NOTE Hayes: A statistical method for evaluating age-length keys for Melanogrammus aeglefinus 55 1 



teria outlined by Penttila (1988) and Jensen and Wise 

 (1962). By convention, a 1 January birthdate was used. 



Statistical analysis 



Age-length keys are commonly formed first by obtain- 

 ing a matrix of numbers at age by length interval 

 (Table 1), and then by converting this to a matrix of 

 proportion at age for each length interval. For statisti- 

 cal tests between age-length keys, however, I used the 

 matrix of numbers at age by length. Age-length keys 

 were compared by making tests of significance sepa- 

 rately for each length interval present in both keys 

 where the sample size was greater than six for each 

 age-length key. Fisher's exact test (Siegel, 1956) was 

 used in these comparisons. Because of the large num- 

 ber of tests needed to compare age-length keys, 

 experimentwise error was compensated for by adjust- 

 ing the significance level for the individual tests. The 

 significance level for n individual tests (a*) needed to 

 maintain a desired experimentwise error (a exp ) was de- 

 termined by the following formula derived from Sokal 

 and Rohlf( 1981): 



lnll- 



= l-e 



This method can be quite conservative if the power of 

 the individual tests is limited because of small sample 

 sizes (Sokal and Rohlf, 1981). Owing to the conserva- 

 tive nature of this method, two subjective criteria for 

 evaluating test results were used. 



The first criterion was the number of tests exceed- 

 ing the nominal significance level (i.e., a=0.05) in the 

 set of comparisons of interest. A second criterion for 

 evaluating the significance of individual tests was the 

 pattern of nominally significant tests. If significant dif- 

 ferences were observed between quarters for a given 

 length interval, adjacent length intervals were also 

 expected to show significant differences. Thus, tests 

 suggesting nominally significant differences between 

 quarters for a single length interval adjacent to length 

 intervals where tests indicate no difference were sus- 

 pected of occurring by random chance. 



Age-length keys from the first and second, second 

 and third, and third and fourth quarters were 

 compared to determine which quarters could be com- 

 bined into a single age-length key. Tests were con- 

 ducted by comparing keys within a year because com- 

 bining age-length keys between years can introduce 

 bias in the resulting key (Westrheim and Ricker, 1978). 

 Additional tests were conducted comparing NEFSC 

 spring survey age-length keys with combined first and 

 second quarter commercial age-length 

 keys. 



Estimation of catch at age and 

 variance 



As a check on the potential for intro- 

 ducing bias by combining age-length 

 keys, estimates of the age composition 

 of the commercial catch for each year 

 from 1982 to 1988 were made by us- 

 ing age-length keys combined in four 

 different ways. First, age-length keys 

 were constructed for each quarter by 

 using only fish sampled commercially 

 during that quarter. These catch-at- 

 age estimates served as a basis for 

 comparison since they correspond to 

 the level of temporal aggregation 

 (quarterly) that has commonly been 

 used in Georges Bank haddock assess- 

 ments (Clark et al, 1982; Gavaris and 

 Van Eeckhaute, 1990). The second set 

 of catch-at-age estimates was formed 

 by combining commercial age data 

 from the first half of the year into a 

 single age-length key that was then 

 applied to the first and second quar- 



