Statistical test data

This sum, when divided by the number of data points minus the number of degrees of freedom, approximates the overall variance of errors. It is a measure of the overall fit of the equation to the data. Thus, two different models with the same number of adjustable parameters yield different values for this variance when fit to the same data with the same estimated standard errors in the measured variables. Similarly, the same model, fit to different sets of data, yields different values for the overall variance. The differences in these variances are the basis for many standard statistical tests for model and data comparison. Such statistical tests are discussed in detail by Crow et al. (1960) and Brownlee (1965). 

Statistical test for comparing paired data to determine if their difference is too large to be explained by indeterminate error. 

Statistical test for deciding if an outlier can be removed from a set of data. 

Dixon s Q-test statistical test for deciding if an outlier can be removed from a set of data. (p. 93) dropping mercury electrode an electrode in which successive drops of Hg form at the end of a capillary tube as a result of gravity, with each drop providing a fresh electrode surface, (p. 509)... 

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. 

Guide for the statistical analysis of Thermal Life Test data Motor and generators ratings, construction, testing and performance... 

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. 

Statistical Methods for Nonelectronic Reliability, Reliability Specifications, Special Application Methods for Reliability Prediction Part Failure Characteristics, and Reliability Demonstration Tests. Data is located in section 5.0 on Part Failure Characteristics. This section describes the results of the statistical analyses of failure data from more than 250 distinct nonelectronic parts collected from recent commercial and military projects. This data was collected in-house (from operations and maintenance reports) and from industry wide sources. Tables, alphabetized by part class/ part type, are presented for easy reference to part failure rates assuminng that the part lives are exponentially distributed (as in previous editions of this notebook, the majority of data available included total operating time, and total number of failures only). For parts for which the actual life times for each part under test were included in the database, further tables are presented which describe the results of testing the fit of the exponential and Weibull distributions. 

Figure 10.24a and the allosteric model in Figure 10.24b. The circled data points were changed very slightly to cause an F-test to prefer either model for each respective model, illustrating the fallacy of relying on computer fitting of data and statistical tests to determine molecular mechanism. As discussed in Chapter 7, what is required to delineate orthosteric versus allosteric...

While statistical tests are helpful in discerning differences in data, the final responsibility in determining difference remains with the researcher. While a given statistical test may indicate a difference, it will always do so as a... 

The same conclusion can be drawn from another statistical test for model comparison namely, through the use of Aikake s information criteria (AIC) calculations. This is often preferred, especially for automated data fitting, since it is more simple than F tests and can be used with a wider variety of models. In this test, the data is fit to the various models and the SSq determined. The AIC value is then calculated with the following formula... 

A statistical test is performed to determine whether or not the data may be fit to a set of curves of common maximal response and slope or if they must be fit to individual equations. For this example, Aikake s information criteria are calculated (see... 

These test procedures and standards are subject to change, so it is essential to keep up to date if one has to comply with them. It may be possible to obtain the latest issue on a specific test (such as a simple tensile test or a molecular weight test) by contacting the organization that issued it. For example, the ASTM issues new annual standards that include all changes. Their Annual Books of ASTM Standards contain more than seven thousand standards published in sixty-six volumes that include different materials and products. There are four volumes specifically on plastics 08.01-Plastics 1 08.02-Plastics 11 08.03-Plastics III, and 08.04-Plastic Pipe and Building Products. Other volumes include information on plastics and RPs. The complete ASTM index are listed under different categories for the different products, types of tests (by environment, chemical resistance, etc.), statistical analyses of different test data, and so on (56,128,129). 

Testing the robustness of a (best) model (and second-best contenders) by evaluating sets of statistically similar data created with program SIMILAR if the derived decisions remain unaffected by measurement noise, the model is adequate. 

The previous sections show you how to extract / -values for a commonly used set of statistical tests. This section describes a general step-by-step approach for getting your statistics from a SAS procedure into data sets for clinical trial table or graph reporting. Here are the steps to follow ... 

Alternatively, methods based on nonlocal projection may be used for extracting meaningful latent variables and applying various statistical tests to identify kernels in the latent variable space. Figure 17 shows how projections of data on two hyperplanes can be used as features for interpretations based on kernel-based or local methods. Local methods do not permit arbitrary extrapolation owing to the localized nature of their activation functions. 

A statistical test of these data gave a correlation coefficient of 0.968 (19), with only 0.834 required for 1% significance. Thus the elimination rates are functions dependent... 

Statistical tests make it possible, objectively to compare and interpret experimental data. They base on a test statistic to verify a statistical hypothesis about a ... 

Generalizations which go beyond the given data are normally not possible. Statistical tests can be carried out with measured values, y, and analytical values, x, respectively, if there exists a linear relationship between... 

A simple statistical test for the presence of systematic errors can be computed using data collected as in the experimental design shown in Figure 34-2. (This method is demonstrated in the Measuring Precision without Duplicates sections of the MathCad Worksheets Collabor GM and Collabor TV found in Chapter 39.) The results of this test are shown in Tables 34-9 and 34-10. A systematic error is indicated by the test using... 

Table 35-1 illustrates the ANOVA results for each individual sample in our hypothetical study. This test indicates whether any of the reported results from the analytical methods or locations is significantly different from the others. From the table it can be observed that statistically significant variation in the reported analytical results is to be expected based on these data. However, there is no apparent pattern in the method or location most often varying from the others. Thus, this statistical test is inconclusive and further investigation is warranted. 

This efficient statistical test requires the minimum data collection and analysis for the comparison of two methods. The experimental design for data collection has been shown graphically in Chapter 35 (Figure 35-2), with the numerical data for this test given in Table 38-1. Two methods are used to analyze two different samples, with approximately five replicate measurements per sample as shown graphically in the previously mentioned figure. 

Y data. The data set used for this example is from Miller and Miller ([1], p. 106) as shown in Table 58-1. This dataset is used so that the reader may compare the statistics calculated and displayed using the formulas and figures described in this reference with respect to those shown in this series of chapters. The correlation coefficient and other goodness of fit parameters can be properly evaluated using standard statistical tests. The Worksheets provided in this chapter series can be customized for specific applications providing the optimum information for particular method comparisons and validation studies. 

But for ordinary data, we would not expect such a sequence to happen. This is the reason most statistics work as general indicators of data performance the special cases that cause them to fail are themselves low-probability occurrences. In this case the problem is not whether or not the data are nonlinear, the problem is that they are nonrandom. This is a perfect example of the data failing to meet a criterion other than the one you are concerned with. Therefore the Durbin-Watson test fails, as would any statistical test fail for such data they are simply not amenable to meaningful statistical calculations. Nevertheless, a blind computation of the Durbin-Watson statistic would give an apparently satisfactory value. But this is a warning that other characteristics of the data can cause it to appear to meet the criteria. 

Over time, statisticians have devised many tests for the distributions of data, including one that relies on visual inspection of a particular type of graph. Of course, this is no more than the direct visual inspection of the data or of the calibration residuals themselves. However, a statistical test is also available, this is the x2 test for distributions, which we have previously described. This test could be applied to the question, but shares many of the disadvantages of the F-test and other tests. The main difficulty is the practical one this test is very insensitive and therefore requires a large number of samples and a large departure from linearity in order for this test to be able to detect it. Also, like the F-test it is not specific for nonlinearity, false positive indication can also be triggered by other types of defects in the data. 

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