don characteristics were selected as representative of the range of 

 values for the coefficient of variation observed in the historical data 

 sets for selected metals and organic compounds in marine organisms 

 (TetraTech 1986b). For a series of individual fish samples taken from 

 the corresponding populations used in Analysis 1, the 95 percent 

 confidence intervals would range from 1.7 to 35.4 concentration units 

 (e.g., ppm). 



To demonstrate the effect of sample compositing on the power of the 

 statistical test of significance, Tetra Tech (1986b) performed statistical 

 power analyses using a one-way Analysis of Variance (ANOVA) 

 model. In these analyses (Figure D-2), the number of stations (5), 

 number of replicate composite samples at each station (5), significance 

 level of the test (0.05), residual error variance level, and level of 

 minimum detectable difference (100 percent of overall mean) were 

 fixed. The power of the test (i.e., the probability of detecting the 

 specified minimum difference) was then calculated as a function of the 

 number of subsamples constituting each replicate composite sample. 



Power analyses were conducted for three levels of sample variability. 

 All design parameters except the residual error variance were identical 

 in each set of analyses. Values of the residual error variance were 

 selected to represent the range of values found in the historical data 

 sets described by Tetra Tech (1986b). The coefficients of variation 

 selected for these three sets of analyses were 45.5, 101.6, and 203.5. 



As shown in Figure D-2, the probability of statistically detecting a 

 difference equal to the overall sample mean among stations increases 

 with the collection of replicate composite samples at each station and 

 as the number of subsamples constituting the composite increases. The 

 results of both sets of analyses shown in Figure D-2 also demonstrate 

 the phenomenon of diminishing returns for continued increases in the 

 number of subsamples per composite. In Analysis Set 1, for example, 

 virtually no increase in the power of the statistical test was achieved 

 with increasing the subsample size above three. In the second analysis 

 set, substantial increases in statistical power were achieved by increas- 

 ing the number of subsamples in each composite from 2 to 10. However, 

 with each successive increase in subsample size, the relative benefit was 

 reduced until very little was gained by increasing the subsample size 

 above 10. For moderate levels of variability, 6-10 subsamples within 

 each of 5 replicate composite samples may be adequate to detect a 

 treatment difference equal to 100 percent of the mean among treat- 

 ments. At the highest level of variability analyzed, the collection of 

 replicate composite samples composed of 25 subsamples each is re- 

 quired to obtain a testing power of 0.80 (Figure D-2). 



