Before any experiments are conducted, the researcher must be aware of the limitations of sampling.
SAMPLING
Before
any experiments are conducted, the researcher must be aware of the limitations
of sampling. The usefulness of any analytical method is based on the adequacy
of sampling from the original population. Sampling techniques range in
complexity from random methods through stratified sampling to spatial and
adaptive sampling (Thompson, 2002). Sampling can be invasive, for example,
thieves to remove samples from batches of powder blend, or non-invasive, as
exemplified by laser optical techniques for particle sizing or spec-troscopy,
which are limited by the viewing volume usually dictated by the dimensions of
the laser. The bias introduced by unrepresentative sampling can be sufficient
to impair decisions and lead to erroneous conclusions about a process.
Consequently, representative sampling is a prerequisite to process analysis.
The
use of statistics in quality control is not novel. Indeed the principles were
established 70 years ago (Deming, 1938; Shewhart, 1939). These methods have
since been incorporated into concepts of statistical process control (Oakland
and Followell, 1986).
The
basic principles of statistical analysis are beyond the scope of this volume
and are the subject of a large number of foundational texts. In the realms of
experimental design, Box, Hunter, and Hunter published the seminal text on
“Statistics for Experimenters” in 1978. This remains a readable and informative
text for those beginning to develop statistical tools to investigate processes
with numerous variables.
Statistical
methods mitigate the experimental difficulties associated with error (noise),
confusion of correlation and causation, and complexity of the effects studied.
There are many sources of experimental error that can be overcome with adequate
experimental design and analysis. Frequently, exam-ples of apparent
correlations occur when two variable exhibit similar patterns that may exist
because of their independent relationship to a third variable. Sound principles
of experimental design, specifically randomization, provide a sound basis for
deducing causation. Effects are sometime so complex that they do not conform to
linearity or additive interpretation. Certain experimental designs allow for
interactive and nonlinear effects to be estimated with little transmission of
experimental error.
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