LAI ET AL.: AGE DETERMINATION OF PACIFIC COD 



Table 3. — Test for the independence of percent agreement {R) of age 

 readings correlated to age-class {A) and ageing method (M). 



Model 



Proba- 

 df G2 bility 



M. + Xf* + \;^ + \« + \MR + ),AR + xMA + \MAR Q 0.00 1 .0000 



' I k ik ik II Ilk 



(jL + \W + \>< + XR + \Mfl + )^AR + xMA 

 I I k ik jk ij 



H + \'^< + \^ + \f + X'Wf? + ),AR 

 I I k IK jk 



u. + \M + X^* + \fl + \AR + XMA 

 I ] k jk I] 



u. + XW + x>< + xR + xMR + },MA 

 I j k ik ij 



28 28.08 0.4603 



32 48.87 0.0285 



56 241.75 0.0000 



35 125.03 0.0000 



which impHed that percent agreement was corre- 

 lated to age-class and ageing method, and the 

 estimated age frequencies differed by ageing 

 method. However, these pairwise relationships 

 between any two factors are unrelated to the 

 third. 



Because we are interested in the effects of age- 

 ing method and age class on repeatability, it is 

 reasonable to look at the ratio between agree- 

 ment (^ = 1) and disagreement (k = 2) for each 

 combination of ageing method and age class, i.e., 

 myi/my2 for ^ll i andj. The logarithm of this ratio 

 is known as the logit model (Fienberg 1981, chap- 

 ter 6). The logit model for Equation (2) can be 

 derived as 



Table 4. — Estimated logit effects corresponding to the loglin- 

 ear model In Equation (2). 



logitiij) = log (miji/mij2) = w -I- co 



M 



+ Ui^ 



(3) 



O) 



(Xf 



Xf) 



X^„^). The ef- 



where, the logit effects, 

 wf = (X^^ - Xj^«), and cof = {\ff ,. 2 '• ^"^ ^^ 

 fects (X's) without factor R in Equation (2) are 

 cancelled out by subtraction in Equation (3). The 

 values of X's can be obtained from the BMDP pro- 

 gram and substituted into Equation (3). The re- 

 sults show that there was a significant declining 

 effect on agreement as age increased (Table 4). 

 This indicated that percent agreement decreased 

 with increasing age. Age determination using 

 coracoids and dorsal fin rays had a positive effect 

 on agreement, which indicated that agreement of 

 these methods was higher than the average of the 

 five methods, but the other ageing methods had a 

 negative effect, i.e., agreement was lower than 

 average. 



Table 5 shows that the effect of ageing method 

 was significant for all fish older than age 3. There 

 was no significant difference (5% level) between 

 readings except for ages 5-6. This difference prob- 

 ably resulted from differences between readings 

 for otoliths and pectoral fin rays (Table 6). Mean 

 square (MS) for the ageing method eff'ect in- 



creased with age and was the predominant com- 

 ponent in the within-subject variation for all age 

 categories. Therefore, variability in age determi- 

 nation was mainly due to ageing method rather 

 than inconsistent annulus interpretation by the 

 reader. 



Using the Q -statistic, the mean ages of the two 

 readings were not significantly different except 

 for age group 5-6 using otolith and pectoral fin- 

 ray ageing methods (Table 6). Significant differ- 

 ences between ageing methods were found in all 

 age categories except the youngest. Age readings 

 from dorsal fin rays and pectoral fin rays were not 

 significantly different for fish younger than age 6. 

 Age readings from otoliths and pectoral fin rays 

 were not significantly different for fish older than 

 age 7. Otolith readings were older than other 

 methods for fish younger than age 6 but were 

 younger than dorsal fin-ray readings for fish 

 older than age 7. Scale readings gave consistently 

 younger ages than the other methods. 



Bakkala and Wespestad (1984) reported that 

 recruitment of the 1977 year class was uniquely 

 strong when compared to its neighboring year 

 classes. The modal length of this year class can be 



717 



