Statistical tests, application

Roggo, Y., Duponchel, L., and Huvenne, J.-P. (2003), Comparison of supervised pattern recognition methods with McNemar s statistical test Application to qualitative analysis of sugar beet by near-infrared spectroscopy, Anal. Chim. Acta, All, 187-200. 

There are several statistical tests for reaching such a decision, the most popular probably being the "Chauvenet" criterion. Application of this criterion here uses the results shown in figure 7. 

Results from the analysis of the RM and the certified value and their uncertainties are compared using simple statistical tests (Ihnat 1993,1998a). If the measured concentration value agrees with the certified value, the analyst can deduce with some confidence that the method is applicable to the analysis of materials of similar composition. If there is disagreement, the method as applied exhibits a bias and underlying causes of error should be sought and corrected, or their effects minimized. 

Before undertaking a discussion of the mathematics involved in the determination of reaction rates is undertaken, it is necessary to point out the importance of proper data acquisition in stability testing. Applications of rate equations and predictions are meaningful only if the data utilized in such processes are collected using valid statistical and analytical procedures. It is beyond the scope of this chapter to discuss the proper statistical treatments and analytical techniques that should be used in a stability study. Some perspectives in these areas can be obtained by reading the comprehensive review by Meites [84], the paper by P. Wessels et al. [85], and the section on statistical considerations in the stability guidelines published by FDA in 1987 [86] and in the more recent Guidance for Industry published in June 1998 [87],... 

Y data. The data set used for this example is from Miller and Miller ([1], p. 106) as shown in Table 58-1. This dataset is used so that the reader may compare the statistics calculated and displayed using the formulas and figures described in this reference with respect to those shown in this series of chapters. The correlation coefficient and other goodness of fit parameters can be properly evaluated using standard statistical tests. The Worksheets provided in this chapter series can be customized for specific applications providing the optimum information for particular method comparisons and validation studies. 

Table 2.5, together with the subsequent worked examples, illustrates the application of the statistical tests to real laboratory situations. Equation (2.10) is a simplified expression derived on the assumption that the precisions of the two sets of data are not significantly different. Thus the application of the F-test (equation (2.8)) is a prerequisite for its use. The evaluation of t in more general circumstances is of course possible, but from a much more complex expression requiring tedious calculations. Recent and rapid developments in desk top computers are removing the tedium and making use of the general expression more acceptable. The references at the end of the chapter will serve to amplify this point. 

Let us consider again the system defined in Example 5.1. From the application of the global statistical test, gross errors were detected among the data set as indicated in Example 7.1. Now the serial elimination strategy will be applied to isolate the source of gross error, that is to identify which set of measurements contains gross error. 

The FID library was applied to the task of predicting the protein folds encoded in complete genomes using the recently developed program IMPALA, which is a modification of PSI-BLAST that effectively reverses the search protocol (Schaffer et al., 1999). PSI-BLAST compares a PSSM to a database of sequences by contrast, a single search by IMPALA is a comparison of a sequence to a library of PSSMs (Fig. 3B). Statistical tests with IMPALA have shown that the theory used for the evaluation of BLAST results is applicable with minimal modifications. 

Some statistical tests are specific for evaluation of normality (log-normality, etc., normality of a transformed variable, etc.), while other tests are more broadly applicable. The most popular test of normality appears to be the Shapiro-Wilk test. Specialized tests of normality include outlier tests and tests for nonnormal skewness and nonnormal kurtosis. A chi-square test was formerly the conventional approach, but that approach may now be out of date. 

Notification and updated batch record Stability Application/ compendial requirements plus multipoint dissolution profiles in three other media (e.g., water, 0.1/VHC1, and USP buffer media at pH 4.5 and 6.8) until >80% of drug released or an asymptote is reached Apply some statistical test (f2 test) for comparing dissolution profiles No biostudy... 

The distinction between electrophilic and electron-transfer mechanisms of addition reactions to vinyl double bonds of ArX—CH=CH2 (X = S, O, Se) has been achieved by studying substituent effects. Specifically, the effects of meta and para substituents on the rates of electrophilic additions correlated with Hammett radical cations correlates with statistical tests. The ofclcctrophilicj/o-1 (FT) dichotomy is in accord with the conventional paradigm for cr/cr+ correlations and further support has been found by ah initio calculations. Interestingly, the application of this criterion to the reactions of aryl vinyl sulfides and ethers with tetracyanoethylene indicates that cyclobutanes are formed via direct electrophilic addition to the electron-rich alkene rather than via an electron-transfer mechanism.12... 

Rpl =0.179, Rp2 = 0.202, Ral =0.207, and Ra2 = 0.249. Statistical tests show that model a2 can be rejected in favor of aj. The choice between the parallel models pj and p2 is more difficult but examination of model p2 shows that this model cannot be fully hydrogen bonded, and hence p2 is rejected in favor of pj, which also gives better x-ray agreement. Thus models pj and aj were taken as the most likely parallel and antiparallel models for further refinement. At this point the unobserved data were included, calculating weighted R and R" where w = l for observed and w=l/2 for unobserved reflections. F(hkl) for an unobserved reflection was set at two thirds an assigned threshold and was included only if the calculated structure amplitude exceeded the threshold. The final residuals for the two models were Rpi = 0.233, R = 0.299, and Rj = 0.215, R j = 0.270. Application of the Hamilton statistical test (13) to these data indicates that the a model can be rejected at the 99.5% level. 

The Reliability of Measurements. The Analysis of Data. The Application of Statistical Tests. Limits of Detection. Quality Control Charts. Standardization of Analytical Methods. 

A promising study of the lattice gas model is the computer statistical tests (by the Monte Carlo method). Such calculations have been carried out since the mid-1960s (see, for example, refs. 66 and 105). For calculations of gas adsorption on metals, see refs. 106-110. However, no systematic application of the Monte Carlo method to heterogeneous reactions has been carried out it is to be done in the future. 

The choice between the baseline and alternative conditions is easy if the mean concentration significantly differs from the action level. But how can we determine, which of the two conditions is correct in a situation when a sample mean concentration approximates the action level This can be achieved by the application of hypothesis testing, a statistical testing technique that enables us to choose between the baseline condition and the alternative condition. Using this technique, the team defines a baseline condition that is presumed to be true, unless proven otherwise, and calls it the null hypothesis (H0). An alternative hypothesis (Ha) then assumes the alternative condition. These hypotheses can be expressed as the following equations ... 

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