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August, 2004
Are Your Samples Degenerate?
Several sampling tools and
techniques are useful for splitting an entire lot of loose, solid
material, such as grains, pellets, and soil, into two or more fractions.
Each fraction separated from the lot is a potential sample, and the
actual sample is "selected" from among these. Splitting is a
form of subsampling that can be done in sequence using the same or
different methods to obtain smaller and smaller quantities for the amount
required for chemical and/or physical analyses. The riffle splitter,
discussed in our last E-Newsletter (What's
Wrong With This Picture?), is a good example. The most important principle
to follow with a splitting technique is to select the fraction that is to
be the sample (1) after the lot has been split and (2) at random.
If these two conditions are not satisfied, then the splitting is said to
be degenerate (Chapter 22
from Gy, reference below). Knowing in advance which fraction is to be the
sample provides opportunities for unconscious bias or even fraud. This
happens, for example, when one of the receiving bins from a riffler is not
chosen at random after the lot has been split in two.
In previous newsletters, we have given Gy's Principle of
Correct Sampling. All constituent elements of the lot have an equal
opportunity of being in the sample, and the sample integrity is preserved
both during and after sampling. Correct Selection in a splitting
process is defined in a similar way. All fractions separated from the lot
are potential samples that have equal probabilities of being
selected as the actual samples. This means that an
equiprobable random selection process must be used after the
split. We give three examples of correct and incorrect selection. Example 1: The
material is moving, and the sampling device is stationary. The
riffle splitter discussed earlier is a case in point. Two potential
samples, one in each receiving bin, are produced after passing the
material through the riffler. One of the two potential samples is
chosen at random, such as by tossing a fair coin, and becomes the actual
sample. Degenerate sampling occurs in this case when the bin is
selected in advance. Gy reports a bias of over 10% on the mass and over 2%
on the lead content of a galena ore in a case where two sampling errors
occurred. The riffler was used incorrectly, and the same bin was selected
for the next stage of riffling in a sequence of four splits. Example 2: The material is stationary, and the sampling tool is moving. With alternative shoveling, shown below, alternate scoops or shovels of material are put into two piles. Each pile is a potential sample, and a coin toss can be used to select the actual sample. Degenerate sampling occurs when one of the piles is selected in advance. For example, when the lot contains coarse fragments with a diameter larger than about 1/3 of the shovel width and which contain more of the constituent of interest, the operator can influence the result. If s/he is able to preselect the pile that will be the actual sample, then s/he can selectively help some of the coarsest fragments fall from the shovel when desired. 
Example 3: Both the material
and the sampling tool are moving. A sectorial divider feeds a lot
of material into a set of receiving bins. Either the feeder rotates over
the bins, or the bins rotate under the feeder. As in the previous
examples, the material in each bin is a potential sample. The actual
sample selection must be done at random and after the
splitting is complete. Unfortunately, some dividers are used not to split
the entire lot but rather to feed material only until a specified mass is
obtained. This technique violates Gy's Principle of Correct Sampling
because part of the lot has no chance of being in the sample. Moral: To avoid degenerate splitting, select
the fraction that is to be the actual sample (1) after splitting
the entire lot and (2) at random. More information about sampling equipment and
procedures for solids, liquids, and gases is available in the short
introductory book A Primer for Sampling
Solids, Liquids, and Gases, by Dr. Patricia L. Smith.
"Your decisions are
only as good as your samples." Newsletters | About
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