58 



Fishery Bulletin 89(1), 1991 



data for making decisions on aspects of their data 

 analysis and modeling. 



We examined the question of consistency between 

 the percentage agreement and coefficient of variation 

 measures of variability when analyzing between-reader 

 data. Earlier we showed that assuming a constant coef- 

 ficient of variation, and the normal error model, the 

 percentage agreement can be predicted for all nominal 

 ages. By comparing these theoretical curves with 

 estimated percentage agreements calculated from data 

 (Tables 1-6), some confidence in the consistency of the 

 two measures can be derived. However, this compari- 

 son is crude due to the probable existence of between- 

 reader biases that are not factored into the analysis. 



Four different values for the coefficients of variation 

 were used to calculate theoretical percentage agree- 

 ment curves (Fig. 1A). These curves were then com- 

 pared with estimated percentage agreement values for 

 yellowfin sole (CV = 0.032, Fig. IB), walleye pollock 

 (CV = 0.050, Fig. 1C), and sablefish (CV = 0.129, Fig. 

 ID). 



The percentage agreements for all three species ap- 

 pear consistent with the hypothesis that the coefficient 

 of variation is constant over a wide age range, although 

 the percentage agreements for pollock are biased low. 

 These results support averaging the coefficient of 

 variation across age ranges, and generally support 



using the coefficient of variation for interpreting preci- 

 sion data from age-determination studies. However, 

 there is considerable variation in these data which 

 makes our results somewhat tentative. 



An important factor that also affects the ageing 

 process is the presence of a strong year-class. For 

 example, if two adjacent year-classes have absolute 

 strengths of 10 and 100 fish, a 10% imprecision of 

 + 1 year will add 5 fish from the strong cohort to the 

 weak one (a 50% change) but only one-half a fish from 

 the weak year-class to the strong (a 0.5% change). The 

 data on Pacific whiting (Table 1) show how this phe- 

 nomenon can lead to poor percentage agreements for 

 weaker year-classes. 



Users of age data are often concerned that after 

 some age, say 9 years, for example, the dominant year- 

 classes become spread over several ages. Since percent- 

 age agreement by such an age has often decreased to 

 50% or less, it is expected that age distributions will 

 be smoothed. The only reason the ages would not be 

 smoothed is if the dominant year-class is being antici- 

 pated by the age-reader. For example, if samples are 

 90% 10-year-olds, it would be difficult for the age- 

 reader not to anticipate that age and between-reader 

 agreement would be high. However, if say 9-, 10-, and 

 11-year- olds occur in equal numbers, the agreement 

 would not be nearly as good. 



Two possible ways of handling this problem are evi- 

 dent. A controversial method would be to assure that 

 all age-readers are reasonably coached as to the prob- 

 able occurrence of a strong year-class; the other is to 

 group the older ages in any model analyzing these data 

 (e.g., Deriso et al. 1989). Both approaches avoid ask- 

 ing the age-reader to perform the impossible. 



Finally, interpretation and analysis of repeated read- 

 ings given here assume that the repeated readings 

 were statistically independent. In the present context, 

 this simply means that each reader did not have infor- 

 mation regarding the other reader's results. When 

 repeated readings are not made on an independent 

 basis, or are of inadequate sample size, the data will 

 be difficult or impossible to interpret statistically. From 

 such a database, it is impossible to make assertions 

 regarding precision. 



Acknowledgments 



Mr. George Hirschhorn had the foresight to initiate the 

 reader/tester quality control system. We thank the age 

 readers of the Ageing Unit at the Alaska Fisheries 

 Science Center who provided the data for this study. 

 We also thank the Scientific Editor and three anon- 

 ymous referees whose comments contributed 

 significantly to this paper. 



