Statistical analysis, of data

When designing and evaluating an analytical method, we usually make three separate considerations of experimental error. First, before beginning an analysis, errors associated with each measurement are evaluated to ensure that their cumulative effect will not limit the utility of the analysis. Errors known or believed to affect the result can then be minimized. Second, during the analysis the measurement process is monitored, ensuring that it remains under control. Finally, at the end of the analysis the quality of the measurements and the result are evaluated and compared with the original design criteria. This chapter is an introduction to the sources and evaluation of errors in analytical measurements, the effect of measurement error on the result of an analysis, and the statistical analysis of data. 

The probabilistic nature of a confidence interval provides an opportunity to ask and answer questions comparing a sample s mean or variance to either the accepted values for its population or similar values obtained for other samples. For example, confidence intervals can be used to answer questions such as Does a newly developed method for the analysis of cholesterol in blood give results that are significantly different from those obtained when using a standard method or Is there a significant variation in the chemical composition of rainwater collected at different sites downwind from a coalburning utility plant In this section we introduce a general approach to the statistical analysis of data. Specific statistical methods of analysis are covered in Section 4F. 

The following experiments may he used to introduce the statistical analysis of data in the analytical chemistry laboratory. Each experiment is annotated with a brief description of the data collected and the type of statistical analysis used in evaluating the data. 

The stretching properties of polymers are investigated by examining the effect of polymer orientation, polymer chain length, stretching rate, and temperature. Homogeneity of polymer films and consistency between lots of polymer films also are investigated. Statistical analysis of data includes Q-tests and f-tests. 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Analysis and prediction of side-chain conformation have long been predicated on statistical analysis of data from protein structures. Early rotamer libraries [91-93] ignored backbone conformation and instead gave the proportions of side-chain rotamers for each of the 18 amino acids with side-chain dihedral degrees of freedom. In recent years, it has become possible to take account of the effect of the backbone conformation on the distribution of side-chain rotamers [28,94-96]. McGregor et al. [94] and Schrauber et al. [97] produced rotamer libraries based on secondary structure. Dunbrack and Karplus [95] instead examined the variation in rotamer distributions as a function of the backbone dihedrals ( ) and V /, later providing conformational analysis to justify this choice [96]. Dunbrack and Cohen [28] extended the analysis of protein side-chain conformation by using Bayesian statistics to derive the full backbone-dependent rotamer libraries at all... 

Statistical analysis of data from tests with an apparatus by Wesley has demonstrated satisfactory reproducibility of results not only among specimens in a particular test, but also from test to test undertaken at different times. 

Two important aspects are internal audits and product quality review. Internal audits are implemented to regularly monitor the compliance activities in drug manufacture and to ensure rectification to these activities if deviations occur. Trending and statistical analysis of data provide early warning of impending problems. Product quality review checks the relevance and adequacy of the manufacturing activities. It provides input to update and improve the quality system. 

In general, statistical analysis of data should always be used just as a tool. Under certain circumstances it may be more important to look for data clusters rather than just for statistical significances. As an example, if a compound decreases both litter size and fetal weight and leads to an increase in anomalies, this should always alert the investigator, independently of the statistical significance of each individual trend. 

Equipment used to generate, measure, or assess data should undergo a validation process to ensure that such equipment is of appropriate design and adequate capacity and will consistently function as intended. Examples of such equipment include scales balances analytical equipment (HPLC, GC, etc.) hematology, blood chemistry, and urine analyzers computerized equipment for the direct capture of data and computers for the statistical analysis of data. Because the data generated, measured, or assessed by such equipment are the essence of a nonclinical laboratory study, the proper functioning of such equipment is essential to valid study results. 

Although sample preparation was conducted under great care to minimize the analytical error, the potential for contamination does exist. As a precaution, tungsten and cobalt were removed from consideration during the statistical analysis of data because samples were powdered using a tungsten carbide cell grinder in which W is a major component and Co is a minor component. 

Oral contraceptives, cervical neoplasms, and adenosis A 1988 statistical analysis of data from the Royal College of General Practitioners study in Britain pointed clearly to an association between oral contraceptive use and... 

Manufacturing and environmental factors Recording and statistical analysis of data... 

Fig. 7.2. Statistical analysis of data on deposition of inhaled particles in the head (after Yu et al., 1981).

Statistics should follow the technical scrutiny, not the other way round. A statistical analysis of data of an interlaboratory study cannot explain deviating results nor can alone give information on the accuracy of the results. Statistics only treat a population of data and provide information on the statistical characteristics of this population. The results of the statistical treatment may give rise to discussions on particular data not belonging to the rest of the population, but outlying data can sometimes be closer to the true value than the bulk of the population (Griepink et al., 1993). If no systematic errors affect the population of data, various statistical tests may be applied to the results, which can be treated either as individual data or as means of laboratory means. When different methods are applied, the statistical treatment is usually based on the mean values of replicate determinations. Examples of statistical tests used for certification purposes are described elsewhere (Horwitz, 1991). Together with the technical evaluation of the results, the statistical evaluation forms the basis for the conclusions to be drawn and the possible actions to be taken. 

The confidence limits for the first three variables were estimated on the basis of judgment and experience. The last was determined from a statistical analysis of data from 10 individual measurements with Eqs. (8) and (29). From Eq. (51) we calculate... 

Response variables can be plotted in a number of ways. The statistical analysis of data derived from radioligand-antibody interactions and the added information that can be derived from logit-log plots has been considered in detail. ... 

The computer is an excellent tool for statistical analysis of data and for solving mathematical problems. Commercial software packages (Table 1) are generally used for statistical analysis. The scientist often works with the statistician to design an experiment and determine the most appropriate statistical method to analyze the... 

Trend analysis of results at individual sample locations may be more useful than statistical analysis of data summaries because each sampling location probably reflects a unique situation. Non-traditional groupings of data may also be valuable. For example, grouping all locations where a specific activity was noted on the sample collection form, grouping all data collected during a specific time frame (i.e., just after lunch, or near the end of a production cycle), or grouping all data for each operator may reveal specific problem areas. 

Cluster analysis A statistical analysis of data with respect to certain characteristics in order to find out whether those data fall into recognizable groups (clusters). 

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