20 Joshua Laerm, M. A. Menzel, and J. L. Boone 



test for homogeneity of group variances, respectively. Inspection of 

 residuals revealed that 12 of 2,400 measurements (200 specimens by 

 12 measurements) were found to be extreme (>5 standard deviations 

 from the mean). Five of these extreme measurements were attributed 

 to two individuals, and both individuals (USNM 75167, USNM 296566) 

 were deleted from the analysis. The other extreme measurements were 

 attributed to six different individuals. These six measurements and 

 11 other missing observations were replaced with the within-group 

 mean of the character in question so that these individuals could be 

 included in the multivariate analyses. After the extreme observations 

 were corrected, we assumed multivariate normality based on marginal 

 normality and multivariate homogeneity of variance based on failure 

 of rejection in the test of equality of group covariance matrices using 

 Box's M (P = 0.082). 



Differences among repeated measures, adult age classes, and sexes 

 were tested with analysis of variance, and type-1 error rates were corrected 

 with the sequential Bonferrioni adjustment (Rice 1989) where necessary. 

 Taxa were classified using stepwise discriminant analysis. Variables 

 were included in the models based on minimizing Wilk's lambda, prior 

 probabilities were equal to sample size, and varimax rotation was employed. 

 Stepwise discriminant analysis will find an optimal solution based on 

 the data; however, depending on which variables enter the model first, 

 it may find a local optimum rather than the global optimum. To help 

 avoid this optimization problem, we removed variables that entered 

 the model in the first steps and repeated the analysis. All analyses 

 were performed on raw data without transformation and without removing 

 size (Rohlf and Bookstein 1987), because this produced the simplest 

 tool for future classification of new specimens consistent with a goal 

 of a high degree of group separation. 



The model separating S. cinereus and S. longirostris was validated 

 in two ways. First it was validated internally by randomly selecting 

 subsets of the data (approximately 80% of the data selected without 

 regard to species), constructing the disciminate model, and using that 

 model to classify the remaining 20% of the specimens. This procedure 

 was repeated 200 times. Second, because the skulls were originally 

 measured utilizing a non-traditional approach, the model was validated 

 externally with additional specimens (six test specimens of each species) 

 measured with dial calipers under a disecting microscope. 



RESULTS AND DISCUSSION 



In the analysis of the repeated measures, no significant difference 

 was found among measurements for any of the 11 cranial characters. 



