SCHERBA and GALLUCCI: SYSTEMATIC SAMPLING OF INFAUNA 



(a = 0.05, 6 df). All six of the null hypotheses (2) 

 were rejected. Thus the bivalve distributions 

 between subareas are different. To investigate the 

 sources of this difference in distribution, the 

 bivalve assemblage on similarly numbered strata, 

 in all combinations of subarea pairs and season 

 were examined using chi-square tests (a = 0.05, 2 

 df). Nineteen of these 36 null hypotheses of 

 homogeneity (2) were rejected. Thus, the bivalve 

 distribution is not consistent in either time 

 (season) or space (sample subareas). 



The homogeneity (2) of the bivalve assemblage 

 between the three seasons for a single stratum 

 was examined using chi-square tests (a = 0.05, 4 

 df). Four of the eight null hypotheses were reject- 

 ed. The homogeneity (2) of the bivalve assemblage 

 between strata, in a given subarea, in a given 

 season was also examined using chi-square tests 

 (a = 0.05, 2 df ). Two of the 12 null hypotheses were 

 rejected. Thus, a definitive statement about the 

 dependence between bivalve presence and season 

 cannot be made. Furthermore, the differences 

 between the strata of a single subarea are appar- 

 ently minimal. 



DISCUSSION 



The sediment and macrofauna data collected in 

 the Garrison Bay study were analyzed under the 

 assumption of intrasample independence within 

 each subarea (i.e., the contents of one sampling 

 unit neither predicts nor influences the contents of 

 any other unit). The assumption is based upon the 

 homogeneity of macrofauna and sediment compo- 

 sition within study subareas. Macrofaunal 

 homogeneity is defined here as meaning that all 

 members of a given species on a given stratum are 

 described by the same spatial probability dis- 

 tribution. Although specific probability distribu- 

 tions were not fit to the data, chi-square and 

 Kolmogorov-Smirnov tests are legitimately ap- 

 plied to the sample data. 



There are K different systematic samples, each 

 of size n, that could be chosen (recall N = nK); one 

 of these is selected at random. The sample mean of 

 the rth such systematic samples, y,, and the 

 population mean, Y, are defined respectively as: 



^i =( i 2/ij)/nand 



i" = ( 2 i yuVnK 

 i = 1 y = 1 



where y^, is the attribute of interest in the sample 



(e.g., the number of individuals of a given species 

 in the jth sample). Since systematic sampling is a 

 probability sampling scheme, a valid expression 

 for the variance of the sample mean is 



var(^) = ( V {% -Yf)/K 



i = 1 



(Sukhatme and 

 Sukhatme 1970). 



Alternative expressions of this quantity have been 

 derived (Cochran 1963). No difficulties arise in 

 using any of these forms of var {ij, ) in theoretical 

 studies, but in applications of systematic sam- 

 pling, no reliable estimate of var {y) is known 

 from taking only one sample of size n from an 

 area. This is a disadvantage of SSS. In practice, 

 approximations to var {y, ) are used as estimators 

 of this statistic. The texts by Cochran (1963:224- 

 227) and Sukhatme and Sukhatme (1970:369-370) 

 present several methods to approximate var {%) 

 from a single systematic sample. However, if m 

 (^2) independent systematic samples (each of size 

 n) are taken on the same stratum at the same time, 

 an exact (as opposed to an approximate) estimate 

 of var {%) is possible. Letting % represent the 

 sample mean from one of the m systematic sam- 

 ples, then 



n 



var {y) = ^ | j {y^ - yf/m{m - 1) 



where ^ = ( i '% )/m 



i = 1 



(Sukhatme and 

 Sukhatme 1970). 



In this study the estimate of the variance of the 

 sample means was approximated by the variance 

 calculated for a simple random sample (Cochran 

 1963). This is reasonable because of the within- 

 area homogeneity of the sediment and 

 macrofauna in each of the four study areas. Of 

 course, it is preferable to take at least two in- 

 dependent systematic samples, each of size n. 



Cochran (1963) discussed the difference in 

 precision between random and systematic sam- 

 pling based on the results of these methods upon 

 certain types of population data. Special attention 

 should be given to data which is either inherently 

 periodic or subject to a periodic input, e.g., tidal 

 forces. Under these circumstances, K must be 

 carefully selected. Periodic variation in the north- 

 south direction in Garrison Bay is considered to be 



unlikely. 



The use of SSS allows strata to be placed at tidal 

 heights where experimental interest is focused. 

 Thus, samples may be taken at fixed tidal levels as 



945 



