Statistical methods data evaluation

The purpose of statistical evaluation of sample data is to extrapolate from a collection of individual events (e.g., 30 min of process time) to the entire population of events (e.g., 8-h shift). Because microbial monitoring data usually measure the impact of human activity, which is not reproducible exactly from one event to the next, results usually do not fit standard statistical models for normal distributions. In spite of this limitation, it is necessary to summarize the data for comparison to limits. The best statistical methods of evaluation are determined by the nature of the data. Wilson suggests that microbial monitoring data histograms generally resemble Poisson or negative... 

A conventional statistical method of evaluating the various possible procedures is to calculate the variance of the determination of the parameter. Suppose that one were to have a large number ( ) of sets of m data points, each of the points being chosen at random from the distribution. Then suppose that one uses each of these sets to make successive determinations of some parameter p. The n determinations of p will all be slightly different, and the variance is defined to be... 

This chapter highlights the important aspects of the analytical transfer processes as they relate to process, compliance, analytical data, and documentation. Types of method transfers and the timeline of transfer activities are discussed. The risk assessment prior to initiation of transfer activities is also described. The chapter describes content and utility of the transfer protocol and final report, as well as documents that govern analytical method transfers (i.e., SOPs and master plan). The importance of selecting appropriate method transfer acceptance criteria and use of statistical methods to evaluate results are described. The significance of the inclusion of an adequate level of detail in the methods, protocol(s), and other documents cannot be overly stressed. Last of all, the process for transfer of technical ownership of the analytical methods is discussed. Other chapters in this text should be consulted for elaboration on the various important facets of technical transfer, including method development, method validation, documentation, and stability. 

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

A complete re-evaluation of a-values by statistical methods, as demanded in 1953, has been attempted by one of the present authors by a cumbersome interative procedure. This work was abandoned, however, when it was found that the resulting values were extremely sensitive to minor changes in the data used. Consequently, the carefully selected normal values of McDaniel and Brown, derived from... 

Statistical and algebraic methods, too, can be classed as either rugged or not they are rugged when algorithms are chosen that on repetition of the experiment do not get derailed by the random analytical error inherent in every measurement,i° 433 is, when similar coefficients are found for the mathematical model, and equivalent conclusions are drawn. Obviously, the choice of the fitted model plays a pivotal role. If a model is to be fitted by means of an iterative algorithm, the initial guess for the coefficients should not be too critical. In a simple calculation a combination of numbers and truncation errors might lead to a division by zero and crash the computer. If the data evaluation scheme is such that errors of this type could occur, the validation plan must make provisions to test this aspect. 

In most studies, phytoestrogen intake has been estimated by direct methods that evaluate food intake either by recall (food-frequency questionnaires -FFQs) or by record (food diary), and subsequently by composition databases based on information of this kind. Food-frequency questionnaires are widely administered to subjects involved in epidemiological studies. Their validity and reproducibility is considered sufficient when statistically correlated to data obtained from dietary records (a properly-completed and comprehensive food diary) and from analysis of blood and urine samples (Kirk et ah, 1999 Huang et al, 2000 Yamamoto et al, 2001 Verkasalo et al, 2001). FFQs can be repeated several times a year and may be administered to large populations. Such an approach provides an easy and low-cost method of assessing the... 

This chapter deals with handling the data generated by analytical methods. The first section describes the key statistical parameters used to summarize and describe data sets. These parameters are important, as they are essential for many of the quality assurance activities described in this book. It is impossible to carry out effective method validation, evaluate measurement uncertainty, construct and interpret control charts or evaluate the data from proficiency testing schemes without some knowledge of basic statistics. This chapter also describes the use of control charts in monitoring the performance of measurements over a period of time. Finally, the concept of measurement uncertainty is introduced. The importance of evaluating uncertainty is explained and a systematic approach to evaluating uncertainty is described. 

Keil, D. et al., Evaluation of multivariate statistical methods for analysis and modeling of immunotoxicology data, Toxicol. Sci. 51, 245, 1999. 

Linearity is evaluated by appropriate statistical methods such as the calculation of a regression line by the method of least squares. The linearity results should include the correlation coefficient, y-intercept, slope of the regression line, and residual sum of squares as well as a plot of the data. Also, it is helpful to include an analysis of the deviation of the actual data points for the regression line to evaluate the degree of linearity. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

There is no agreement on which statistical methods should be used for evaluating experimental data on developmental toxicity. However, some of the factors relevant to this issue are discussed in the US EPA... 

QPPR can be derived from thermodynamic principles or by statistical analysis of measured data. In the latter case, a set of compounds for which Fand Pi, P2, , Pm are known is required to develop the model (the training set). An additional evaluation set of compounds with known F, Pi, P2, , Pm is recommended to evaluate the reliability and predictive capability of the model proposed. For a detailed description of the statistical methods, the reader is referred to [25], standard statistical texts, and to articles listed in the Toolkit Bibliography. 

Statistical methods of data analysis generate statistical parameters which show the significance of any effects. Although standardization does not affect the statistical parameters, visual evaluation may be confusing, if methods of standardization are used incorrectly. 

Multivariate statistical methods should be preferred for evaluating such multidimensional data sets since interactions and resulting correlations between the water compounds have to be considered. Fig. 8-1, which shows the univariate fluctuations in the concentrations of the analyzed compounds, illustrates the large temporal and local variability. Therefore in univariate terms objective assessment of the state of pollutant loading is hardly possible. 

Stability data (not only assay but also degradation products and other attributes as appropriate) should be evaluated using generally accepted statistical methods. The time at which the 95% one-sided confidence limit intersects the acceptable specification limit is usually determined. If statistical tests on the slopes of the regression lines and the zero-time intercepts for the individual batches show that batch-to-batch variability is small (e.g., p values for the level of significance of rejection are more than 0.25), data may be combined into one overall estimate. If the data show very little degradation and variability and it is apparent from visual inspection that the proposed expiration dating eriod will be met, formal statistical analysis may not be necessary. 

There is an analysis of the results of the study adequate to assess the effects of the drug. The report of the study should describe the results and the analytic methods used to evaluate them, including any appropriate statistical methods. The analysis should assess, among other things, the comparability of test and control groups with respect to pertinent variables, and the effects of any interim data analyses performed. 

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