Confidence level, definition

The basic condition of the Standard application - the availability of stable coupled probabilistic or the multiple probabilistic relations between then controlled quality indexes and magnetic characteristics of steel. All the probabilistic estimates, used in the Standard, are applied at confidence level not less than 0,95. General requirements to the means of control and procedure of its performance are also stipulated. Engineers of standard development endeavoured take into consideration the existed practice of technical control performance and test at the enterprises that is why the preparation of object control for the performance of nondestructive test can be done during the process of ordinary acceptance test. It is suggested that every enterprise is operated in correspondence with direct and non-destructive tests, obtained exactly at it, for detailed process chart and definite product type, however the tests have long since been performed after development of the Standard displayed that process gives way to unification. 

Long and Winefordner along with several other authors agree on a value of k = 3, which allows a confidence level of 99.86% if the values of xb follow a normal distribution, and 89% if the values of Xb do not follow a normal distribution. A value of k = 2 has also been used by some workers, but this decreases the confidence level in Cl. The definition of LOD was later expanded on by lUPAC in 1995 to include the probabilities of false positives and negatives. 

Quantification of the limits of detection (LOD), or minimum detectable levels (MDL statistically defined in Section 13.4), is an important part of any analysis. They are used to describe the smallest concentration of each element which can be determined, and will vary from element to element, from matrix to matrix, and from day to day. Any element in a sample which has a value below, or similar to, the limits of detection should be excluded from subsequent interpretation. A generally accepted definition of detection limit is the concentration equal to a signal of twice (95% confidence level) or three times (99% confidence) the standard deviation of the signal produced by the background noise at the position of the peak. In practice, detection limits in ICP-MS are usually based on ten runs of a matrix matched blank and a standard. In this case ... 

The Reasoner combines evidence from all sources and makes deductions from this evidence. The combination of evidence results in a single "confidence level" for each substructure. These confidence levels designate the degree to which the evidence supports the presence of the substructure in the unknown compound. They range from -100% (substructure definitely absent), through 0% (no information), to +100% (substructure definitely present). The confidence levels are ultimately derived from statistical analysis of representative spectral libraries. Details of the generation and propagation of confidence levels will be described in a separate report.(28)... 

As would be expected, in order to be able to have at least 95% confidence that the true CV p does not exceed its target level, we must suffer the penalty of sometimes falsely accepting a "bad" method (i.e. one whose true CV p is unsatisfactory). Such decision errors, referred to as "type-1 errors", occur randomly but have a controlled long-term frequency of less than 5% of the cases. (The 5% probability of type-1 error is by definition the complement of the confidence level.) The upper confidence limit on CV p is below the target level when the method is judged acceptable... 

If a statement of comparability at any confidence level needs to be made then other information is essential. The uncertainty of the results is needed [6], because only results accompanied by measurement uncertainty are comparable. To obtain consistent and useful measurement results, it is important that both a chain of comparisons to reference standards, and the uncertainties associated with these comparisons, are established. These principles lead directly to the definition of traceability in the International Vocabulary of Basic and General Terms in Metrology (VIM) as Property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties [4]. 

Usefulness of the normal distribution curve lies in the fact that from two parameters, the true mean p. and the true standard deviation true mean determines the value on which the bell-shaped curve is centered, and most probability concentrated on values near the mean. It is impossible to find the exact value of the true mean from information provided by a sample. But an interval within which the true mean most likely lies can be found with a definite probability, for example, 0.95 or 0.99. The 95 percent confidence level indicates that while the true mean may or may not lie within the specified interval, the odds are 19 to 1 that it does.f Assuming a normal distribution, the 95 percent limits are x 1.96 where a is the true standard deviation of the sample mean. Thus, if a process gave results that were known to fit a normal distribution curve having a mean of 11.0 and a standard deviation of 0.1, it would be clear firm Fig. 17-1 that there is only a 5 percent chance of a result falling outside the range of 10.804 and 11.196. 

The alpha spectrometry results were also significantly different at a 99% confidence level from the assigned NPL values (which deviations are 0% by definition). Application of the non-parametric Wilcoxon Signed Rank test, which, like the Rank Sum test, does not assume a normal distribution and does not require the removal of outliers, also resulted in a significant difference at a 99% confidence level between the alpha spectrometry results and the assigned NPL values (the absolute z-value being 3.72). 

Check if the bias can be neglected through a test of the trueness The definition of trueness (Prichard, 2005) is detailed in Appendix A. The criterion Cobs is compared with 1. It is considered as acceptable if it is less than 1 at a confidence level of 95% (Feinberg, 2001). Where the bias found is judged to be nonsignificant, the uncertainty associated with the bias is simply the combination of the standard uncertainty on the CRM value with the standard deviation associated with the bias (Eurachem, 2000). 

The second and preferred method is to apply appropriate statistical analysis to the dataset, based on linear regression. Both EU and USFDA authorities assume log-linear decline of residue concentrations and apply least-squares regression to derive the fitted depletion line. Then the one-sided upper tolerance limit (95% in EU and 99% in USA) with a 95% confidence level is computed. The WhT is the time when this upper one-sided 95% tolerance limit for the residue is below the MRL with 95% confidence. In other words, this definition of the WhT says that at least 95% of the population in EU (or 99% in USA) is covered in an average of 95% of cases. It should be stressed that the nominal statistical risk that is fixed by regulatory authorities should be viewed as a statistical protection of farmers who actually observe the WhT and not a supplementary safety factor to protect the consumer even if consumers indirectly benefit from this rather conservative statistical approach. 

