PELLA and ROBERTSON: ASSESSMENT OF STOCK MIXTURES 



ally the application of our methods is inappropri- 

 ate because Cook and Lord used individuals of test 

 samples from the segregated stocks both to modify 

 an original set of rules from the learning samples 

 as well as to estimate 4>. Because our purpose is 

 only to illustrate the computations, we will treat 

 their observations as though the test samples had 

 been used exclusively to estimate "t". Using the test 

 samples in developing the rules, as Cook and Lord 

 did, should produce greater precision in estima- 

 tion of composition of a mixture: the disadvantage 

 at present is the inability to assess the precision of 

 these enhanced estimates. In developing the 

 variance-covariance matrix i,:,, we assumed 't> 

 and A are statistically independent. Such is un- 

 true if the test samples are used as by Cook and 

 Lord both to develop the rules used to estimate .\ 

 as well as to estimate ^. 



Test samples from the segregated stocks of the 

 three rivers were assigned by the rules to these 

 stocks iTable li. Then the rules were applied to 

 101 fish caught on the high seas. Of these, 25 were 

 assigned to Egegik, 22 to Kvichak, and 54 to Nak- 

 nek. We identify Egegik, Kvichak, and Naknek as 

 the first, second, and third streams in our sub- 

 script use. Computations using these data produce 

 the following results: 



cU 



G = 



H 



(Our B is f7 of Cook and Lord (1978): their errors in 

 evaluating /?^^ are responsible for the discrepancy 

 with our estimate B.) 



0.00184 



0.00197 



0.00975 



-0.00053 

 0.00169 



-0.00050 

 0.00230 



0.00208 

 0.014.54 



-0.00131 



-0.00115 



0.00246 



-0.00146" 



-0.00180 



0.00326 



-0.01184' 



-0.01662 



0.02846 



<i> = 



0.80000 

 0.04000 

 0.16667 



0.08000 

 0.74000 

 0.20833 



0.12000 

 0.22000 

 0.62500 



(Our <t) is the transpose of C of Cook and Lord 

 (1978).) 



0.24752 

 0.21782 

 0.53465 



( Our .\ is the same statistic as R^^ of Cook and Lord 

 ( 1978): apparently they have numerical'errors in 

 their evaluation of/?,.) 



In computing i,-^,, and 1,,, B is used as the esti- 

 mate of B. 



The 90'f confidence set from Equation (15) 

 using B is as follows: 



-0.074 

 -0.208 

 0.449 ^ 



H 



0.350 



«., s 0.310 

 «.^ =£ 1.173. 



The elements of B must lie between and 1: there- 

 fore, we can set the lower limits of the first two 

 intervals to 0, and the upper limit of the third 

 interval to 1. The actual composition was esti- 

 mated by Cook and Lord (1978) from returning 

 adults to Bristol Bay as 



T.ABLE 1. — Numbers of sockeye salmon in test samples from 

 three Bristol Bay I Alaska I rivers — Egegik, Kvichak, and 

 Naknek — assigned by rules to these rivers (source: Cook and 

 Lord 19781. 



B 



0.325 

 0.061 

 0.614 



which falls within the intervals of the confidence 

 set as would be expected. However, recall that the 

 condition that test samples be used exclusively to 

 evaluate the rules was violated: therefore, the 

 confidence set is not valid. Further, Cook and Lord 



393 



