Data analysis errors

The sonrces of errors (SE) in deconvolution may be classified as intrinsic errors and methodological errors, with the latter type of errors divided into experimental errors and data analysis errors. 

The merit of deconvolution methods proposed in PK analysis only partially discussed by others - is appropriately judged by the extent to which data analysis errors discussed in this section are considered. 

And the end, various results have been compared detected defects (1), non detected defects (2) and errors (3). The following figures illustrate some factors which have been extracted from final data analysis. 

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. 

Despite the variety of methods that had been developed, by 1960 kinetic methods were no longer in common use. The principal limitation to a broader acceptance of chemical kinetic methods was their greater susceptibility to errors from uncontrolled or poorly controlled variables, such as temperature and pH, and the presence of interferents that activate or inhibit catalytic reactions. Many of these limitations, however, were overcome during the 1960s, 1970s, and 1980s with the development of improved instrumentation and data analysis methods compensating for these errors. ... 

This section reflects on the limitations of the PSA process and draws extensively from NUREG-1050. These subjects are discussed as plant modeling and evaluation, data, human errors, accident processes, containment, fission product transport, consequence analysis, external events, and a perspective on the meaning of risk. 

To provide data for error analysis methods by pinpointing error-likely situations... 

If concentrations are known to —1-2 percent, a minimum of 10-fold excess over the stoichiometric concentration is required to evaluate k to within a few percent. The origins of error have been discussed.14,15 If the rate law is v = fc[A][B], with [B]o = 10[AJo, [B1 decreases during the run to 0.90[A]o. The data analysis provides k (the pseudo-first-order rate constant). To obtain k, one divides k by [B]av- If data were collected over the complete course of the reaction,... 

A good model is consistent with physical phenomena (i.e., 01 has a physically plausible form) and reduces crresidual to experimental error using as few adjustable parameters as possible. There is a philosophical principle known as Occam s razor that is particularly appropriate to statistical data analysis when two theories can explain the data, the simpler theory is preferred. In complex reactions, particularly heterogeneous reactions, several models may fit the data equally well. As seen in Section 5.1 on the various forms of Arrhenius temperature dependence, it is usually impossible to distinguish between mechanisms based on goodness of fit. The choice of the simplest form of Arrhenius behavior (m = 0) is based on Occam s razor. 

Phillips, G. R., and Eyring, E. M., Error Estimation Using the Sequential Simplex Method in Nonlinear Least Squares Data Analysis, Anal. Chem. 60, 1988, 738-741. 

Adverse events need to be coded consistently with respect to letter case. Problems can occur when there is discordant coding using all capital letters, all lower-case letters, or combinations thereof, as computer software will interpret these capitalization variations as different events. Letter case sensitivity can be important when two or more words are used to describe an adverse event. For example, some databases utilizing the Medical Dictionary for Regulatory Activities (MedDRA) coding dictionary employ a coding system in which only the first letter of the first word of an adverse event is capitalized (e.g., Atrioventricular block complete ). Failing to adhere to uniform letter case conventions across the data can result in severe errors in data analysis. 

Finally, Chapter 16 provides information about the handling of U-series data, with a particular focus on the appropriate propagation of errors. Such error propagation can be complex, especially in the multi-dimensional space required for U- " U- °Th- Th chronology. All too often, short cuts are taken during data analysis which are not statistically justified and this chapter sets out some more appropriate ways of handling U-series data. 

Uncertainty in Process Discriminants. Because processes operate over a continuum, data analysis generally produces distinguishing features that exist over a continuum. This is further compounded by noise and errors in the sensor measurements. Therefore, the discriminants developed to distinguish various process labels may overlap, resulting in uncertainty between data classes. As a result, it is impossible to define completely distinguishing criteria for the patterns. Thus, uncertainty must be addressed inherently. 

An optimization criterion for determining the output parameters and basis functions is to minimize the output prediction error and is common to all input-output modeling methods. The activation or basis functions used in data analysis methods may be broadly divided into the following two categories ... 

Frequency domain performance has been analyzed with goodness-of-fit tests such as the Chi-square, Kolmogorov-Smirnov, and Wilcoxon Rank Sum tests. The studies by Young and Alward (14) and Hartigan et. al. (J 3) demonstrate the use of these tests for pesticide runoff and large-scale river basin modeling efforts, respectively, in conjunction with the paired-data tests. James and Burges ( 1 6 ) discuss the use of the above statistics and some additional tests in both the calibration and verification phases of model validation. They also discuss methods of data analysis for detection of errors this last topic needs additional research in order to consider uncertainties in the data which provide both the model input and the output to which model predictions are compared. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Biochips produce huge data sets. Data collected from microarray experiments are random snapshots with errors, inherently noisy and incomplete. Extracting meaningful information from thousands of data points by means of bioinformatics and statistical analysis is sophisticated and calls for collaboration among researchers from different disciplines. An increasing number of image and data analysis tools, in part freely accessible ( ) to academic researchers and non-profit institutions, is available in the web. Some examples are found in Tables 3 and 4. 

Chromatographic procedures applied to the identification of proteinaceous paint binders tend to be rather detailed consisting of multiple analytical steps ranging from solvent extractions, chromatography clean up, hydrolysis, derivatisation reactions, and measurement to data analysis. Knowledge of the error introduced at each step is necessary to minimise cumulative uncertainty. Reliable results are consequently obtained when laboratory and field blanks are carefully characterised. Additionally, due to the small amounts of analyte and the high sensitivity of the analysis, the instrument itself must be routinely calibrated with amino acid standards along with measurements of certified reference proteins. All of these factors must be taken into account because many times there is only one chance to take the measurement. 

Data analysis was reduced to a separate one-way analysis of variance on the data from individual laboratories in order to examine the difference between types of sampling bottle on a single (common) hydrowire, and to determine the influences of the three types of hydrowire using a single type of sampling bottle (modified GO-FLO). Samples were replicated so that there were, in all cases, two or more replicates to determine the lowest level and analytical error. 

Correlations are inherent in chemical processes even where it can be assumed that there is no correlation among the data. Principal component analysis (PCA) transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components, and is an effective tool in multivariate data analysis. In the last section we describe a method that combines PCA and the steady-state data reconciliation model to provide sharper, and less confounding, statistical tests for gross errors. 

Although HTS can process up to a million compounds per day, it has a high possibility of producing both false-negative and false-positive results. Replicate measurements in combination with statistical methods and careful data analysis may help to identify and reduce such errors [69]. 

Theory for the transformation of the dependent variable has been presented (Bll) and applied to reaction rate models (K4, K10, M8). In transforming the dependent variable of a model, we wish to obtain more perfectly (a) linearity of the model (b) constancy of error variance, (c) normality of error distribution and (d) independence of the observations to the extent that all are simultaneously possible. This transformation will also allow a simpler and more precise data analysis than would otherwise be possible. 

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