Ranking tests, applications

The alpha spectrometry results were also significantly different at a 99% confidence level from the assigned NPL values (which deviations are 0% by definition). Application of the non-parametric Wilcoxon Signed Rank test, which, like the Rank Sum test, does not assume a normal distribution and does not require the removal of outliers, also resulted in a significant difference at a 99% confidence level between the alpha spectrometry results and the assigned NPL values (the absolute z-value being 3.72). 

The choice of an appropriate statistical method is important, and a method suitable for the comparison of two groups in terms of an ordinal outcome measurement is the Mann-Whitney/Wilcoxon rank-sum test (not to be confused with the Wilcoxon matched-pairs signed ranks test, which is appropriate for paired data - see later). It is both inefficient and inappropriate to use a qualitative data test (such as a simple chi-square) for such a measurement, and the application of quantitative data tests (such as one of the f-tests) is also invalid. 

The appeal is the ease of computation and applicability. The resulting statistics or p-values for the chosen filter method are then ranked and a cutoff chosen to select the most significant features. Examples of filter methods are t-tests, Wdcoxon rank-sum or signed-rank tests, Pearson correlation estimates, log-rank tests, and univariate regression techniques such as linear, logistic, or Cox proportional hazards. 

Following on from the above, various methods have been described to test and/or rank the livingness of polymerization processes." Ul7 20 All of these tests have limitations.. The following list paraphrases a set of criteria for living polymerization set out by Quirk and Lee11 who also critically assessed their applicability primarily in the context of living anionic polymerization. 

The results of such multiple paired comparison tests are usually analyzed with Friedman s rank sum test [4] or with more sophisticated methods, e.g. the one using the Bradley-Terry model [5]. A good introduction to the theory and applications of paired comparison tests is David [6]. Since Friedman s rank sum test is based on less restrictive, ordering assumptions it is a robust alternative to two-way analysis of variance which rests upon the normality assumption. For each panellist (and presentation) the three products are scored, i.e. a product gets a score 1,2 or 3, when it is preferred twice, once or not at all, respectively. The rank scores are summed for each product i. One then tests the hypothesis that this result could be obtained under the null hypothesis that there is no difference between the three products and that the ranks were assigned randomly. Friedman s test statistic for this reads... 

In the literature it is easy to obsetve that different types of fatigue tests rank materials in different orders. Thus, to predict a material s behavior for specific long-term end-use application, it is important to select the correct fatigue test. 

Although the uniaxial test has traditionally received the most attention, such tests alone may be insufficient to characterize adequately the mechanical capability of solid propellants. This is especially true for ultimate property determinations where a change in load application from one axis to several at once may strongly affect the relative ranking of propellants according to their breaking strains. Since the conditions usually encountered in solid rocket motors lead to the development of multiaxial stress fields, tests which attempt to simulate these stress fields may be expected to represent more closely the true capability of the material. 

Mann-Whitney Rank Sum Test, Sigmastat v 2.0 2 PERE = Potential Effluent Related Effect 3 ANOVA Analysis, a = 0.05 4 Canadian EEM database, unpublished data 5 not available, not applicable or not calculated 6 % PERE = Percent Potential Effluent Related Effect Observed = no. of expected effects divided by no. of endpoints calculated and multiplied by 100 7 LTF = lab-to-field. 

The development or application of new or existing toxicity ranking systems, based on the use of a battery of tests inspired by the WaterTox Program are presented. 

After completion of the WaterTox program, the test battery continued to be applied by laboratories from Argentina, Chile and Colombia to assess different types of environmental matrices. These initiatives facilitated the development or application of new or existing ranking systems that enabled evaluation of the effectiveness of biological treatment for the toxicity reduction of wastes and combined effluents. These studies are described herein. 

The proposed hazard assessment scheme (HAS) used in Colombia is a ranking system where toxicity data obtained from the application of a test battery enables one to determine the degree of toxicity of liquid samples on a relative basis. Test battery results are then integrated into the Potential Ecotoxic Effects Probe (PEEP) index formula developed by Environment Canada for the comparison of wastewaters (Costan et al., 1993). This index can be applied to evaluate the potential toxicity of industrial and municipal wastewaters, and to assess the effectiveness of toxicity abatement measures for effluents. This procedure is easy to apply and can be used with different batteries of tests (see Chapter 1 of this volume). 

Abrasion tests indicate the relative resistance of the polyurethane to two-bodied wear. When choosing a test, the test most suited to the application should be used. The ranking of the results varies with the type of... 

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