Statistical bias

FIGURE 7.14 Attenuation plots for BTB junctions at five temperatures, all obtained with a 1 V bias. Statistics indicate P values for fixed thickness ranges, across several samples and temperatures, as described in Ref. [54]. 

Relative Bias—Statistically significant relative biases betw n Procedures A and Procedure B were observed in the data from the cooperative program described in Note 9. These biases can be corrected by applying the appropriate correlation equation listed below, that calculates a dry vapor pressure equivalent value for Procedure A (DVPE, Procedure A), from values obtained by Procedure B ... 

Relative Bias—Statistically significant relative biases were observed in the 1991 interlaboratory cooperative test program between the total pressure obtained using instruments described in this test method and the dry vapor pressure obtained using Test Method D 49S3, Procedure A. These biases are corrected by applying Eq. 1. 

Bias (statistics) A systematic error that contributes to the difference between the mean of the measurement and an accepted reference or true value. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

Each observation in any branch of scientific investigation is inaccurate to some degree. Often the accurate value for the concentration of some particular constituent in the analyte cannot be determined. However, it is reasonable to assume the accurate value exists, and it is important to estimate the limits between which this value lies. It must be understood that the statistical approach is concerned with the appraisal of experimental design and data. Statistical techniques can neither detect nor evaluate constant errors (bias) the detection and elimination of inaccuracy are analytical problems. Nevertheless, statistical techniques can assist considerably in determining whether or not inaccuracies exist and in indicating when procedural modifications have reduced them. 

Analytical chemists make a distinction between error and uncertainty Error is the difference between a single measurement or result and its true value. In other words, error is a measure of bias. As discussed earlier, error can be divided into determinate and indeterminate sources. Although we can correct for determinate error, the indeterminate portion of the error remains. Statistical significance testing, which is discussed later in this chapter, provides a way to determine whether a bias resulting from determinate error might be present. 

The "feedback loop in the analytical approach is maintained by a quality assurance program (Figure 15.1), whose objective is to control systematic and random sources of error.The underlying assumption of a quality assurance program is that results obtained when an analytical system is in statistical control are free of bias and are characterized by well-defined confidence intervals. When used properly, a quality assurance program identifies the practices necessary to bring a system into statistical control, allows us to determine if the system remains in statistical control, and suggests a course of corrective action when the system has fallen out of statistical control. 

In a performance-based approach to quality assurance, a laboratory is free to use its experience to determine the best way to gather and monitor quality assessment data. The quality assessment methods remain the same (duplicate samples, blanks, standards, and spike recoveries) since they provide the necessary information about precision and bias. What the laboratory can control, however, is the frequency with which quality assessment samples are analyzed, and the conditions indicating when an analytical system is no longer in a state of statistical control. Furthermore, a performance-based approach to quality assessment allows a laboratory to determine if an analytical system is in danger of drifting out of statistical control. Corrective measures are then taken before further problems develop. 

Statistical designs for experiments maximize information and reduce research time and costs. These techniques are less likely to miss synergistic factors affecting performance or product quaUty, minimize the element of human bias, eliminate less productive avenues of experimentation by taking... 

Statistical Control. Statistical quahty control (SQC) is the apphcation of statistical techniques to analytical data. Statistical process control (SPC) is the real-time apphcation of statistics to process or equipment performance. Apphed to QC lab instmmentation or methods, SPC can demonstrate the stabihty and precision of the measurement technique. The SQC of lot data can be used to show the stabihty of the production process. Without such evidence of statistical control, the quahty of the lab data is unknown and can result in production challenging adverse test results. Also, without control, measurement bias cannot be determined and the results derived from different labs cannot be compared (27). 

Preferably the transferring lab provides a sample which has already been analyzed, with the certainty of the results being known (41). This can be either a reference sample or a sample spiked to simulate the analyte. An alternative approach is to compare the test results with those made using a technique of known accuracy. Measurements of the sample are made at the extremes of the method as well as the midpoint. The cause of any observed bias, the statistical difference between the known sample value and the measured value, should be determined and eliminated (42). When properly transferred, the method allows for statistical comparison of the results between the labs to confirm the success of the transfer. 

Reduce the effect of bias by using statistic ly proven methods of estimation based on experience. 

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. 

The above assumes that the measurement statistics are known. This is rarely the case. Typically a normal distribution is assumed for the plant and the measurements. Since these distributions are used in the analysis of the data, an incorrect assumption will lead to further bias in the resultant troubleshooting, model, and parameter estimation conclusions. 

