A simple method to determine the sampling numbers in decision-making units with unknown variations of soil cadmium

Sampling number is one critical issue to achieve credible results when surveying soil contamination and making remediation decisions. Traditional methods based on a normal distribution for determining numbers of samples are not always optimal because most distributions of soil heavy metal concentrations followed a log-normal distribution. Moreover, the variation of soil heavy metal concentrations is a prerequisite for previous methods to determine sampling numbers. Unfortunately, the variation is often unknown before soil sampling. Therefore, a simple method under the log-normal distribution without relying on variation to determine quickly the sampling number (QSN) was developed for soil cadmium and compared with other methods based on classical statistics and Chebyshev inequality. Results showed that an equation as a function of sampling areas could be used to determine QSN (QSN = 18.44 × A^0.54 + 8.69, A is sampling areas, km²), with acceptable errors ranging from 13 to 33% at the sampling areas of 0.03-10 km². The developed simple method for QSN was easy to use and cost-effective without prerequisite on the estimation of variation. Moreover, when the sampling cost was enough and the improved accuracy was requested, the increased sampling numbers were recommended as 1.53 times as the number calculated by the simple method. Therefore, the proposed method is believed as a simple and cost-effective method to determine the sampling numbers of soil Cd in decision-making units with unknown variations.