FISHERY BULLETIN: VOL. 78. NO. 3 



0.324. This indicates that the assumption of in- 

 dependence is reasonable. 



Even though our results indicate that system- 

 atic sampling is slightly more precise for the type 

 of survey studied, the consequence of using a 

 systematic design when another design may be 

 more appropriate should be considered. 



We first examine the effects of using a system- 

 atic design when in actuality the data are ran- 

 domly distributed. Under these conditions the 

 expected value of S ^st of Equation (5) is equal to 

 the expected value of S^sys of Equation (6) and is 

 related to the expected value of S^ran of Equa- 

 tion (4) as follows: 



E (S'J 



nk-1 

 nk —n 



E (S;a„) 



Thus, random sampling will produce the lowest 

 variance and if total sampling effort ink) is 

 constant, the variance of systematic and stratified 

 random sampling will decrease relative to random 

 sampling as n decreases. All three design strate- 

 gies will result in unbiased estimates of the mean. 

 If there is a linear trend in the data such as 

 shown below 



Transect 12 3 4 5 6 7 8 

 Value 1 1.5 2 2.5 3 3.5 4 4.5, 



then as Cochran (1964:217) showed, stratified 

 random sampling is the same or more precise than 

 systematic sampling, which is the same or more 

 precise than random. The discrepancies increase 

 as 77 increases. 



If there are cycles in the data with a periodicity 

 equal to or a multiple of spacing of transects 

 such as 



Transect 12 3 4 5 6 7 8 

 Value 12 12 12 12, 



then systematic sampling is less precise than 

 stratified random sampling, which is less pre- 

 cise than random sampling. The discrepancies 

 increase as n increases. In addition, a single 

 systematic sample would result in a biased esti- 

 mate of the mean. 



Systematic sampling is equal to or more precise 

 than stratified random sampling which is equal to 

 or more precise than random sampling if a popula- 



tion in which a plot of correlations between pairs 

 of transects against distance between transects is 

 concave upward and greater than or equal to 

 (Cochran 1964). Since systematic sampling was 

 the most precise in this study, bias due to periodic- 

 ity in the data should not be a problem. 



Often in practice, investigators use a systematic 

 sampling scheme with only one sample and cal- 

 culate the variance as if the scheme is random. If 



V (j'sys' is <V (jranK as it appears to be for 

 rockfishes, the resulting confidence limits would 

 be conservative. The choice between precision and 

 estimation of V (5'sys) would depend on the objec- 

 tives of the survey and the difference between 

 V(jran) and V (5'sys). If V(ysys) is <V(5'ran) and 

 total number of transects is constant, increasiiig 

 the number of systematic samples {k) in order to 

 estimate V (^sys) causes the sampling scheme to 

 become more like a random scheme and results in 

 a corresponding increase in V (5'sys* relative to 



V (3' ran) (compare average variances shown in 

 Tables 4 and 5). 



A review by Cochran (1964) of a small number of 

 surveys of terrestrial populations also indicated 

 that systematic sampling is more precise than 

 stratified random. Although Cochran did not state 

 so, it also appeared that systematic sampling 

 would be more precise than random sampling. 



Two studies were found in the literature on 

 marine populations. Venrick (1978) found that on 

 the average systematic samples of chlorophyll in 

 the water column produced estimates of total 

 chlorophyll that were closer to the true value than 

 stratified random samples, but was not able to 

 compare precision of estimates for a given water 

 column because only one systematic sample was 

 taken from each column. She expressed a pref- 

 erence for stratified random sampling, because 

 there tended to be more temporal correlations of 

 deviations of the estimated values from the true 

 values for the systematic samples than for the 

 stratified random samples. The deviations were 

 usually < 5% and the temporal correlations prob- 

 ably could have been eliminated if the starting 

 points of the systematic samples were observed at 

 random instead of being fixed at the surface as 

 was done in her study. Fiedler (1978) examined 

 the relative precision of random, systematic, and 

 stratified systematic transect surveys of northern 

 anchovy, Engraulis mordax, school groups. He 

 found that random sampling was the least precise 

 of the three schemes. He also found that stratified 



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