This is a formidable analysis problem. The number and impact of uncertainties makes normal pant-performance analysis difficult. Despite their limitations, however, the measurements must be used to understand the internal process. The measurements have hmited quahty, and they are sparse, suboptimal, and biased. The statistical distributions are unknown. Treatment methods may add bias to the conclusions. The result is the potential for many interpretations to describe the measurements equaUv well. 

Representativeness can be examined from two aspects statistical and deterministic. Any statistical test of representativeness is lacking becau.se many histories are needed for statistical significance. In the absence of this, PSAs use statistical methods to synthesize data to represent the equipment, operation, and maintenance. How well this represents the plant being modeled is not known. Deterministic representativeness can be answered by full-scale tests on like equipment. Such is the responsibility of the NSSS vendor, but for economic reasons, recourse to simplillcd and scaled models is often necessary. System success criteria for a PSA may be taken from the FSAR which may have a conservative bias for licensing. Realism is more expensive than conservatism. 

It is often assumed that the measurements taken with a calibrated device are accurate, and indeed they are if we take account of the variation that is present in every measuring system and bring the system under statistical control. Variation in measurement systems arises due to bias, repeatability, reproducibility, stability, and linearity. 

It is important to keep in mind that statistically based studies by themselves can never prove the e.xistence of a cause and effect relationship. However, such obseix ations may be used to generate or to test a hypothesis. Many possibilities exist for introducing bias in this type of investigation, and statistical correlations may be fortuitous. 

Also, the statistics available on materials are often presented so as to favor a particular bias, which complicates the process of... 

Definition and Uses of Standards. In the context of this paper, the term "standard" denotes a well-characterized material for which a physical parameter or concentration of chemical constituent has been determined with a known precision and accuracy. These standards can be used to check or determine (a) instrumental parameters such as wavelength accuracy, detection-system spectral responsivity, and stability (b) the instrument response to specific fluorescent species and (c) the accuracy of measurements made by specific Instruments or measurement procedures (assess whether the analytical measurement process is in statistical control and whether it exhibits bias). Once the luminescence instrumentation has been calibrated, it can be used to measure the luminescence characteristics of chemical systems, including corrected excitation and emission spectra, quantum yields, decay times, emission anisotropies, energy transfer, and, with appropriate standards, the concentrations of chemical constituents in complex S2unples. 

Accuracy is the term used to describe the degree of deviation (bias) between the (often unknown) true value and what is found by means of a given analytical method. Accuracy cannot be determined by statistical means the test protocol must be devised to include the necessary comparisons (blanks, other methods). 

Thompson, M., Robust Statistics and Functional Relationship Estimation for Comparing the Bias of Analytical Procedures over Extended Concentration Ranges, Anal. Chem. 61, 1989, 1942-1945. 

Immunological abnormalities were reported in 23 adults in Woburn, Massachusetts, who were exposed to contaminated well water and who were family members of children with leukemia (Byers et al. 1988). These immunological abnormalities, tested for 5 years after well closure, included persistent lymphocytosis, increased numbers of T-lymphocytes, and depressed helper suppressor T-cell ratio. Auto-antibodies, particularly anti-nuclear antibodies, were detected in 11 of 23 adults tested. This study is limited by the possible bias in identifying risk factors for immunological abnormalities in a small, nonpopulation-based group identified by leukemia types. Other limitations of this study are described in Section 2.2.2.8. A study of 356 residents of Tucson, Arizona, who were exposed to trichloroethylene (6-500 ppb) and other chemicals in well water drawn from the Santa Cmz aquifer found increased frequencies of 10 systemic lupus erythematosus symptoms, 5 (arthritis, Raynaud s phenomenon, malar rash, skin lesions related to sun exposure, seizure or convulsions) of which were statistically significant (Kilbum and Warshaw 1992). 

The data summarization procedures will depend on the objectives and type of data. Statistical calculations should be supported with graphical analysis techniques. A statement of precision and bias should be Included with all Important results of the study. 

Historical data on the indicator. Existing information on the statistical variation, bias, and other interpretational attributes of potential biological indicators should be examined and considered in the design of a sampling program for assessing trends in mercury bioaccumulation. 

To account for inhomogeneity in bubble sizes, d in Eq. (20-52) should be taken as / Ln,dffLn,d, and evaluated at the top of the vertical column if coalescence is significant in the rising foam. Note that this average d for overflow differs from that employed earlier for S. Also, see Bubble Sizes regarding the correction for planar statistical sampling bias and the presence of size segregation at a wall. 

The result from a measurement on a RM is commonly a difference between the observed value and the certified value. This difference is called measurement bias, and can, appreciating both the uncertainty on the RM as well as the imcertainty added during the measurement, be tested for (statistical) significance. ISO Guide 33... 

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