724 



Fishery Bulletin 100(4) 



collected 10 specimen or more were included, and only 

 groups with at least four such hauls. The null hypothesis 

 of equal variance was not rejected for any of the length 

 groups (P-values from Bartlett's test are giyen in Table 

 2). It is seen that of is highest for small fish, and the 

 bootstrapped standard errors indicate that the difference 

 is statistically significant. Indeed, let D = o'^,„,„ii - ^f /nr/;<> 

 denote the difference in measurement error between small 

 (<30 cm) and large (>30 cm) fish. If (Tf ,.,„„// and o-/^^^,^ are 

 independent and normally distributed (their bootstrap 

 distributions are approximately normal) with standard 

 errors as given in Table 2, it follows that D-NiO. 0.0140- + 

 0,0083^) under the null hypothesis of equal measurement 

 errors. The corresponding one-sided P-value for the 

 observed D is 0.0016. 



The hauls differed in towed distance, with the two most 

 frequently recorded values being 1 and 1.5 nmi which 

 correspond to 20 and 30 minutes tow duration. Stratifying 

 on tow duration (which is recorded more precisely than 

 towed distance), with hauls of less than 25 minutes 

 duration (33%) in group A and the remaining hauls (67%) 

 in group B, and estimating the measurement error for 

 each group separately, we get ct^=0.0707 and 0.0656 for 

 group A and B, respectively. Thus, there is no significant 

 difference due to tow duration. For fish less than 30 cm, 

 the corresponding estimates are 0.115 and 0,107 for group 

 A and B, respectively. 



No significant relationship was found between the mag- 

 nitude of the catches and their differences, A regression 

 analysis was performed with the absolute value of the 

 mean-adjusted differences in catch rate, \2',\, as the de- 

 pendent variable and the average catch y, = (y, i + .v, 2)/2 

 as the independent variable. The regression equation 

 was |2' I =0.20-1-0. 019v, and the P-value under the null 

 hypothesis of no relationship was 0,31, However, the 

 residuals from the analysis were skewed with a long 

 right-hand tail; therefore a bootstrap test was also done, 

 resulting in an empirical P-value of 0.137, and again the 



null hypothesis of no relationship was not rejected at a 



5% level. 



Discussion 



We have estimated the measurement error (a^) of a trawl 

 haul by using data from parallel trawling experiments, 

 including 130 parallel hauls from 10 groups of experi- 

 ments. No significant differences in o'j among the groups 

 were found. Thus, o'j seems to be independent of year, time 

 of the year, and geographical position at which the haul 

 was taken. It also seems to be independent of the catch 

 size on a logarithmic scale. The magnitude of o'j is small 

 ( = 2-5%) compared with the total variability in the survey 

 trawl catches. The results are preliminary in that they are 

 based on a limited set of hauls and more extensive experi- 

 ments would be of interest to check their consistency. 

 In another investigation, Pelletier (1998) examined the 

 vessel effect between two research vessels. These data 

 could possibly be used to test the general pattern revealed 

 by analyses of data in the current study. Stromme and 

 lilende (2001) examined a total of 365 paired hauls from 

 intercalibration experiments off Namibia in 1998 and 

 1999 between the research vessel Dr. Fndtjof Nansen and 

 commercial trawlers. These data of Namibian hake (catch 

 in kg/h) were kindly made available to us, and an estimate 

 of 6'j=QAd was obtained for the measurement error. The 

 variance of y, for all the 365 hauls was 2,0; the measure- 

 ment error for this study on the log scale was about 10% of 

 the survey variance. 



Actually o'j may be an overestimation of the measure- 

 ment error because all the explanatory variables are 

 not exactly the same for the two sets of measurements 

 in Equation 1, For example the geographical location is 

 not the same and the fish densities may differ from one 

 vessel to the other because of the distance between them. 

 However, because the towed distance is typically 5-10 



