Appendix E 



Evaluation of the Effects of Sample 

 Replication on Statistical Power of a 



Sampling Design 



Statistical power analysis can be used to evaluate alternative sampling 

 designs with varying levels of replication (Cohen 1977; Gordon et al. 

 1980; Tetra Tech 1986b). In statistical power analysis, relationships 

 among the following study design parameters are evaluated: 



• Power - Probability of detecting a real difference among treat- 

 ments (e.g., species, stations, times) 



• Type I error (a ) - Probability of wrongly concluding that there 

 are differences among treatments 



• Minimum detectable difTerence - Magnitude of the smallest 

 difference that can be detected for given power and Type I 

 error 



• Residual error - Natural variability 



• Number of stations 



• Numlier of replicate samples. 



The analyses presented below were conducted with the objective of 

 providing guidance in selecting levels of sampling replication. This 

 objective was addressed by determining the magnitudes of difference 

 among variables that can be reliably detected with varying levels of 

 sampling effort. A one-way ANOVA model was used to evaluate 

 statistical sensitivity relative to level of sample replication. Tetra Tech 

 (1986b,d) provides details of the ANOVA model and results of the 

 analyses. All power analyses were conducted using the Ocean Data 



