UCHIDA: REEVALUATION OF FISHING EFFORT 

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MEAN (METRIC TON) 



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Figure 2. — Relationship between mean and standard devia- 

 tion of catch per effective trip, before and after logarithmic 

 transformation and elimination, by vessel size classes and 

 areas, 1965-70. 



values. Because the application of routine statis- 

 tical procedures requires a normal distribution 

 and independence of the mean and standard de- 

 viation, a transformation of the data was re- 

 quired. A logarithmic transformation was 

 selected because the standard deviations tended 

 to be proportional to their means (Figure 2A). 



Transformation of the Data 



A logarithmic transformation has several 

 theoretical advantages in analyzing catch data 

 (Murphy and ElHott 1954; Gulland 1956). Usually 

 the transformation tends to stabilize the var- 

 iances and make them independent of the mean. 

 Furthermore, the random components tend to be 

 independently and normally distributed about 

 zero mean and with a common variance. 



After the transformation, the means and stan- 

 dard deviations continued to be significantly but 

 negatively correlated (r = -0.458; df = 22; 

 P<0.05). Examination of the transformed data 

 revealed that there were two points (Figure 2B) 

 that were aberrant and diverged from the cluster 

 of other points. These points represented data for 

 class 1 vessels fishing offshore in 1969 and in- 

 shore in 1970. The original monthly catch data 

 showed that the catch rates were affected by very 

 low C/ET, all of which were 0.15 MT (metric ton) 

 or less. These catch rates fell close to or beyond 

 IJL±3cr and their elimination from subsequent 

 analysis reduced the correlation between the 

 means and standard deviation (Figure 2C) and 

 stabilized the variances (r = 0.058; df = 22; 

 P>0.05). Tests for homogeneity of variances also 

 indicated that the transformed data for all years 

 could now be grouped by areas within size classes. 



Figure 3 shows the frequency distribution and 

 fitted normal curve of the deviations from the 

 mean of log C/ET for each area within the size 

 classes. None of the histograms departed sig- 

 nificantly from normality when chi-square tests 

 were applied. Therefore, the fit of the normal 

 curve is as good as can be expected (x^ ranged 

 from 2.18 to 7.59; P<0.05). 



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DEVIATION FROM MEAN LOG C/ET 



Figure 3. — Frequency distribution and fitted normal curve 

 of the deviations from the mean of log C/ET. 



63 



