Error estimating total

Using your optimized expression for W, calculate the estimated total energy of each of these atoms and ions. Also calculate the percent error in your estimate for each ion. What physical reason explains the decrease in percentage error as Z increases ... 

Note the test condition is with the vessel full of water for the hydraulic test. In estimating total weight, the weight of liquid on the plates has been counted twice. The weight has not been adjusted to allow for this as the error is small, and on the safe side . 

Using the data with built-in error generated in the previous section (six replications per data set), for every c value, two test data sets (b = 0.5 and b = 1.5) were separately compared with a reference data set (b = 1). The estimated total amount dissolved (W0) of the test and the reference data sets were compared by constructing confidence intervals at the 0.05 level for their mean differences. Estimated shape parameter, c, and scale parameter, b, of the test and the reference... 

A commonly used invalid estimate is called the re-substitution estimate. You use all the samples to develop a model. Then you predict the class of each sample using that model. The predicted class labels are compared to the true class labels and the errors are totaled. It is well known that the re-substitution estimate of error is highly biased for small data sets and the simulation of Simon et al. (14) confirmed that, with a 98.2% of the simulated data sets resulting in zero misclassifications even when no true underlying difference existed between the two groups. 

The protein-to-protein variation observed with the various protein assay methods makes it obvious why the largest source of error for protein assays is the choice of protein for the standard curve. If the sample contained IgG as the major protein and BSA was used for the standard curve, the estimated total protein concentration of the sample will be inaccurate. Whether the concentration was underestimated or overestimated depends upon which total protein assay method was used. If the Coomassie... 

The relevance of systematic errors in the total error budget depends on whether optimistic or conservative error estimates are used. Further studies are needed to attain realistic error estimates and to reduce those error components which may have a contribution larger than noise error. 

For the second case, a hollow ball was dipped inside a jar filled with water and scanned. The diameters of the ball and jar were 6.98 and 18.95 cm, respectively, as shown in Fig. 5a. A scan area of 27 cm in diameter was reproduced using the reconstruction algorithm. The dimensions of the objects as reproduced by the scan were 6.97 and 19.20 cm, respectively, as shown in Fig. 5b, which give a maximum spatial error of about 2.5 mm. This is good enough to resolve relatively small maldistribution, if it exists, inside the 30.48-cm-diameter column used in this study. The figure shows that the overall error in the estimated total holdup is within 12.8%. 

Table 1. Known theoretical contributions to the gj factor of an electron bound in the ground state of 12C5+. All values axe given in units of 10 9. The error estimates are discussed in the text. If no error is given, it is less than 0.5 x 10-10. The errors for the total value axe due to the (Za) expansion fox the xecoil contxibution, the numerical uncertainties for the QED effects of order (a/ir), and the estimated error for the bound-state QED contribution of order (a/7r)2. In order not to underestimate any systematic effect, the numerical errors were linearly added...

The uncertainty of the dispersion function determination reported in Table 1 is the estimated total uncertainty of the factors that contribute to the determination. The overall contribution of calibration source size and alignment uncertainty is 5 ppm. The statistical error associated with calibration lines is 2-3 ppm and the error associated with calibration profile fitting is < 5 ppm. 

Throughout this paper, the experimental errors are quoted in the following way Least-squares standard deviations in parentheses as units of the last digit, e.g., 1.107(1) A, and estimated total errors are quoted as error limits, e.g., 1.184 0.003 A. 

The limit of detection for As(III) and As(V) with this technique is 3 jig/L with an error of 70% at the 95% confidence interval. Concentrations between 3 and 10 p.g/L have an error of 40% at the 95% confidence interval. Concentrations between 10 and 40 pg/L have an error of 15% at the 95% confidence interval, and concentrations greater than 40 pg/L have an error of 10% at the 95% confidence interval. Error estimates were determined for 15 different concentrations ranging from 3 pg/L to 500 pg/L. There were 15 replicates at each concentration. Periodic analyses of replicate samples for total As by ICP were within the confidence intervals stated above. 

Krouwer JS. Estimating total analytical error and its sources. Arch Pathol Lab Med 1992 116 726-31. 

True cone. Estim. error fixed bias Estim. error rel. bias (0.0114x) Estim. total error due to bias Predicted cone. Measured cone. Residual Residual [2]... 

