Kimura and Lyons: Between-reader bias and variability in age-determinations 



55 



When the main purpose of an analysis is to compare 

 criteria of the age readers, the nominal age for classi- 

 fication should be the tester age. When the overall char- 

 acteristics of ageing a species is of interest, perhaps 

 x is the better nominal age. The estimated statis- 

 tics by age look different depending on which nominal 

 age is being used. For example, if x is used, the per- 

 centage agreement for younger ages will appear larger. 



Both the average percent error (Beamish and Four- 

 nier 1981) and the coefficient of variation have been 

 proposed as an "age independent" method of estimat- 

 ing precision for age-determination studies. Assuming 

 normality, Chang (1982) favored the coefficient of 

 variation on the basis of efficiency, and we favor the 

 coefficient of variation on the basis of common usage. 

 Under differing distributional assumptions, the aver- 

 age percent error may actually be superior. 



If age determinations are independently and normal- 

 ly distributed about some true age, then the percent- 

 age agreement at each age can be predicted from the 

 area under the normal curve. Suppose the age of an 

 "a"-y ear-old fish can be determined with a certain coef- 

 ficient of variation. The difference between two in- 

 dependent age determinations (b and c, say), would be 

 distributed as 



z = b - c ~A7[0,2CV 2 a 2 ]. 



The predicted percentage agreement (ppa) at age "a" 

 is then 



ppa = [<t>(z 2 ) - cp( Zl )] x 100, 



where <J> = the cumulative distribution function of 

 the unit normal distribution, 

 Zl = -0.5/[(1.4142)(CV)(a)] and, 

 z 2 = +0.5/[(1.4142)(CV)(a)]. 



Results and discussion 



The above statistics were calculated for several species 

 sampled in 1986 and subsequently aged (Tables 1-6). 

 These are overall statistics calculated using data from 

 all readers and testers, and therefore represent group 

 rather than individual performance. A summary of 

 percentage agreements and coefficients of variation 

 averaged over all ages is given below: 



Percentage 



