244 A Biometrical Study of Conjugation in Paramecium 
TABLE X. 
Index Correlation in Paramecium. 
Series 
Group 
Characters 
Gross 
Spurious 
Net 
No. 
.1 
n 
Conjugants 
Non -Conj ugants 
)) " 
Index and Length 
,, Breadth 
„ Length 
„ Breadth 
- -4096 ± -0387 
•4864 + '0355 
-•1797+ ^0450 
•3685 ± -0402 
- -5804+ •0309* 
•5804+ -0309 
- -5931 + -0302 
•5931 ± ^0302 
•1 708 + ^0452* 
-•0940+ -0461 
•4134+^0386 
- -2246 ± ^0442 
210 
210 
210 
210 
c 
•>•) 
Conjugants 
Non-Conjugant8 
Index and Length 
„ Breadth 
„ Length 
,, Breadth 
- ^6002 + ^0304 
•6102+ -0298 
- ^2728 + -0439 
•3943+ ^0401 
- •6851 + ^0252 
•6851 + ^0252 
-■6420 ±-0279 
•6420 ±-0279 
•0849 + -0471 
-•0749 + ^0472 
•3692 + ^0410 
- ^2477 ± -0445 
202 
202 
202 
202 
E 
It 
Non -Conjugants 
)) J) 
Index and Length 
„ Breadth 
- ^3263+ -0525 
•3855 ± ^04998 
-•6819 + ^0314 
•6819 ±-0314 
•3556 ± -0513 
-•2964f0535 
132 
132 
while that for index and breadth is in every case negative. In the case of the 
conjugants for both series the net index-breadth vakies are probably not sig- 
nificant. The spurious values are very high and of roughly the same order of 
magnitude in all cases. Just as where the characters length and breadth are 
considered separately, the correlations are here always higher for non-conjugants 
than for conjugants. It is also quite clear, considering the net organic relation- 
ship, that the index is throughout more highly correlated with length than with 
breadth. There would appear to have been no significant change in the index 
correlations during the history of the culture. 
As there seems to be some doubt in the minds of many biologists as to whether 
the expression p — po, measuring the portion of a gross index correlation due to the 
organic correlation of the characters entering into the index, has any real signifi- 
cance, or if it has, what this significance is, I have prepared the two diagrams 
which follow with the hope that they may make the matter somewhat clearer. It 
seems to me that the difficulty regarding the expression p — po comes largely from 
the fact that biologists usually think of correlation in terms of regression, and the 
effect of spurious correlation has not hitherto, so far as I know, been expressed in 
those terms. Diagrams IV. and V. bring out this relation quite clearly. The plan 
on which these diagrams have been constructed is as follows ; in the first place the 
characteristic equation showing the actually observed relation of index to length 
* It should be stated that the probable errors tabled in the " spurious," and "net" cokimns were 
calculated from the formula P.E. of r = -07449 . This procedure assumes that the coefficients are 
actual coefficients of correlation obtained from tables by the formula r = f , which, of course, is 
Jycr^a.2 
not the case. In all probabihty the probable errors as given in the table are not widely divergent from 
the true values. 
