Data confidence

Number and type of record The number of data points or tables of data presented in the resource or the number of events the data set reflects where available, the form in which the data are presented, such as failure rates or availability data, confidence intervals or error factors the raw data source used, sueh as surveys, plant records, tests, or judgment. 

Cloud Point Measurements Cloud points were recorded by the visual observation of aqueous solutions containing 1% W/V surfactant. The measurement defines the temperature at which the system under test shows a characteristic transitional change from a clear solution to an opalescent or cloudy state. All cloud points were recorded in both ascending and descending temperature cycles to ensure data confidence. The influence of salt and/or oils on the cloud point were systematically evaluated. 

The deconvolution procedure has been validated for triple exponential fits using synthetic test data. Confidence in the procedure is also enhanced by the high signal to noise ratio obtainable with pulsed laser excitation. It should be noted that dual exponential decay would be anticipated on the basis of Scheme 1. 

The purpose of validation of a computer system is to ensure an acceptable degree of evidence (documented, raw data), confidence (dependability and thorough, rigorous achievement of predetermined specifications), intended use, accuracy, consistency and reliability. 

The determination of kinetic parameter values from column experiments is predicated upon the ability of the mathematical model to successfully simulate the experimental data. Confidence in the robustness of the parameter values so determined is attained only with a unique solution (i.e., when one suite of parameter values provides a solution that is significantly better than all others). For cases wherein a system is near equilibrium or under extreme nonequilibrium, attainment of a unique solution may prove difficult. A modified miscible-displacement technique, involving flow interruption, that enhances the potential for achieving unique solutions, and thus increases the robustness of optimized values of kinetic parameters, was presented by Brusseau et al. (1989a). In addition, the method has increased sensitivity to nonequilibrium, making it useful for process-level investigation of sorption kinetics. This method would appear to be especially useful for systems com-... 

When you have a lot of data Confidence interval knowing the population mean and standard deviation... 

The application of discriminant analysis can be extended to include probabilities of class membership and, assuming a multivariate normal distribution of data, confidence intervals for class boundaries can be calculated. The Bayes rule for classification simply states that an object should be assigned to that... 

This descriptive technique does not require statistical analysis of the data confidence is derived from the reliability of skilled panelists collective judgment. The data are reported in tabular or graphic form. One disadvantage of this method is that the panel s opinion may be affected by a dominant personality so that not all the panel members provide an equal input to the consensus. 

Technology Use control, system integrity, data confid tiality, restriction of data flow, req)onse to event in time, availability of resource. 

Using the original data shows that the second point (77 = 1,314) is potentially an outlier, since its residual is extremely large. Thus, the row corresponding to this point (row 4 in the original layout) was deleted and the regression analysis was redone. The results are shown in Figs. 8.30 and 8.31. The results are much better as there are now no clear outliers and the data confidence intervals, especially for C3, are much smaller. 

Providing the coincidence correction is less than 5% see Table XVII), the precision of counts made with the Coulter Counter is a function of the number of particles counted. The precision decreases with the total number of particles counted but is independent of the size of the aperture tube employed. The following data will serve as a guide to the precision of count data. (Confidence limits given are two standard deviations.)... 

When there are sufficient data at different temperatures, the temperature dependence of the parameters is reflected in the confidence ellipses (Bryson and Ho, 1969 Draper and Smith,... 

Figure 4-2. UNIQUAC parameters and their approximate confidence regions for the ethanol-cyclohexane system for three isotherms. Data of Scatchard and Satkiewicz, 1964.

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

The optimum parameters for furfural-benzene are chosen in the region of the overlapping 39% confidence ellipses. The ternary tie-line data were then refit with the optimum furfural-benzene parameters final values of binary parameters were thus obtained for benzene-cyclohexane and for benzene-2,2,4-trimethyl-pentane. Table 4 gives all optimum binary parameters for this quarternary system. 

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

Large confidence regions are obtained for the parameters because of the random error in the data. For a "correct" model, the regions become vanishingly small as the random error becomes very small or as the number of experimental measurements becomes very large. 

For the acetone-methanol data of Othmer, the correlation coefficient is -0.678, indicating a moderate degree of correlation between the two van Laar parameters. The elongated confidence ellipses shown in Figure 2 further emphasize this correlation. 

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. 

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

Figure 1.3. Frontier orbital energies (eV) and confidents for acrolein and protonated acrolein. In the latter case the upper numbers refer to the situation where bond lengths and angles correspond to those of acrolein. The lower numbers are more suitable for a hydroxyallyl cation. The actual situation is assumed to be intermediate. The data are taken from ref. 104.

There will be incidences when the foregoing assumptions for a two-tailed test will not be true. Perhaps some physical situation prevents p from ever being less than the hypothesized value it can only be equal or greater. No results would ever fall below the low end of the confidence interval only the upper end of the distribution is operative. Now random samples will exceed the upper bound only 2.5% of the time, not the 5% specified in two-tail testing. Thus, where the possible values are restricted, what was supposed to be a hypothesis test at the 95% confidence level is actually being performed at a 97.5% confidence level. Stated in another way, 95% of the population data lie within the interval below p + 1.65cr and 5% lie above. Of course, the opposite situation might also occur and only the lower end of the distribution is operative. 

There is a temptation when analyzing data to plug numbers into an equation, carry out the calculation, and report the result. This is never a good idea, and you should develop the habit of constantly reviewing and evaluating your data. For example, if analyzing five samples gives an analyte s mean concentration as 0.67 ppm with a standard deviation of 0.64 ppm, then the 95% confidence interval is... 

This confidence interval states that the analyte s true concentration lies within the range of -0.16 ppm to 1.44 ppm. Including a negative concentration within the confidence interval should lead you to reevaluate your data or conclusions. On further investigation your data may show that the standard deviation is larger than expected. 

The probabilistic nature of a confidence interval provides an opportunity to ask and answer questions comparing a sample s mean or variance to either the accepted values for its population or similar values obtained for other samples. For example, confidence intervals can be used to answer questions such as Does a newly developed method for the analysis of cholesterol in blood give results that are significantly different from those obtained when using a standard method or Is there a significant variation in the chemical composition of rainwater collected at different sites downwind from a coalburning utility plant In this section we introduce a general approach to the statistical analysis of data. Specific statistical methods of analysis are covered in Section 4F. 

Unpaired Data Consider two samples, A and B, for which mean values, Xa and Ab, and standard deviations, sa and sb, have been measured. Confidence intervals for Pa and Pb can be written for both samples... 

If experimental values of Rg are observed to be independent of 0, then Rayleigh scattering is established and Eq. (10.60) can be applied to the data with confidence. 

HETP values obtained in this way have been compared to measured values in data banks (69) and statistical analysis reveals that the agreement is better when equations 79 and 80 are used to predict and than with the other models tested. Even so, a design at 95% confidence level would require a safety factor of 1.7 to account for scatter. 

Analytical investigations may be undertaken to identify the presence of an ABS polymer, characterize the polymer, or identify nonpolymeric ingredients. Fourier transform infrared (ftir) spectroscopy is the method of choice to identify the presence of an ABS polymer and determine the acrylonitrile—butadiene—styrene ratio of the composite polymer (89,90). Confirmation of the presence of mbber domains is achieved by electron microscopy. Comparison with available physical property data serves to increase confidence in the identification or indicate the presence of unexpected stmctural features. Identification of ABS via pyrolysis gas chromatography (91) and dsc ((92) has also been reported. 

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