VENRICK: SYSTEMATIC SAMPLING IN ECOSYSTEM 



(run test, P = 0.10). With the sampling interval 

 employed here, the biases of individual estimates 

 average out over the entire study. Had the inter- 

 val been twice as large, a consistent overestimate 

 or underestimate would have resulted, with re- 

 spective magnitudes of -i-5.8'7f and -1.9*^, until 

 25 September when the phase relationship ap- 

 pears to have shifted. 



Tables 2 and 3 also present the results of the four 

 stratified random designs, based upon the means 

 of 20 replicates. The consistent underestimates 

 resulting from SR-2 were sufficiently unexpected 

 that a second series of 20 SR-2 samples were 

 drawn from each population. This series showed 

 no evidence of bias and, thus, it appears that the 

 initial results were the product of random chance. 



Precision 



Precision, in its strictest sense, could only be 

 examined in the case of the stratified random de- 

 signs, for which replicates were available. The 

 designs employing 10 strata, each with one sam- 

 ple, SR-1 and SR-3, offered greater precision than 

 designs with fewer strata. However, there was a 

 highly significant concordance (Kendell 

 coefficient, P<0.01i between the precisions of all 

 designs with respect to the profiles giving the most 

 precise result. Examination of the individual 

 profiles indicated that the precision of the results 

 was inversely related to the strength of the 

 chlorophyll maximum and to the amount of 

 small-scale variability along the vertical axis, or, 

 in other words, to the structural complexity of the 

 population. Later, the accuracy of the systematic 

 designs (discussed below) was found to show the 

 same relationship. 



For all stratified random designs, the variance 

 between replicates was trivial compared with the 

 variance between the nine populations. Analyses 

 of variance gave /"s ^g ratios ranging from 54 to 344 

 (all P«0.01). When all nine profiles were consi- 

 dered to be replicates of the same population, the 

 variance between the nine estimates from each 

 systematic cast could be compared with the var- 

 iance between single stratified random casts, one 

 from each population (Figure 4A). On this scale, 

 there were no differences in precision between any 

 of the sampling designs. The large variation be- 

 tween populations masked any difference in per- 

 formance. Thus, when the concept of the sampled 

 population is expanded to include spatial and 

 temporal variations, RSS appears to offer neither 



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Figure 4. — The results of the computer simulation sampling 

 study, study A, showing the relative precisions and accuracies of 

 the four restricted systematic sampling designs (RSS) and four 

 stratified random designs (SR). 



advantages nor disadvantages with respect to pre- 

 cision of estimates. 



Accuracy 



The accuracy of the various designs was also 

 compared using sets of unreplicated stratified 

 random casts (Figure 4B). The greater accuracies 

 of stratified random designs SR-1 and SR-3 rela- 

 tive to SR-2 and SR-4 undoubtedly reflected their 

 greater precision; and perhaps the greater accu- 

 racy of SR- 1 relative to SR-3 was due to selection of 

 more appropriate strata. The systematic designs 

 were generally more accurate than the stratified 

 random designs. Only stratified random design 

 SR-1 achieved the accuracy of the systematic de- 

 signs. 



623 



