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University of California Publications in Geological Sciences 



nificance test, and the discriminant function is used to place an individual speci- 

 men in the proper group. 



Often in paleontological work a single specimen will have some features that 

 seem to differ from those of a population of which it is possibly a member: many 

 such specimens seem to be intermediate between two groups. The problem is to 

 determine which of the two groups it came from or whether it came from a third 

 group not before considered. Evidence from the single specimen alone can de- 

 termine to which group it belongs. 



TABLE 4 

 Pooled Estimates of Correlation Coefficients and Standard Deviations 



cranium 



Character 



POc 



MxT 



LBR 



BzB 



InB 



FHA 



FHP 



P*L 



POc 





.8421 



.6726 



.7678 



.6131 



.6296 



.5287 



.6726 



MxT 







.7707 



.8198 



.7232 



.6571 



.5796 



.7787 



LBR 









.7604 



.7006 



.6116 



.6980 



.6779 



BzB 











.8088 



.6707 



.7063 



.6890 



InB 













.6753 



.6569 



.5636 



FHA 















.5696 



.5933 



FHP 

















.5652 



P*L 



















S.D 



4.500 



4.723 



2.592 



7.583 



2.987 



2.725 



2.203 



1.343 







mandible 



Character 



M T L 



M T B 



MnT 



HRD 



HRB 



MiL 





.8554 



.7799 



.6628 



.7199 



M T B 







.7647 



.7031 



.7414 



MnT 









.7755 



.6777 



HRD 











.7901 



HRB 













S.D 



1.546 



0.649 



4.681 



2.166 



1.079 







The method applied here is a variant of the Z> 2 analysis discussed above and 

 fulfills the same logical requirements. Because a different set of coefficients is 

 needed, an altered procedure is used to obtain the uncorrected variables. 



A variance-covariance matrix, analogous to the coefficient of correlation matrix 

 referred to in the description of Tf analysis, is set up. The values should preferably 

 come from the samples under consideration, but a set based on a closely related 

 group will suffice. The samples are assumed to have equal variance-covariance 

 matrices. A unit matrix is appended to the variance-covariance matrix to obtain 

 the uncorrected factors and the combination is transformed by the pivotal con- 

 densation method (Rao, 1952). 



To test a single specimen, the values for the number (p) of characters used to 

 describe the specimen are substituted into the linear equation derived from the 

 matrix. This is also done with the mean values of the same characters for the two 



