Statistical criteria

Usually, 10 to 20 measurements are made of the isotope ratio for one substance. Sometimes, one or more of these measurements appears to be sufficiently different from the mean value that the question arises as to whether or not it should be included in the set at all. Several statistical criteria are available for reaching an objective assessment of the reliability of the apparently rogue result (Figure 48.10). Such odd results are often called outliers, and ignoring them gives a more precise mean value (lower standard deviation). It is not advisable to remove such data more than once in any one set of measurements. 

Statistical Criteria. Sensitivity analysis does not consider the probabiUty of various levels of uncertainty or the risk involved (28). In order to treat probabiUty, statistical measures are employed to characterize the probabiUty distributions. Because most distributions in profitabiUty analysis are not accurately known, the common assumption is that normal distributions are adequate. The distribution of a quantity then can be characterized by two parameters, the expected value and the variance. These usually have to be estimated from meager data. 

Different tests for estimation the accuracy of fit and prediction capability of the retention models were investigated in this work. Distribution of the residuals with taking into account their statistical weights chai acterizes the goodness of fit. For the application of statistical weights the scedastic functions of retention factor were constmcted. Was established that random errors of the retention factor k ai e distributed normally that permits to use the statistical criteria for prediction capability and goodness of fit correctly. 

On the other hand, it is all too easy to find QSARs that fail one or other of the statistical criteria, or have other faults. An early example, involving the tumor-promoting ability of aniline mustard drugs, was [46] ... 

Usually aquatic toxicity of chemicals with general narcosis mechanism of action is described by the octanol/water partition coefficient [73]. However, log is a composite descriptor which has components of molecular volume and H-bond acceptor terms. Raevsky and Dearden [74] therefore used molecular polarizabihty (as a volume-related term) and the H-bond acceptor factor instead of log to model aquatic toxicity (log LC50) to the guppy for 90 chemicals with general narcosis mechanisms. This excellent correlation has statistical criteria better than that obtained for the same data using log Pofy, ... 

Sample size and test intervals based on statistical criteria for each attribute examined to assure valid estimates of stability ... 

TableCurve. Jandel Scientific, 65 Koch Road, Corte Madera CA 94925. Automatically fits 3000 different xy relations with statistical criteria. 

C. P. Brink and A. L. Crumbliss, Inorg. Chem. 23, 4708 (1984). A number of LFER are included with a short discussion of the strict statistical criteria for isokinetic relationships. 

How the baseline measurement will be used in relation to the critical evaluable endpoints must be determined before analysis. Comparison of two or more treatments usually takes into account the differences between baseline values between treatment groups at the point of randomisation. The way in which the analysis will influence the report and publications needs to be decided, as some regulatory authorities have their own statistical criteria that need to be observed (e.g. for bioequivalence studies ). 

But even when the constitution of the polymer may be regarded as essentially homogeneous, considerations analogous to the previous ones may apply at the stereochemical level. For this reason the study of macromolecular stereoisomerism calls for a twofold approach. On the one hand, one must turn to ideal models that permit the identification of the type of structure existing in the polymer on the other, statistical criteria must be used to determine to what... 

Analysis of the poly(methyl methacrylate) sequences obtained by anionic polymerization was undertaken at the tetrad level in terms of two different schemes (10) one, a second-order Markov distribution (with four independent conditional probabilities, Pmmr Pmrr, Pmr Prrr) (44), the other, a two-state mechanism proposed by Coleman and Fox (122). In this latter scheme one supposes that the chain end may exist in two (or more) different states, depending on the different solvation of the ion pair, each state exerting a specific stereochemical control. A dynamic equilibrium exists between the different states so that the growing chain shows the effects of one or the other mechanism in successive segments. The deviation of the experimental data from the distribution calculated using either model is, however, very small, below experimental error, and, therefore, it is not possible to make a choice between the two models on the basis of statistical criteria only. 

We are fortunate in this example to have represented our data by a form of equation which happened to match exactly that obtained from the theoretical mechanism. Often a number of different equation types will fit a set of experimental data equally well, especially for somewhat scattered data. Hence, to avoid rejecting the correct mechanism, it is advisable to test the fit of the various theoretically derived equations to the raw data using statistical criteria whenever possible, rather than just matching equation forms. 

Validation of QSAR models is one of the most critical problems of QSAR. Recently, we have extended our requirements for the validation of multiple QSAR models selected by acceptable statistics criteria of prediction for the test set (19). Additional studies on this critical component of QSAR modeling should establish reliable and commonly accepted good practices for model development, which should make models increasingly useful for virtual screening. 

The form of the equation is specified in advance, and the best correspnding values of any constants are found by least squares. The goodness of fit of several assumed equations are compared by statistical criteria such as the correlation coefficient or the F-test. When the number of sets of data equals the number of unknown constants in the equation, the constants are found by simultaneous solution. Otherwise a least squares regression is used. 

While none of the changes with regard to size have as yet met the statistical criteria set forth here, they are in their... 

While this subjective approach was perfectly justifiable for a small experimental analysis, it could play no part in the large analysis contemplated for which all decisions had to be made in an automatic blackbox fashion. We dealt with this problem by writing a piece of software that automatically cut out the innermost parts of rotation curves that were judged, according to objectively defined statistical criteria, to be unusually affected by the presence of the bulge. The effectiveness of this process was tested by means completely independent of the present considerations. 

An analysis of EPA s STORET (STOrage and RETrieval) database for 1980-82 showed that based on the statistical criteria used, 2,3,7,8-TCDD was detected but at concentrations too low to be quantified in surface-water samples collected at sampling sites (Staples et al. 1985). The sampling sites in the STORET database included both ambient and pipe sites. Ambient sites included streams, lakes, ponds, wells, reservoirs, canals, estuaries, and oceans and were intended to be indicative of general U.S. waterway conditions. Pipe sites referred to municipal or industrial influents or effluents (Staples et al. 1985). 

Nonlinear regression should be used for curve-fitting. For A) experiments, the inhibition equation that best fits the data determined by statistical criteria reflects the type of inhibition and Ki value. 

It is important to stress here that for the present discussion we do not vary the model rather, we determine the best parameters for a given model. The determination of the correct model is a task that is significantly more difficult. One possible approach is to fit the complete set of possible models and select the best one defined by statistical criteria and chemical intuition. Because there is usually no obvious limit to the number of potential models, this task is rather daunting. As described in Chapter 11, Multivariate Curve Resolution, model-free analyses can be a very powerful tool to support the process of finding the correct model. 

Assay performance criteria for biopharmaceuticals are often highly variable therefore strict statistical criteria that attempt to rigorously establish traditional in vivo bioequivalence may not always be appropriate. In some cases an assessment of rate and extent of absorption as indicated by the maximum concentration (Cmax), time of maximum concentration (Tmax) and area under the curve (AUC) may be needed. In other cases complicating factors related to binding proteins, endogenous concentration, and unusual concentration-time profiles may need to be considered [15]. In cases where complications may arise from immune response to heterologous proteins, cross-over designs are inappropriate. 

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