where: 

 VarX 



VarZ 

 n 



= variance of the mean of individual samples from all 

 composites 



= variance of the mean of composite samples 



= number of subs2imples constituting each composite 

 sample. 



This equation assumes that replicate observations from individual and 

 composite samples are normally distributed. Also, the composites 

 must each consist of subsamples of equal mass (i.e., the same mass of 

 tissue is taken from each organism). For unequal proportions of com- 

 posite subsamples (i.e., tissue mass), the variance of the series of 

 composite samples increases and, in extreme cases, exceeds the 

 variance of grab samples. Thus, it is recommended here that the same 

 mass of tissue be taken from each organism contributing to a composite 

 sample of a single species (Tetra Tech 1986b). For the analyses 

 presented below, it was assumed that the composite samples consist of 

 subsamples of equal proportions. 



Two special cases of composite sampling are "space-bulking" and 

 "time-bulking" (PhiUips and Segar 1986). Space-bulking involves sam- 

 pling of individual organisms from several locations and combining 

 tissue samples into one or more composite samples for analysis. Time- 

 bulking involves taking multiple samples over time from a single loca- 

 tion and compositing these samples. Time-bulking over a harvest 

 season is especially appropriate where short-term variations in con- 

 taminant concentrations in tissue samples are significant and budget 

 constraints preclude repeated analyses over time. 



The adoption of space-bulking or time-bulking strategies ultimately 

 relates to the objectives of the exposure assessment. Because exposure 

 concentrations are typically averaged over time in risk assessment 

 models, time-bulking may be more justified than space-bulking. In any 

 case, one should use these strategies with extreme caution since sig- 

 nificant information on spatial and temporal heterogeneity may be lost. 

 Selection of space-bulking or time-bulking techniques should be sup- 

 ported by analyses of available data or data from preliminary sampling. 

 Tiered analyses of samples can also be used to evaluate the ap- 

 propriateness of compositing strategies. For example, individual 

 samples may be stored separately over the entire harvest season. At 

 the end of sample collection, preliminary analyses of individual tissue 

 samples from a selected series of sites and times could be performed 

 to evaluate temporal and spatial heterogeneity and to devise an ap- 

 propriate compositing strategy. 



Tetra Tech (1986b) evaluated the effects of composite sampling on the 

 statistical power of a sampling design (see Appendix D). Their results 

 demonstrate that the confidence in the estimate of the mean concentra- 

 tion of contaminant in tissue increases as the number of individual 

 samples in the composite increases. The statistical power (i.e., the 

 probability of detecting a specified minimum difference among treat- 

 ments) increases dramatically with the number of individual samples 

 in each replicate composite sample. However, the increase in power 

 associated with adding more individual samples to each composite 



45 



