Statistical analysis precision

In addition to references to specific literature sources, a bibliography is given at the end of the chapter for appropriate statistical textbooks and for ASTM and ISO standards that iipply to quality assurance, statistical analysis, precision, bias and uncertainty, laboratory accreditation, and proficiency testing. The listing of standards is not exhaustiv e only those that are anticipated to be worthwhile for the topic of this chapter are included. These standards, with some exceptions as noted, were developed by committees on statistics and quality as generic standards that apply in principle to all testing and measurement operations. 

A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. A f-test is used to compare mean values, and an F-test to compare precisions. Comparisons between two sets of data require an initial evaluation of whether the data... 

The role of quality in reliability would seem obvious, and yet at times has been rather elusive. While it seems intuitively correct, it is difficult to measure. Since much of the equipment discussed in this book is built as a custom engineered product, the classic statistical methods do not readily apply. Even for the smaller, more standardized rotary units discussed in Chapter 4, the production runs are not high, keeping the sample size too small for a classical statistical analysis. Run adjustments are difficult if the run is complete before the data can be analyzed. However, modified methods have been developed that do provide useful statistical information. These data can be used to determine a machine tool s capability, which must be known for proper machine selection to match the required precision of a part. The information can also be used to test for continuous improvement in the work process. 

The specification development process is a data-driven activity that requires a validated analytical method. The levels of data needed include assay precision, replicate process results (process precision), and real-time stability profiles. A statistical analysis of these data is critical in setting a realistic specification. Most often, aggregation and fragmentation degradation mechanisms are common to protein and peptide therapeutics. Therefore, the SE-HPLC method provides a critical quality parameter that would need to be controlled by a specification limit. 

The precision stated in Table 10 is given by the standard deviations obtained from a statistical analysis of the experimental data of one run and of a number of runs. These parameters give an indication of the internal consistency of the data of one run of measurements and of the reproducibility between runs. The systematic error is far more difficult to discern and to evaluate, which causes an uncertainty in the resulting values. Such an estimate of systematic errors or uncertainties can be obtained if the measuring method can also be applied under circumstances where a more exact or a true value of the property to be determined is known from other sources. 

Precise thickness measurements by TEM require sections transverse to the basal lamellar surface. Conversely, only lamellae that can be identified as untilted "edge-on" or "flat-on" in AFM images are suitable for thickness analysis. The average thickness obtained by these techniques is based on sampling microscopic areas and will only be correct if the morphology is uniform in the sample. Micrographs taken from different areas of the specimen are usually studied, and statistical analysis of histograms used for quantitative analysis [255,256]. 

The primary goal of this series of chapters is to describe the statistical tests required to determine the magnitude of the random (i.e., precision and accuracy) and systematic (i.e., bias) error contributions due to choosing Analytical METHODS A or B, and/or the location/operator where each standard method is performed. The statistical analysis for this series of articles consists of five main parts as ... 

Analysis precision, n - a statistical measure of the expected repeatability of results for an unchanging sample, produced by an analytical method or instrument for samples whose spectra represent an interpolation of a multivariate calibration. The reader is cautioned to refer to specific definitions for precision and repeatability based on the context of use. 

The estimation of the overall precision of a methodfrom its unit operations A frequent problem in analysis is the estimation of the overall precision of a method before it has been used or when insufficient data are available to carry out a statistical analysis. In these circumstances the known precision limits for the unit operations of the method (volume measurement, weighing, etc.) may be used to indicate its precision. Table 2.6 gives the normal precision limits for Grade A volumetric equipment. 

The best fit is obtained by a search, which iterates through a sequence of trials to minimize the error between the calculated overall deuterium shift, AD, and the experimentally measured shift by varying the unknown parameters (/ , Do, AD ). The average data (at least two runs) are used for the curve fitting to give mean values for the unknown parameters (yS , AD , Do). The macroscopic JC values are calculated from yS values. Finally, a resampling statistical analysis is used to evaluate the precision for each parameter in the search. 

The SAP will also often contain table templates that allow the precise way in which the statistical analysis will be presented to be set down well in advance of running the analyses on the final trial data. 

The amount of data generated by low-precision analyses is often insufficient for sophisticated statistical analysis. Even so, it is important to minimize manual data handling as this allows subjective interpretation to enter the interpretive stages. 

The purpose of the statistical analysis is to estimate the bias and the precision (measured by the CVp of the total precision error of a subject method) and resolve the latter error into components CVg due to the sampling method (less pump error), due to the analytical method (including error in the desorption efficiency factor), and CVp (an assumed level of pump error). Appendix II gives the definitions and computational formulae for the statistical analysis. 

Evaluation of precision and other statistical data by an accepted method of statistical analysis (Cochran, Grubbs)... 

If an infinite number of identical, quantitative measurements could be made on a biosystem, this series of numerical values would constitute a statistical population. The average of all of these numbers would be the true value of the measurement. It is obviously not possible to achieve this in practice. The alternative is to obtain a relatively small sample of data, which is a subset of the infinite population data. The significance and precision of these data are then determined by statistical analysis. 

The previous discussion of standard deviation and related statistical analysis placed emphasis on estimating the reliability or precision of experimentally observed values. However, standard deviation does not give specific information about how close an experimental mean is to the true mean. Statistical analysis may be used to estimate, within a given probability, a range within which the true value might fall. The range or confidence interval is defined by the experimental mean and the standard deviation. This simple statistical operation provides the means to determine quantitatively how close the experimentally determined mean is to the true mean. Confidence limits (Lj and L2) are created for the sample mean as shown in Equations 1.6 and 1.7. 

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