Statistics - Field Sampling: Principles and Practices in Environmental Analysis - page 160

TABLE 6.7 Abbreviated Table of Critical F Values

Numerator degrees of freedom

1 2

1 161.4 199.5

2 18.51 19.0

3 10.13 9.55

4 7.71 6.94

5 6.61 5.79

6 5.59 5.14

7 5.59 4.74

a Denominator degrees of freedom.

The above calculation using eight means rather than the 32 observations is not a good
approach because it does not account for variability in the observations. It assumes that
grids B3 through B6 are equivalent and that grids C3 through C6 are equivalent, which is
a huge assumption. It is possible to use a more complicated version of ANOVA to test
both the differences among grids and between areas at the same time; however, such a
procedure is beyond the scope of this topic. Two areas could be tested using the t-test;
however, it is subject to interpretation errors when applied to more than three areas.

6.11. LINEAR REGRESSION

Linear regression is used extensively in analytical procedures to determine the accuracy
of calibration curves. These calculations are thus extremely important because they
determine the accuracy of many analytical results. Because these are mostly used in the
commercial laboratory they will not be discussed here.

6.12. GEOSTATISTICS

There are many tools that have been and are used for estimating the unknown amount of
a component when it is between or surrounded by known amounts of the same
component. Simple linear interpolations using nearest neighbors, distance and a
weighting factor, and other methods have been developed and used. A method that has
gained much use and recognition is called kriging, which is based on geostatistics [9]. In
this discussion mathematics will be minimized and the results of various geostatistical
operations illustrated without the corresponding calculations.
The basic assumption of geostatistics is that samples taken close together are more
similar than those taken further apart; that is, there is a definable relationship between