Abstract.- At the Alaska Fish- 

 eries Science Center, one in five age 

 readings produced for routine stock 

 assessments are re-aged indepen- 

 dently by a second age-reader. The 

 Center now has a large database of 

 repeated age readings that covers a 

 variety of groundfish species and 

 years. The purpose of this paper is 

 to point out the problems and utility 

 of interpreting such a database. The 

 main problem of interpretation is 

 fundamental, and relates to the fact 

 that the true age of a fish is seldom 

 known. Nevertheless, from a prag- 

 matic point of view, these data can 

 still provide useful insights into the 

 age-determination process. Data from 

 six marine fish species are used to 

 show the overall levels of between- 

 reader bias, agreement, and variabil- 

 ity that have occurred on production 

 age readings. Other uses for these 

 data include objectively ranking the 

 relative difficulty in ageing different 

 species, maintaining quality control, 

 examining between-reader differ- 

 ences in ageing criteria, and evalu- 

 ating the possible importance of 

 between-reader bias and variability 

 in later analysis and modeling ap- 

 plications. Assuming reader bias 

 is negligible, modeling results pre- 

 sented here indicate that estimated 

 percentage agreements are consis- 

 tent with the hypothesis that age 

 determinations are normally distrib- 

 uted with a constant coefficient of 

 variation over relatively wide age 

 ranges. This result supports use of 

 the coefficient of variation for mea- 

 suring variability in age precision 

 studies. 



Between-Reader Bias and Variability 

 \n the Age -Determination Process 



Daniel K. Kimura 

 Julaine J. Lyons 



Alaska Fisheries Science Center. National Marine Fisheries Service, NOAA 

 7600 Sand Point Way NE, Seattle. Washington 981 15-0070 



Manuscript accepted 6 August 1990. 

 Fishery Bulletin, U.S. 89:53-60 (1991). 



In this paper we evaluate a unique 

 database developed for all marine 

 fish species being routinely aged at 

 the Alaska Fisheries Science Center. 

 Here, large subsamples (one in five 

 age readings produced for routine 

 stock assessments) have been re-aged 

 independently by a second experi- 

 enced age-reader, mainly for the pur- 

 pose of maintaining quality control. 

 However, it became apparent that 

 this database could be used to provide 

 additional insights into the age-deter- 

 mination process. 



Most everyone familiar with the 

 ageing of fish knows this process is 

 fraught with difficulties. At the very 

 least, there must be random variabil- 

 ity about some true age. Most likely 

 there is also bias in the ageing meth- 

 odology at some ages, as well as 

 between-reader differences. Because 

 reader bias is probably affected by 

 the individual reader, the true age of 

 the fish being aged, and perhaps even 

 individual fish, the analysis of re- 

 peated age readings made by differ- 

 ent readers does not easily fall under 

 the purview of classical statistical 

 theory. 



The types of analysis that can be 

 performed on age-determination data 

 are dependent on the kind of data col- 

 lected and the assumptions the data 

 analyst is willing to make. For exam- 

 ple, if replicated readings are made 

 by each reader, it is possible to per- 

 form a variance components analysis, 

 assuming that reader effects are ran- 

 dom and unbiased (Kimura et al. 

 1979). Comparative calibration is the 

 area of statistical analysis that com- 

 pares different methods of measure- 



ment (e.g., different readers) where 

 all methods of measurement are as- 

 sumed to contain error, and perhaps 

 bias (Theobald and Mallinson 1978). 

 Recently Kimura (unpubl.) examined 

 the limits of possible inference for the 

 functional comparative calibration 

 model. 



In the analyses presented here we 

 examine between-reader bias and 

 variability based on subsamples aged 

 independently by two age-readers. 

 For these types of data, we define 

 between-reader bias as the average 

 difference (a^ - a 2 ) in ages assigned 

 by these readers when ageing the 

 same specimens of the same nominal 

 age. Thus between-reader bias pre- 

 sumably arises from the two readers 

 using different ageing criteria. If the 

 average difference between age- 

 readers is negligible at some nominal 

 age, then between-reader bias at that 

 age is defined to be negligible, re- 

 gardless of what the unknown abso- 

 lute bias of the readers might be. 



Estimates of between-reader age- 

 ing variability from these types of 

 data can be computed by averaging 

 the sample variances calculated from 

 the two age readings (df = 1) from 

 each age structure over some nom- 

 inal age. These sample variances 

 (between-reader variances) probably 

 overestimate measurement error, 

 because they include a component of 

 variability that might be thought of 

 as between-reader bias. 



Age determination is a statistical 

 process that has a characteristic level 

 of variability. This variability is spe- 

 cies-dependent, and provides a basis 

 for comparing the ageing of different 



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