A common task in regional studies of soil is to determine the mean values of particular soil properties from samples. Estimates of the number of observations needed for this purpose have usually been based on classical sampling theory without regard to spatial dependence in the data. As a result they have been unduly exaggerated and have often daunted investigators from pursuing their aims. This paper demonstrates a method for determining sample size, that is, the number of observations, taking account of spatial dependence. The method depends on knowing the semivariogram for the property of interest, which is used to calculate the variances in the neighborhood of each observation point. The variances are then pooled to form the global variance from which the standard error can be calculated The pooled value is minimized for a given sample size if all neighborhoods are of the same size, i.e., if the sampling points lie on a regular grid. If variation is isotropic, then an equilateral triangular grid is slightly better than a square one, though the latter will usually be preferred for convenience. Where there is simple anisotropy, a nonsquare rectangular grid aligned with its longer intervals in the direction of least variation is practically optimal. Examples show the relations between standard errors and sample sizes when sampling on regular grids and from which sample sizes can be chosen to achieve any desired precision. In all instances the sampling effort determined this way is less, and can be very much less, than would have been judged necessary using the classical approach.
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McBratney et al. (1983) studied this question.