Significance testing problem

There are two goals for significance testing. The first is to estimate ttie number of clusters in the data and the second is to identify the amount of overlap between ttie various clusters. Unfortunately, no completely satisfactory statistical test exists. One is faced with a difficult decision, either to ignore the problem or to make do with available testing methods. The simplest, most straight-forward test is chosen for this study, the sum of squares ratio test. Even though the test method may be flawed, it is necessary to underscore the importance and usefulness of statistical measures of cluster separation. 

The Group 6 compounds glucose and glycine were not tested at the small-scale level because previous work suggested that they would not be soluble in supercritical fluid CO2. Additionally, chloroform was not tested at this level because it is undoubtedly extractable but would pose significant trapping problems because of its relatively high vapor pressure. 

The asymmetric spin boson model presents a significantly more challenging non-adiabatic condensed phase test problem due to the asymmetry in forces from the different surfaces. Approximate mean field methods, for example, will fail to reliably capture the effects of these different forces on the dynamics. 

The Northern States Power facility experienced significant operational problems with their electrolyzed pebble bed scrubber during tests burning from 7 to 9 percent TDF (mixed with woodwaste) in a retrofitted fluidized combustion bed boiler. The electrostatic voltage dropped to near zero on several occasions on others, the collection efficiency declined continually. Several reasons for this are suggested. First, the ash during the test was more cohesive... 

One outcome of the dependence of the NOEL/ NOAEL on the statistical significance test is that it tends to penalize chemicals for which there is more or better data. To remedy this problem, the benchmark dose (BMD) concept was introduced as an alternative approach. The BMD depends on the specification of a low level effect that would typically be unobservable. The endpoint may be the specified percentage (5 or 10%) above background of a population for an endpoint deemed to be adverse. Since the endpoint is defined, determinations for different chemicals and different data sets tend to be more comparable. 

The previous problem made use of the Prandtl s boundary layer approach. Although it is widely applied, it would be worth to examine this approximation on a test problem, where the complete Navier-Stokes equations should be solved. Here is such a test problem that has also its own significance. 

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