Statistics - Field Sampling: Principles and Practices in Environmental Analysis - page 157

From Table 6.5 we see that there is no value given for 3-1 or n =2; thus we cannot use
this method to make this determination.
Extreme care should be taken in disregarding or discarding data. It is very easy to
produce skewed or biased data by discarding data without a firm, unbiased basis for their
elimination. The best reason for discarding a data point is having recorded data showing
how, why, and where an error has occurred [5].
6.9. HOW MANY SAMPLES?
Another area of concern is to determine how many samples need to be taken. The
concern is both from the standpoint of obtaining an accurate description of the situation
occurring in the field and in minimizing the cost of sampling and analysis.
A simple method of calculating the needed number of samples is given by the equation
In this equation n =the number of samples to be taken. The t is from the t -table (Table 6.5)
for the confidence interval needed. The variability in the samples is represented by s 2 ,
which is the variance. D is the acceptable variability in the mean estimate. There are two
ways of handling this equation. One is to assume that the area is to be remediated to no or
0 contamination. The other is to define the level to which the contaminant is to be
reduced.
This relationship can be handled in several ways, depending on the sampling needs.
One could specify a value for n and calculate either s 2 or D 2 . On the other hand, s 2 and
D 2 may be known or assumed and n calculated. One way to estimate s 2 is to use (R/n).
Here R is the expected range in the sampling, or in this example ( R /4) 2 is an estimator of
the true s 2 for area B5.
The applicability of this equation is complicated by several factors. One is that the
variance or variability may be different at different places or depths in a field. If materials
are to be removed, only the number of samples needed to determine the boundary
between an acceptable and unacceptable level of a component needs be calculated. If this
is done and the cutoff is 500 ppm, then in B5 we could use 724.5-500=224.5 as R . This
would then be used to calculate the number of samples to be taken. In this case, (224.5/4)
2 or (56.12) 2 would be used as an estimator of s 2 .
If the samples have very different means and small standard deviations, it is not
necessary to take large numbers of samples. This is also true if the sample means are far
from the target level. Only when the level is close to or below the target or desired level
will one need to use this equation [6, 7].