Nonrandom sampling

The KS limits make no distributional assumptions, but they do require that the samples are independent and identically distributed. Additional distributional assumptions can be made that could tighten the KS limits. For instance, assuming the nnderlying distribntion from which the samples came is normal yields a much tighter p-box. In practice, the assnmption abont independence of the individual samples may sometimes be hard to justify, such as when contamination hotspots are the focns of targeted sampling efforts. Techniqnes to account for nonrandom sampling are a topic of cnrrent research. 

Finished water supplies obtained from groundwater sources were tested by ERA for contaminants. It was reported that up to 10.8% of 158 nonrandom sample sites from across the United States contained detectable levels of 1,1-dichloroethane. The maximum concentration was 4.2 ppb (Westrick et al. 1984). 1,1-Dichloroethane was detected at a maximum concentration of 220 ppb in samples from 193 private wells in Rhode Island analyzed over a period of nine years (RIDH 1989). A maximum concentration of 40 ppb 1,1-dichloroethane was detected in 6 public drinking water systems in Rhode Island between April 1982, and April 1989 (RIDH 1989). 

Nonrandom samples, such as judgmental and spot samples, are useful in some situations—for example, in the preliminary assessment of a toxic waste site. Probabilistic and random samples, however, are fundamental to obtaining unbiased estimates if the true average value is being sought. A very basic idea, yet one that is often overlooked, is that to get a random sample, every part of the lot to be characterized must have an equal chance of being in the sample. 

However, it is important to understand that nonrandom samples can confirm the presence of a substance but not its absence. Also, while they can confirm presence, they cannot confirm (or estimate statistically) specific quantities. 

Nonrandom Sample Any sample taken in such a manner that some members of the defined population are more likely to be sampled than others. 

We would like the samples to be random, at least approximately, in order to do our inferences. In Chapter 7 we will look at how we can obtain an approximately random sample from the nonrandom sample we have obtained from the Markov chain. 

Nonrandom sampling of initial conditions for So, following Si So internal conversion, has been performed for chloroacetylene (H—C=C—Cl). The rejection method may be used to sample the different Aij transitions according to their relative probabilities. 

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