STATISTICS IN CLASSIFYING RACES OF SHAD 



273 



length and all correlated characters from any 

 racial investigation. 



The choice of characters to be, used in investi- 

 gating races of shad was evident. To avoid the 

 difficulties presented by selectivity of the fishing 

 gear, those characters which are correlated with 

 length were not considered. Thus, depth, thick- 

 ness, weight and all of the other body measure- 

 ments were eliminated, because they increase as 

 the fish grows. Ratios of two such measurements 

 will also be related to length, unless these two 

 measurements increase at the same rate through- 

 out the growth of the fish. These ratios have 

 not been investigated because it is doubtful that 

 this condition exists, particularly when both 

 juveniles and adults are considered. Scatter- 

 grams of gill rakers and length exhibited a para- 

 bolic relation and were therefore eliminated. 

 Scale counts have not been included because 

 notations on the data sheets indicated that some 

 of the scale counts were questionable. Of the 2/i 

 counts and measurements, all were eliminated 

 tor the above reasons except 6 meristic counts 

 (anterior scutes, posterior scutes, dorsal rays, 

 anal rays, pectoral rays, and vertebrae) and these 

 were tested for correlations with length before 

 they were used in any analysis. 



Analysis of variance tables for the regression of 

 these characters on length have been calculated 

 for some of the samples. The assumptions neces- 

 sary for this analysis are: (1) For each length, the 

 character is normally distributed, (2) the variance 

 of the character is homogeneous for each length, 

 and (3) for each length interval, the samples are 

 random. The values of F needed to test for a 

 regression of the characters on length are given 

 in the last column of table 3. F with 1 and 100 

 degrees of freedom is equal to 3.94 at the 5 percent 

 level and 6.90 at the 1 percent level. There are 

 three significant regressions in this table. Two 

 of these regressions are for vertebrae in the Hud- 

 son River samples of 1939 and 1940. It is inter- 

 esting to note that the F-value for vertebrae in 

 the 1941 Hudson River sample is also high (3.11) 

 but not significant. This significance does not 

 occur in any of the other three samples which 

 were tested for a regression of vertebrae on length. 

 Of course, this is not enough evidence in itself to 

 say that it is a racial difference between the popu- 

 lations, but it raises the question as to why this 

 difference occurs for the Hudson River samples 



476260—59 2 



Table 3. — Regression analyses to Its! meristic characters 

 for correlation with length 



Source of variation 



Anterior Scutes 



Hudson River, 1940 

 Regression 



Deviation from regression- 



Total. 



St. Johns River, 1940 



Regression 



Deviation from regression 



Total 



Connecticut River, 1945 



Regression 



Deviation from regression 



Total 



Posterior Si utes 



Hudson River, 1940 

 Regression 



Deviation from regression 



Total 



St. Johns River, 1940 



Regression 



[ deviation from regression 



Total 



Connecticut Kiyeh, 1945 

 Regression 



Deviation from regression 



Total 



Anal Rays 



Hudson- River, 1940 

 Regression 



1 deviation from regression. 



Total. 



St. Johns River, 1940 



Regression 



Deviation from regression- 

 Total 



Pectoral Rays 



Hudson River, 1940 

 Regression 



Deviation from regression. 



Total . 



St. Johns River, 1940 

 Regression 



Deviation from regression- 



Total. 



Connecticut River, 1945 



Regression 



Deviation from regression- 

 Total 



Vertebrae 



Hudson River, 1939 



Regression 



Deviation from regression 



Total. 



Hudson River. 1940 

 Regression 



Deviation from regression 



Total 



Hudson River, 1941 

 Regression 



Deviation from regression- 



Total. 



Footnote at end of table. 



rlf 



1 



103 



104 



1 



lot 



inn 



1 

 103 



1 

 104 



in:, 



1 



103 



Sum of 

 squares 



Mean 



Square 



1 



104 



0. 236 



52. 310 



52. 546 



II. 1124 

 57. 176 



2. 390 

 03. 800 



60. 190 



0. 151 

 102. 382 



0. 002 

 106. 762 



106. 764 



0.644 

 40. 346 



40. 990 



o 111)2 

 43. 847 



1.425 



I,;, 117.-, 



1.270 

 0. 436 



1.241 

 0. 532 



0. 180 

 0.402 



(I. 236 

 0. 508 



