FISHERY BULLETIN: VOL. 86, NO. 3 



Table 2.— Slope area sizes (km^. 



2\1 



Depth 

 (m) 



Slope area (km'') 



Shumagin Chlrikof Kodiak Yakutat Southeast 



'Shumagin, Chirikof, and Kodiak areas and Yakutat area from long. 

 147-I440W; data from E. Brown (NWAFC Seattle Laboratory, NMFS. NOAA, 

 7600 Sand Point Way NE. Seattle, WA 98115, pers. commun. December 

 1985). Yakutat area from long. 144-137°W. and Souttieastern area; data from 

 R. Haight (NWAFC Auke Bay Laboratory, NMFS, NOAA, P.O. Box 210155, 

 Auke Bay, AK 99821, pers. commun. 1986). 



across statistical areas to calculate an RPN for the 

 Gulf of Alaska. The bootstrap method (Efron 1982; 

 Efron and Gong 1983) then was applied to the re- 

 sultant RPN's to test the statistical significance of 

 annual changes in the RPN's. 



The bootstrap method is a nonparametric statis- 

 tical procedure based on Monte Carlo methods (see 

 Shreider [1966] for a description of Monte Carlo 

 methods). The bootstrap method is a new technique 

 not common in the fisheries and ecology literature, 

 but examples of its application to survey design and 

 biomass estimation can be found in Kimura and 

 Balsiger (1985) and Haslett and Wear (1985), re- 

 spectively. In addition, Rao and Wu (1984) proved 

 the applicability of the bootstrap method to strati- 

 fied sampling, which is the sampling method used 

 in the longline survey. The bootstrap method is 

 useful when parametric assumptions are difficult to 

 justify; no parametric estimate is readily available 

 for the accuracy of a statistic, e.g., a sample median; 

 or the procedure to compute the statistic of interest 

 is complicated. Simply described, the bootstrap 

 method works as follows: Given the observed data 

 set <Xi,X2,. . .,X^>, the sample <Xi*,X2*,. . ., 

 Xn*> is drawn by independent random sampling 

 with replacement from the observed data set and 

 the desired statistic (e.g., a median) is computed 

 from the sample. The resultant statistic is termed 

 the bootstrap replicate. In the next step, the sam- 

 ple is drawn and the bootstrap replicate is computed 

 some large number B times. The resultant B boot- 

 strap replicates form the bootstrap distribution. An 

 estimate of the accuracy of the median, a standard 

 error, then can be calculated from the bootstrap 

 distribution by standard methods. 



In this study, we used the bootstrap method to test 

 the null hypothesis that the difference RPN^j;. - 

 RPN^jr. = 0, for any RPNjjt , where i = year 

 (1979-86), i' = any subsequent year, and k = sta- 



tistical area (Shumagin, Chirikof, Kodiak, Yakutat, 

 and Southeastern). The bootstrap method was used 

 because parametric assumptions are difficult to 

 justify for the longline survey data and the pro- 

 cedure to compute the statistic of interest, the 

 variance of the RPN, is tedious and error prone. In 

 our application of the bootstrap method, stations 

 were randomly sampled with replacement within 

 each area. A value denoted RPN^ ;^* was computed 

 from the catch per hachi values of the sampled sta- 

 tions by the method of RPN calculation described 

 previously. Stations then were sampled with re- 

 placement from year i' within each area, a second 

 value denoted RPNj ;^* was computed, and the 

 difference RPNj j^* - RPN^j^* was found. Sampl- 

 ing with replacement from the 2 years and the com- 

 putation of the difference were repeated 1,000 times 

 producing a bootstrap distribution of 1,000 

 differences. 



Efron and Tibshirani (1986) outlined three 

 methods for setting an approximate confidence 

 interval from a bootstrap distribution for a statistic 

 of interest, here the difference RPNj /^ - RPN^ /£. 

 Use of the simplest method, the percentile method, 

 is considered correct if the bootstrap distribution of 

 the statistic of interest is described by a normal 

 distribution (Efron and Tibshirani 1986). The nor- 

 mality of the bootstrap distribution for the dif- 

 ference was tested using the D'Agostino D Test 

 (D' Agostino and Stephens 1986) and found to be nor- 

 mal, thus justifying the use of the percentile method. 

 The statistical significance of the difference 

 RPNj /£ - RPNj /£ then was evaluated by the 

 following criteria. If the 95% confidence interval for 

 the difference did not include zero, then the null 

 hypothesis was rejected, the annual change in the 

 RPN was considered statistically significant, and the 

 change in sablefish abundance was considered real. 

 Conversely, if the 95% confidence interval for the 

 difference included zero, the null hypothesis was ac- 

 cepted and the change in sablefish abundance was 

 not considered significant. 



RESULTS 



The RPN for the Gulf of Alaska increased 111% 

 from 1979 to 1986 (Fig. 3). The 95% confidence 

 interval for this increase did not include zero and 

 therefore was judged statistically significant (alpha 

 = 0.05; Table 3), showing that the difference was 

 not due to random error in the survey and that 

 sablefish abundance in the Gulf of Alaska has in- 

 creased markedly since 1979. The difference con- 

 sists of significant increases from 1980 to 1981, 1981 



448 



