables VIII and IX give the means, s.D.'s and coefficients of variation of the 
frequency distributions in Tables V and VI and in addition the calculated con- 
stants for the samples of 30. 
As well as this I have calculated the number of samples which would be 
required to give as great accuracy by the less accurate methods as 100 samples 
determined (1) on the theoretical basis of normal correlation, and (2) on the actual' 
samples by the product moment method using Sheppaii^^'s corrections. 
The object of this is to get an idea of how much time must be saved in order 
to gain by using the rank methods. First however we may note in Table VIII 
the marked difference between the theoretical S.D. and that actually obtained by 
the product moment method. 
