Variation in Crotalus horridus 



63 



Table 3. Results of discriminant analyses. The first analysis was performed on 

 the 13 characters used by Pisani et al. (1973); all 19 characters were 

 used in the second analysis. 





First 



Second 





analysis 



analysis 



Number of variables in 







discriminant function 



5 



4 



Eigenvalue 



1.088 



2.989 



Wilks' lambda 



0.479 



0.251 



Approximate F-value 







(P = 0.01) 



16.103 



48.577 



Canonical correlation 



0.722 



0.866 



Coefficients for 







canonical variable 



-0.156 (BCB) 



-0.109 (HL) 





-0.216 (VS) 



-0.119(VS) 





-0.346 (TCB) 



-0.376 (ADS) 





-0.419 (DSM) 



-2.217 (MS) 





-0.514 (PDS) 





Constant 



57.593 



35.626 



A maximum likelihood factor analysis (Dixon and Brown 1979), in 

 which all variables are evaluated simultaneously, was employed prima- 

 rily to determine the existence of groups that correspond to subspecies. 

 Two factor analyses were conducted, first on the 13 morphological 

 characters used by Pisani et al. (1973), and then on all 19 characters. To 

 analyze group integrity, we used stepwise discriminant analysis, which, 

 like the factor analysis, evaluates all variables simultaneously (Dixon 

 and Brown 1979). Again, two discriminant analyses were conducted, 

 one on the characters used by Pisani et al. (1973) and one on all 19. 



The maximum number of discriminant functions to be derived in a 

 one discriminant analysis is either less than the number of groups or the 

 same as the number of discriminating variables, whichever is smaller 

 (Nie et al. 1975). Because there are only two groups in this study, there 

 is only one discriminant function. Three criteria for evaluating this func- 

 tion are the eigenvalue, canonical correlation, and Wilks' lambda. The 

 eigenvalue is a measure of the total variance explained by the discrimi- 

 nating characters. The canonical correlation is a second measure of the 

 function's ability to discriminate among the groups. Wilks' lambda is an 

 inverse measure of the discriminating power in the characters that have 

 not been removed by the discriminant function. A smaller lambda, then, 

 means more information is accounted for in the discriminant function. 

 In Biomedical Computer Programs (BMDP), the Wilks' lambda is 

 transformed into an approximate F-value. 



Since there is one discriminant function, there can only be one 

 canonical variable, which is the linear combination of variables entered 

 that best discriminates among the groups (the largest one-way ANOVA 

 F-value) (Dixon and Brown 1979). The canonical variable is adjusted so 

 that the pooled within-group variance is one, and its overall mean is 



