Systematic stratified sampling

Figure 2.6 Stratified systematic sampling or systematic nonaligned sampling. This approach combines random and systematic sampling. The site is divided into regular spaced regions, and then a sample unit is chosen randomly within each of these regions.

The most common sampling modes are SRS, discussed previously, stratified random sampling, and systematic random sampling. SRS over time or space consists of identifying times or places totally at random to take the samples. Hie great disadvantage of this approach is that certain portions of the lot or production times may be under or over represented, and process stability cannot be monitored effectively. Consequently, we do not recommend SRS for long-term examination of lot characteristics. 

For stratified random sampling, a random time or spatial point is identified for every stratum, and a sample is taken from each one. For systematic random sampling, a random time or spatial point is identified for the sample for the first stratum only. Samples from all other strata are taken at the same relative time or from the same relative spatial point. For example, if samples are to be taken every hour, and the first time is randomly selected as 21 min past the hour, then every sample after that is also taken at 21 min past the hour. 

Systematic random sampling is very convenient both in a manufacturing environment and in the field because it is simple to implement and can easily be incorporated into a work schedule. A drawback, however, is that a long-term cycle will remain hidden if the selected times or points in space are synchronous (coincide) with that cycle. If cycles are suspected or need to be ruled out, then stratified random sampling should be used. 

A Latin Hypercube sampling method was used in the Risk simulation to generate the input parameter values from the probability distribution functions. This method was chosen over the Monte Carlo technique, which samples randomly from the distribution function and causes clustering when low probability values are not sampled due to insufficient computational sampUng iterations. In contrast, the Latin Hypercube stratified sampling technique systematically samples all segments (stratifications) of the distribution just once, resulting in fewer computational iterations required to produce a representative probability curve. 

One of the tools of sampling that can be used to reduce the variability of the sample is stratified sampling. Strata are identified as regions of the site that are expected to be uniform in character. The variance within the strata should be smaller than the variance between strata. Sampling points within the strata arc selected systematically or by some random process. In the soil environment, strata are often associated with soil types or as areas of known pollution versus areas where pollutants are not expected to be present. 

There are four major types of sampling methods random, stratified, systematic, and cluster. Random is by far the most commonly employed method in toxicology. It stresses the fulfillment of the assumption of avoiding bias. When the entire pool of possibilities is mixed or randomized (procedures for randomization are presented in a later section), then the members of the group are selected in the order that are drawn from the pool. 

Figure 3.2 Basic methods used for sampling (a) random (b) systematic (c) stratified random (1) - sub-division into equal areas (d) stratified random (2) - weight related to sub-area of habitat.

Three major random sampling techniques exist systematic sampling , simple random sampling , and stratified random sampling . (IPCS, 1992). All three techniques have a common purpose, namely that the samples are representative of the population or compartment to be sampled. 

Stratified systematic sampling, in which a single value of the property is taken from each block ... 

Measurement of the IR spectra of an ultrathin film on a powder sample may be carried out using transmission, diffuse transmittance (DT), diffuse reflectance (DR), or ATR techniques. As mentioned in Section 1.10, calculations to model the IR spectra of ultrathin films on powders under a different set of experimental conditions have not yet been realized. Compared to the stratified systems considered in Sections 2.1-2.6, optimization of the measurements on powders is significantly more complicated. Moreover, this problem has not yet been studied in a systematic fashion. Below current knowledge concerning the optimization of such measurements will be presented, with emphasis on the requirements of the sample. The technical aspects (the production of IR spectra of powders) are discussed in Section 4.2. 

---