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Fishery Bulletin 89(2), 1991 



two groups is desired. Canonical variates are the scores 

 from the individual discriminant functions; that is, they 

 are linear combinations of the original variables. The 

 graphical display of canonical variates (for example, 

 canonical variates 1 and 2) is useful for demonstrating 

 differences among groups because fish that belong to 

 the same group appear closer together on the plot than 

 fish from different groups. Ninety-five percent con- 

 fidence circles (Pimentel 1979) for group centroids can 

 also be calculated and plotted. In addition, canonical 

 variates can be used to examine the effectiveness of 

 the size-adjustment procedure. Thus, canonical variates 

 1 and 2 were regressed against total length, and size 

 was considered to be effectively removed if regressions 

 were not significant (Claytor and MacCrimmon 1986). 



Stepwise discriminant analysis was used to choose 

 the combination of variables that "best" separates the 

 groups. The resultant discriminant function was then 

 used to classify individual fish into groups. The dis- 

 criminant analysis was applied to the adjusted morpho- 

 metric characters with variables entered in a forward 

 manner using F = 4.0 for entering, and F = 3.996 for 

 removal. The expected actual error rates of the class- 

 ification function were estimated using Lachenbruch's 

 holdout procedure (Lachenbruch and Mickey 1968, 

 Lachenbruch 1975, Johnson and Wichern 1982). This 

 procedure provides less biased 

 estimates of the misclassification 

 rate than the resubstitution 

 method (Lachenbruch 1975). The 

 holdout procedure, or leaving- 

 one-out method, is based on the 

 classification of single observa- 

 tions that were withheld from 

 model development and later 

 classified. Cohen's kappa (k) 

 statistic and associated 95% con- 

 fidence intervals were used to 

 determine the improvement over 

 chance of the percent-correct 

 classification rates (Titus et al. 

 1984). Given five groups, the 

 chance of correctly classifying a 

 single fish is 20%. 



All statistical analyses were 

 performed on a Micro Vax 3500 

 computer. MINITAB (Ryan et al. 

 1976) was used to perform re- 

 gression analyses and ANOVA 

 procedures; BMDP (Dixon et al. 

 1981) was used to perform 

 ANCOVA procedures and dis- 

 criminant function analyses. 



Results 



Data from male and female yellowfin tuna were pooled 

 in subsequent analyses because two-sample t tests for 

 mean values of adjusted morphometric characters and 

 gill-raker counts of fish from Ecuador and Australia 

 indicated no significant differences between sexes 

 (Table 2). 



Total gill-raker counts and counts from the upper 

 limb and lower limb were significantly different (P< 

 0.01) among yellowfin tuna from the five areas (Table 

 3). Results from the multiple comparison test for the 

 total gill-raker-count data indicate no significant dif- 

 ference between the rank sums for Australia and Japan 

 and those for Mexico and Hawaii, but these pairs are 

 significantly different from each other and from those 

 of Ecuador. Total gill-raker counts appeared to be a 

 better discriminator than either the upper or lower limb 

 counts. 



The regressions for canonical variables 1 and 2 

 against total length (r 0.17, P = 0.14, and r 0.22, 

 P=0.09) were not significant, indicating that size ef- 

 fects had been removed from the morphometric vari- 

 ates. The plot of the first two canonical variates, which 

 account for 57% and 26% of the total variation, shows 

 complete separation of the centroid values for each 



