Power, statistical comparison

There are a plethora of criteria that should be applied to ensure that the experimentally determined parameters provide a true reflection of the physical interactions that they represent. However, if the data are to be credible they must demonstrate an internal consistency. The equilibrium dissociation constant should, for example, be the same if it has been determined from equilibrium saturation assays or by calculation from the appropriate kinetic constants if it is not, this implies that the physical characteristics of the interaction are outside the criteria for which the equations have been developed, i.e., those rehearsed in Section 2.7. Statistical comparison of data sets must also be carefully assessed here the availability of the powerful computation facilities available on most laboratory desks has taken much of the drudgery out of such analysis. 

In thip appendix, a summary of the error propagation equations and objective functions used for standard characterization techniques are presented. These equations are Important for the evaluation of the errors associated with static measurements on the whole polymers and for the subsequent statistical comparison with the SEC estimates (see references 26 and 2J for a more detailed discussion of the equations). Among the models most widely used to correlate measured variables and polymer properties is the truncated power series model... 

A common statistical comparison, is between the test material(s) and the control material(s), to detect any differences beyond those that would occur as a consequence of random probability. In general, the smaller the size of the panel, the lower power the test will have, i.e. it will be less likely to identify genuine differences should they exist. Whether this is an issue hinges on the size of difference that the investigator would like to detect, with the optimum panel size determined by the anticipated variability of the results, which may not be known. A pragmatic approach should be taken toward panel size selection, with a sufficient number to allow some meaningful analysis, but that is not unwieldy in terms of running the study or that is prohibitively costly. 

Tests on Cable Constructions. The Association of Edison Illumination Companies (AEIC) has approved an accelerated cable hfe test in which typical underground distribution power cables can be statistically compared based on their resistance to water treeing (number of days to fail). The comparison can be made by varying the type of insulation and/or other cable layers in an environment that contains hot water (90°C) under 8V/fi (200 V/mil) voltage stresses (four times the typical power cables operating voltages). 

In this paper, we discuss studies based on comparison with background measurements that may have a skew distribution. We discuss below the design of such a study. The design is intended to insure that the model for the comparison is valid and that the amount of skewness is minimized. Subsequently, we present a statistical method for the comparison of the background measurements with the largest of the measurements from the suspected region. This method, which is based on the use of power transformations to achieve normality, is original in that it takes into account estimation of the transformation from the data. 

Using Eqs. (5-42)-(5-46) in Section 5.3.2.2 with iterative calculations, the predicted CHF were compared with Columbia University data (Fighetti and Reddy, 1983). The comparison was made by examining the statistical results of critical power ratios (DNBRs), where... 

On the other hand, it also shares some of the disadvantages of the Durbin-Watson Statistic. It is also based on a comparison of variances, so that it is of low statistical power. It requires many more samples and readings than the Durbin-Watson statistic does, since each sample must be measured many times. In general, it is not applicable... 

Group comparison tests for proportions notoriously lack power. Trend tests, because of their use of prior information (dose levels) are much more powerful. Also, it is generally believed that the nature of true carcinogenicity (or toxicity for that matter), manifests itself as dose-response. Because of the above facts, evaluation of trend takes precedence over group comparisons. In order to achieve optimal test statistics, many people use ordinal dose levels (0,1,2..., etc.) instead of the true arithmetic dose levels to test for trend. However, such a decision should be made a priori. The following example demonstrates the weakness of homogeneity tests. 

Multiple confounding issues make interpretation and comparison of these results difficult. Differences in MTX dose and schedule clearly may limit the reproducibility of studies. Furthermore, incomplete ascertainment of toxicity, particularly when performed retrospectively, may impact on study validity. Finally, modest and heteregenous sample sizes clearly limit the available statistical power to detect clinically meaningful differences in treatment response. 

Criteria for the adequacy of epidemiologic studies are well recognized (Monson, 1990). They include, for example, proper selection and characterization of exposed and comparison groups, adequacy of the duration and quality of follow-up, proper identification and characterization of confounding factors, attention to potential methodologic biases, appropriate consideration of latency effects, valid ascertainment of the causes of morbidity and death, and the ability to detect specific responses. The statistical power to detect a particular response... 

The Wilcoxon s Rank-Sum Test (WRST) is a non-parametric alternative. The WRST is robust to the normal distribution assumption, but not to the assumption of equal variance. Furthermore, this test requires that the two groups of data under comparison have similarly shaped distributions. Non-parametric tests typically suffer from having less statistical power than their parametric counterparts. Similar to the /-test, the WRST will exhibit false positive rate inflation across a microarray dataset. It is possible to use the Wilcoxon test statistic as the single filtering mechanism however calculation of the false positive rate is challenging (48). 

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