In surface tension measurements using the maximum bubble pressure method several sources of error may occur. As mentioned above, the exact machining of the capillary orifice is very important. A deviation from a circular orifice may cause an error of 0.3%. The determination of the immersion depth with an accuracy of 0.01 mm introduces an error of 0.3%. The accuracy of 1 Pa in the pressure measurement causes an additional error of 0.4%. The sum of all these errors gives an estimated total error of approximately 1%. Using the above-described apparatus, the standard deviations of the experimental data based on the least-squares statistical analysis were in the range 0.5% < sd > 1%. 

The underlying assumption in statistical analysis is that the experimental error is not merely repeated in each measurement, otherwise there would be no gain in multiple observations. For example, when the pure chemical we use as a standard is contaminated (say, with water of crystallization), so that its purity is less than 100%, no amount of chemical calibration with that standard will show the existence of such a bias, even though all conclusions drawn from the measurements will contain consequent, determinate or systematic errors. Systematic errors act uni-directionally, so that their effects do not average out no matter how many repeat measurements are made. Statistics does not deal with systematic errors, but only with their counterparts, indeterminate or random errors. This important limitation of what statistics does, and what it does not, is often overlooked, but should be kept in mind. Unfortunately, the sum-total of all systematic errors is often larger than that of the random ones, in which case statistical error estimates can be very misleading if misinterpreted in terms of the presumed reliability of the answer. The insurance companies know it well, and use exclusion clauses for, say, preexisting illnesses, for war, or for unspecified acts of God , all of which act uni-directionally to increase the covered risk. 

In summary, the total capital investment is the sum of several dozen cost components. The challenges in estimating the costs are to include all of the needed items and not to double count, be fully aware of local and federal regulations and legislation so that appropriate items are included and excluded, use clearly defined terms, include error estimates so that the accuracy of estimate is understood, and include the currency, location, and date. 

Statistics can be used to determine the probable error due to random errors if the measurements can be repeated. The probable error due to systematic errors can be estimated by apparatus modification or by guesswork. These errors combine in the same way as the errors in Eq. (11.20). If Sr is the probable error due to random errors and Ss is the probable error due to systematic errors, the total probable error is given by... 

How important is this effect for micas It is apparent from calculations presented by Rancourt (1989) and data in Hargraves et al. (1990) that small spectral contributions are always overestimated when thickness effects are considered. This conclusion has considerable implications for Mossbauer spectra of micas because the Fe peaks are often small relative to those of Fe, and therefore vulnerable to exaggeration by thickness effects. For example, consider a sample with an average value (for micas, cf Rancourt et al. 1994a) off= 0.5, and an ideal absorber thickness of 3.3 x 10 Fe/cm. If a doublet in this sample has an area of 10% of the total area, then its true area when corrected for thickness is 7% (see Fig. 5 in Rancourt 1989). An apparent area of 30% would have a true area of 26%, and so on. These error estimates are only approximations, as they apply to fits using Lorentzian lines that are well-separated the problems are aggravated in situations where peak overlap occurs (as is frequently the case with micas ). 

To assure sufficient accuracy of the numerical integration, we repeatedly halved the integration step size until no significant difference (0.1% ) in solutions occurred. For the fourth-order Runge-Kutta method this required a step size of. 04 sec (43 steps). An upper bound of the total error introduced by the numerical integration procedure can be obtained for the Runge-Kutta method (29). At a step size of 0.04 sec, the error estimate calculated is 0.004% (14). 

The estimated total error in caleulation of the rates is 23% (maximum). This error is cumulative error in measurement of product concentration by GC and determination of enzyme concentration during weighing and lyophilization procedure. 

In a typical experiment set up to evaluate three levels I, 2, and 3 for Factor A, a secondary factor may be designated as qualitative factor O, which of several operators conducts the test. The usual or classical experimental approach is to fix the level of O, i.e., select one operator and evaluate the response when Factor A is varied over the three levels (1,2, and 3) with perhaps three replications for each level. This approach has 6 rf/ for error estimation and nine total test measurements. Testing will evaluate the influence of A with the selected operator but give no indication of operator effects. A more comprehensive approach is to use a block experimental design. Select two diverse operators and for each operator evaluate the response for factor A at levels I, 2, and 3 with two replications per level. The operators are the blocks, and the influence of factor A is evaluated independently in each block. This design also has 6 < for error with now a total of 12 measurements. The investment of 3 more measurements for the second design provides much more information. The influence of factor A is now evaluated for both operators, and any unusual influence or interaction of operators on factor A response can also be determined. 

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