The latter tv/o variables are rather imperfectly correlated, in 

 the present material, with considerable variatior) of body length for 

 each scale length, and also of scale length for each body length. 

 (The coefficient of correlation betvreen body length and scale length 

 was .78, with P of less than .01. The coefficient of regression for 

 scale length on body length was .8U; that for body length on scale 

 length was .73.) There is, of course, no ivay of knowing the true 

 magnitude of correlation between age and either of these two variables. 

 There are these possibilities for consideration, however: 



(A.) Age might be more highly correlated' with scale length than 

 with body length. Then, on measuring scales from a number of fish 

 with identical (or nearly so) body length, we should expect some degree 

 of positive correlation between age and scale length. In addition, 

 if, in our age determinations we had been influenced by the size of 

 the scales, rather than the number of age marks, we should expect the 

 above correlation to be enhanced. To examine this possibility, a col- 

 lection of 987 scale measurements ranging from 190-219 mm. of projected 

 image, and compromising four year classes, was divided into groups of 

 ten-millimeter classes according to body length; and for each of these 

 body-length classes the coefficient of correlation betvfeen age and scale 

 length was calculated. The results, given in table III, show no sig- 

 nificant correlation between these two quantities. The probability 

 (P) is high, averaging .Ul6, that if there were no correlation what- 

 ever, the coefficient could, by random causes alone, be as high as 

 indicated. This lack of correlation is evidence that the age deter- 

 minations w6re not influenced by scale length to any appreciable de- 

 gree. Incidentally, it is also evidence that there is no intrinsic 

 correlation betv/een scale length and agej i.e., no correlation other 

 than what results from the dependence of scale length on body length. 



TABLE III. -Correlation (r) Between Age and Scale Length 

 for Fish of Identical Classes of Standard Length. 



—'Number of ipeciraens 



49 



