Statistics data interpretation

Automated data interpretation will usually be done using some statistical or AI technique. Because statistical classifiers are similar in their use to neural networks [Sarle, 1994] we will not discuss them separately. 

Case-based reasoning. The main advantage of CBR systems for NDT data interpretation is that they can cope with data coming from inspection of varying constructions under varying conditions with various system settings due to their ability to learn from the data classified by the operator. In such situations no reliahle statistical classifier can be designed, and the rule-hased classifiers would be either very inefficient or unpractically complex. 

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

This book focuses on statistical data evaluation, but does so in a fashion that integrates the question—plan—experiment—result—interpretation—answer cycle by offering a multitude of real-life examples and numerical simulations to show what information can, or cannot, be extracted from a given data set. This perspective covers both the daily experience of the lab supervisor and the worries of the project manager. Only the bare minimum of theory is presented, but is extensively referenced to educational articles in easily accessible journals. 

This chapter provides a complementary perspective to that provided by Kramer and Mah (1994). Whereas they emphasize the statistical aspects of the three primary process monitoring tasks, data rectification, fault detection, and fault diagnosis, we focus on the theory, development, and performance of approaches that combine data analysis and data interpretation into an automated mechanism via feature extraction and label assignment. 

PDF approaches represent a statistically formal way of accomplishing local kernel definition. Although intent and overall results are analogous to defining kernels of PCA features, considerable work currently is required for PDF approaches to be viable in practice. It is presently unrealistic to expect them to adequately recreate the underlying densities. Nevertheless, there are advantages to performing data interpretation based on direct PDF estimation and, as a result, work continues. 

In this example, data interpretations are based on g-statistic limits. These are computed by assuming the data are normally distributed in the multivariate sense. The diagnostic limits are used to establish when a statistically significant shift has occurred. Charts based on these statistics and used in this manner are analogous to conventional SPC charts. 

In the following, the stages of the analytical process will be dealt with in some detail, viz. sampling principles, sample preparation, principles of analytical measurement, and analytical evaluation. Because of their significance, the stages signal generation, calibration, statistical evaluation, and data interpretation will be treated in separate chapters. 

A comparison of the imprecision of two methods may assist in the choice of one for routine use. Statistical comparison of values for the standard deviation using the F test (Procedure 1.2) may be used to compare not only different methods but also the results from different analysts or laboratories. Some caution has to be exercised in the interpretation of statistical data and particularly in such tests of significance. Although some statistical tests are outlined in this book, anyone intending to use them is strongly recommended to read an appropriate text on the subject. 

Statistical data can provide general information about how common a condition is, how many people have the condition, or how likely it is that a person will develop the condition. Statistics are not personalized, however—they offer estimates based on groups of people. By taking into account a person s family history, medical history, and other factors, a genetics professional can help interpret what statistics mean for a particular patient. 

The latter danger is, of course, potentially present any time any data interpretation is attempted, particularly if nature is assumed always to follow Eq. (1). The only course of action is to attempt to include as much theory in the model as possible, and to confirm any substantial extrapolation by experiment. It is erroneous, however, to presume that kinetic data will always be so imprecise as to be misleading. The use of computers and statistical analyses for any linear or nonlinear reaction rate model allows rather definite statements about the amount of information obtained from a set of data. Hence, although imprecision in analyses may exist, it need not go unrecognized and perhaps become misleading. 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

These sections include brief discussions of statistics, data presentation, and terminology. The two major points regarding statistics are that the litter (or mating pair) is the unit of comparison, and that significance tests can be used only as a support for the interpretation of results—the interpretation itself must be based on biological plausibility. That the litter is the unit of comparison is a guiding principle ofvirtually all texts on the subject (e.g., see ref 7). It should be stated that this guideline does not require that statistical analyses be performed on every study. It is implied that statistical analyses should be used as a tool for interpretation. 

Historical control data is an essential component of the study directors toolbox for interpreting reproductive and developmental toxicity data. Scientific judgment and expertise should be used to determine if historical control data is needed for interpretation of study data, which historical control data is appropriate, and how it should be used to support interpretation of a finding. This tool can be a valuable addition to a comprehensive assessment of the study data, which includes determining whether a dose-response is present and whether any statistically significant findings occurred. Sound data interpretation requires that the litter, not the fetus or pup, be used as the experimental unit in developmental and reproductive toxicity studies. For continuous data (e.g., fetal weight). 

We can easily quantify measurement error due to existence of a well-developed approach to analytical methods and laboratory QC protocols. Statistically expressed accuracy and precision of an analytical method are the primary indicators of measurement error. However, no matter how accurate and precise the analysis may be, qualitative factors, such as errors in data interpretation, sample management, and analytical methodology, will increase the overall analytical error or even render results unusable. These qualitative laboratory errors that are usually made due to negligence or lack of information may arise from any of the following actions ... 

In presentation and interpretation of results, NARL aims for objectivity, clear presentation, and statistical data treatment that is transparent to participants, internationally accepted and metrologically sound. Sources of chemical standards, statements concerning traceability and estimates of measurement uncertainty are included in the study report. 

When the analytical laboratory is not responsible for sampling, the quality management system often does not even take these weak links in the analytical process into account. Furthermore, if sample preparation (extraction, cleanup, etc.) has not been carried out carefully, even the most advanced, quality-controlled analytical instruments and sophisticated computer techniques cannot prevent the results of the analysis from being called into question. Finally, unless the interpretation and evaluation of results are underpinned by solid statistical data, the significance of these results is unclear, which in turn greatly undermines their merit. We therefore believe that quality control and quality assurance should involve all the steps of chemical analysis as an integral process, of which the validation of the analytical methods is merely one step, albeit an important one. In laboratory practice, quality criteria should address the rationality of the sampling plan, validation of methods, instruments and laboratory procedures, the reliability of identifications, the accuracy and precision of measured concentrations, and the comparability of laboratory results with relevant information produced earlier or elsewhere. 

Virial treatment provides a general method of analysing the low-coverage region of an adsorption isotherm and its application is not restricted to particular mechanisms or systems. If the structure of the adsorbent surface is well defined, virial treatment also provides a sound basis for the statistical mechanical interpretation of the adsorption data (Pierotti and Thomas, 1971 Steele, 1974). As indicated above, Kl in Equation (4.5) is directly related to kH and therefore, under favourable conditions, to the gas-solid interaction. 

Therefore, we have to analyse the variation of the rate of permeation according to the temperature (zj), the trans-membrane pressure difference (Z2) and the gas molecular weight (Z3). Then, we have 3 factors each of which has two levels. Thus the number of experiments needed for the process investigation is N = 2 = 8. Table 5.13 gives the concrete plan of the experiments. The last column contains the output y values of the process (flow rates of permeation). Figure 5.8 shows a geometric interpretation for a 2 experimental plan where each cube corner defines an experiment with the specified dimensionless values of the factors. So as to process these statistical data with the procedures that use matrix calculations, we have to introduce here a fictive variable Xq, which has a permanent +1 value (see also Section 5.4.4). 

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