14 



Fishery Bulletin 9 1 ( I ). 1993 



Standard deviation of the confidence interval 

 length The standard deviation of the 1000 90% CIs 

 calculated for each sample size was consistently lower 

 for the GM than for the AM or FM, both in an absolute 

 sense and relative to the average CI length (Fig. 5). At 

 smaller sample sizes, the standard deviations for the 

 AM were less than those for the FM. However, this 

 pattern was reversed at larger sample sizes such that 

 the FM had the more precise interval estimates (note 

 the crossovers at rc=35 and n=25 in Figs. 5a and 5b, 

 respectively). Overall, the precision of the interval es- 

 timates declined as sample size decreased and as skew- 

 ness increased; the effect was most pronounced for the 

 FM method. The GM response was unique in that pre- 

 cision increased as skewness increased. Of particular 

 note is the dramatic loss of precision of the AM inter- 

 val estimate apparent in Fig. 5a («=40) which, upon 

 investigation, was attributed to a single extreme value. 



Parameter containment within the interval 

 estimate The GM parameter e^ occurred within its 

 interval estimates, as did u within the intervals ob- 

 tained by using FM, at the prescribed 90% confidence 

 level (Fig. 6). The rate of GM containment oscillated 

 within 1-2% of this level under all circumstances. Con- 

 fidence intervals for the FM contained u at the rates of 

 89.1-92.3% (Fig. 6a) and 89.1-93.6% (Fig. 6b); the high- 

 est percentages were associated with the smallest sample 

 size, perhaps due to their relatively greater lengths 

 (Fig. 5). In contrast, AM interval estimates contained 

 u at rates of 47.7-65.8% (Fig. 6a) and 76.9-85.3% 

 (Fig. 6b), well below the prescribed level of confidence. 



Dungeness crab trawl survey data 



We also computed the three estimators for actual C. 

 magister density data to assess the gain in informa- 



10,000 



"£ 8,000 



o 



o 6,000 



Z 



o 



§ 4,000 



£ 



Q 



a 2,000 



i- 



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3,000 



10 



20 



30 



40 



50 



ARITHJVIETIC 



FINNEY 

 GEOMETRIC 



20 30 



SAMPLE SIZE 



Figure 5 



Comparison of standard deviation of the length of 90% confi- 

 dence interval for the three estimators of central tendency 

 according to sample size. (a) LOGN (4,2) data representa- 

 tive of coastal population of Cancer magister used for Monte 

 Carlo simulations, (b) LOGN (6,1) data representative of 

 estuarine population of C. magister used for Monte Carlo 

 simulations. 



100 



20 30 



SAMPLE SIZE 



Figure 6 



Comparison of percent occurrence of the parameter in the 

 909c confidence interval for the three estimators of central 

 tendency according to sample size of Cancer magister. (a) 

 LOGN (4,2) data representative of coastal population of C. 

 magister used for Monte Carlo simulations, (b) LOGN (6,1) 

 data representative of estuarine population of C magister 

 used for Monte Carlo simulations. 



