independent random variables, then the sampling variance of y- is estimated by the equation: 



w = ^^) = ^R 



I ^ lifi)' 



p? 



The sampling variance of the estimated total catch (for individual species and for species 

 groups) was calculated in terms of the expected values and sampling variance of Xj (average 

 catch) and yj (total number of trips) for each stratum. Total catch was not normally 

 distributed and therefore direct examination of the precision of the estimates is difficult. 

 However, simulation experiments indicated that a normal approximation was satisfactory for 

 constructing 95 percent confidence intervals around the estimated total catch. 



PRECISION OF THE ESTIMATES 



Precision refers to the dispersion of the sample measurements used to calculate an 

 estimate and the resultant variability in the estimate. The standard error of an estimate is 

 the square root of the sampling variance of the estimate. Even though an unbiased estimate of 

 the sampling variances can be developed from the sample, no unbiased estimate of the 

 standard error can be calculated from the sample. Nevertheless, the square root of the 

 estimate of sampling variance is a consistent estimate of the standard error of the estimate, 

 and is almost universally used in sample surveys. The standard error is necessary for 

 calculating confidence intervals around an estimate. The width of a confidence interval is a 

 function of the probability level selected, and is determined from the normal distribution. The 

 most commonly used confidence interval is given by: estimate i 1.96 X (estimate of standard 

 error). 



Confidence intervals provide an indication of the precision of the estimated total 

 catch. At the same confidence level a broad interval relative to the estimate indicates a less 

 precise estimate than does a narrow interval. The 95 percent confidence interval indicates 

 that we can be 95 percent certain that the actual total catch is between the upper and lower 

 confidence limits. 



The coefficient of variation (CV) expresses the standard error as a percentage of the 

 estimate. It provides an alternative measure of precision and is useful in comparing the 

 relative precision of two estimates. A small coefficient of variation indicates a more precise 

 estimate than does a large coefficient. 



10 



