Interpreting and Extrapolating (Estimating) Data

ERDC TN-DOER-C15

July 2000

Sample size required. This is distinct from statistical sample size; in this instance sample size

refers to the volume of material that is homogenized and then sampled for analysis. For example, if a

1.8-m (6-ft) core is taken, it will normally be subdivided into smaller sections that are thoroughly

homogenized. Then a very small subsample of each homogenized section is taken for chemical

analysis. Because sediments and the distribution of contaminants within the sediments are typically

very heterogeneous, homogenization volume is a relatively important factor in obtaining data that

are representative of site conditions. Additional information regarding the influence of sample size

and replication in capturing the effects of material heterogeneity is found in Olin-Estes and Palermo

(2000a).

Interpreting and Extrapolating (Estimating) Data. Examining the different ways in which

available data can be grouped and manipulated to reveal trends may be one of the most practical

approaches to determining where to sample and how many samples to take. Isaaks and Srivastava

(1989) present a clear discussion of a number of methods for grouping data and extrapolating

existing data to unsampled points, specifically directed at taking a practical approach to the

application of statistical theory. Although many of these methods will be helpful in maximizing

the information obtainable from a limited data set, the user should be aware that the results obtained

from statistical analysis of the data may differ for different assumptions. Statistical analysis offers

an improvement over "best guess" determinations of parameter distributions, but is not a foolproof

method. One reason in particular is that the geostatistical methods described by Isaaks and

Srivastava (1989) are based on the assumption that the values of interest are spatially continuous.

This is probably a reasonable assumption for natural, undisturbed materials over limited areas. For

disturbed materials, such as dredged material disposed in a CDF, this is a more difficult assumption

to make. However, the distribution of hydraulically placed dredged material in a CDF is a result

of natural processes (settling velocities), assuming the material has not been otherwise disturbed.

Under these circumstances, continuity may be a reasonable assumption for limited areas of the CDF.

For example, gradation of particle size and contaminant levels would be expected in moving from

the inlet area to the outlet of a CDF in which the material is hydraulically placed; two or three distinct

zones might be expected.

Interpreting data.

Univariate Data Data pertaining to a single variable can be presented very simply in a

relative location map (Isaaks and Srivastava 1989). For example, if a uniform grid is imposed

on the sampling area, and a sample taken from the center of each grid, the resulting value for

the parameter of interest can then be superimposed on a map of the area, giving an indication

of spatial distribution. A frequency histogram may also be used to give a quick visual on the

predominantly occurring values. A cumulative frequency table will be useful in illustrating

what percentage of samples fall below a certain threshold; this is a particularly useful

technique where contaminant concentrations are of interest. Tests for normality or lognor-

mality should be conducted as a matter of routine to establish whether or not the distribution

of the data falls within either of these two categories. Typically, environmental data do not,

but this should be done as a matter of practice. Summary statistics, including the mean, range,

minimum, maximum and standard deviation, should be determined for the data, which may

be grouped by zones if that provides a more meaningful result. The spatial distribution of

values will suggest appropriate groupings, if any.