Thus, a broad range of sometimes complementary analytical techniques is available at present for the characterisation of the various PAH/POM emissions. For standardisation purposes, candidate methods must be tested extensively in a collaborative exercise to determine and evaluate repeatability, reproducibility and recovery criteria before final definition and approval. (Recently, the method detection limit, defined as the concentration which can be detected at a specific confidence level, was proposed as one criterion for assessing the performance of an analytical method (18)). 

Figure 2.6 The Gaussian or Normal distribution with definitions of both the standard deviation and the confidence level.

This definition is rather a mouthful, and needs to be thought out quite carefully. It may be easier to visualize in terms of the probability curve mentioned above. A contingency is an amount to be added to the estimated cost (assumed here to be the most probable cost, corresponding to the top of the curve, but not necessarily so) to increase the confidence level to an acceptable probability (say 90 per cent) of a cost that will not be exceeded. In this definition, it is implied that a project has a fixed scope, and any elements of approved scope change will be handled as approved variations to the project budget. 

We shall comment on these three assumptions later. However, we first calculate the absolute value of the experimental discrepancy x — X( and compare this with the value of (taken to be s ) the experimental ratio z= ( x — X( j( /Sx) (Equation [8.13]) can then be interpreted in terms of the probability P i that the value x obtained by a laboratory would be found to lie within (m = z) standard deviations of the true value, for the (assumed) normal distribution defined by (p, = x en o = s ). For this purpose the tabulated values of are essential, a few are shown in Figure 8.6. P is an example of a confidence level, here referring to situations in which the data set includes a sufficiently large number of data points that a use of a Gaussian distribution is justifiable other definitions applicable to small data sets are discussed in Section 8.2.5. 

We now calculate the mean and standard deviation for these differences using Equation [8.2], to give d] 2 = 0.126, SEj = 0.00894. This gives an experimental tj-value for the five individual paired differences of dj2/Sd= 14.1. Now we test the null hypothesis [H, d] 2 = zero] with do/ = (b — 1) = 4 for p = 0.05, for which t = 2.776 (Table 8.1). Clearly tj > /, and the two analytical methods are definitely not statistically indistinguishable at the 95 % confidence level, unlike the conclusion drawn from the (Bl) evaluation of the same data. This is an excellent example of the need to fit the specifics of a t-test to include all of the available information about the raw experimental data. 

Figure 8.11 Graphical representations of the definition and implications of the EPA definition of an MDL. (a). Assumed normal frequency distribution of measured concentrations of MDL test samples spiked at one to five times the expected MDL concentration, showing the standard deviation s. (b) Assumed standard deviation as a function of analyte concentration, with a region of constant standard deviation at low concentrations, (c) The frequency distribution of the low concentration spike measurements is assumed to be the same as that for replicate blank measurements (analyte not present), (d) The MDL is set at a concentration to provide a false positive rate of no more than 1% (t = Student s t value at the 99 % confidence level), (e) Probability of a false negative when a sample contains the analyte at the EPA MDL concentration. Reproduced with permission from New Reporting Procedures Based on Long-Term Method Detection Levels and Some Considerations for Interpretations of Water-Quality Data Provided by the US Geological Survey NationalWater Quality Laboratory (1999), Open-File Report 99-193.

When performing a probabilistic performance assessment, data on the acceptable probabilities of the exceedance of a given limit state are needed. There are different approaches to define acceptable probabilities of exceedance of a given limit state (Melchers 1999). However, in the earthquake engineering community there are no generally accepted values for acceptable probabilities of exceedance of a given limit state. In the example, the acceptable probability was defined as follows the probability of exceedance of the NC limit state should not exceed 2% in 50 years (0.0004) with the 90% confidence level. Basically the same definition was used by Yun et al. (2002). 

To study whether the experimental statistics (Fe p) calculated by the two definitions [eqns (A 1.1) and (A 1.5)] lead to different conclusions, simulations were made by varying the number of data points considered in a calibration ( , from 4 to 500), as well as the magnitude of the variances of the straight line and the alternative non-linear (here, quadratic) model. Plots are presented to demonstrate whether the two Fg p values become higher than the /"tab at the same time. The two common confidence levels, 95% and 99%, were tested. All simulations were made using the common Microsoft Excel spreadsheet. ... 

Qualification, verification and validation of models Qualification refers to the development of the conceptual model. Qualification means that the model needs to be interpreted with a sufficient confidence level. Knowledge incorporated into the model must be re-used without loss or bad interpretation by actors coming from different domains and involved in other decision processes in the enterprise (Chapurlat and Braesch, 2008, 715). Verification checks that the code does what was intended and that the model represents reality. The verification and validation (V V) definitions used in this report are adopted from the 1998 American Institute of Aeronautics and Astronautics (AlAA) Guide (2) "Verification is the process of determining that a model implementation accurately represents the developer s conceptual description of the model and the solution to the model. Validation is the process of determining the degree to which a model is an accurate representation of the real-world from the perspective of the intended uses of the model". Although V V are processes that collect evidence of a model s correctness or accuracy for specific scenarios, V V cannot prove that a model is correct and accurate for all possible conditions and applications. It can provide evidence that a model is sufficiently accurate. Therefore, the V V process is completed when sufficiency is reached. 

---