Absolute errors

Fig. 5.2. Computed percentage error (absolute value) for the He-N2 (j, = 0) system using potential function HFD1. The state to state inelastic cross-sections are compared at several collision energies as a function of A j transitions. The B value for N2 is taken to be about 2 [207],...

In usual practice an accurate result is the one which matches very nearly with true value of a measured amount. The comparison is normally done with regard to the errorand the accuracy is inversely proportional to it the greater the accuracy, the smaller is the error. Absolute error is the difference between the experimental value and the true value. 

Figure 5.9 Uninhibited incipient hydrate T and P errors (absolute) for all hydrates (1685 pts).

FIGURE 5.10 Hydrate formation T error (absolute) for all inhibited hydrates. 

VS data are used to select the regression model and curve fitting. The regression model and weighting that generate the lowest total error (Absolute Bias + Intermediate Precision) of the VS should be chosen. 

Applying the principles of propagation of error (absolute variances in numerator additive, relative variances in the division step additive), we calculate that x = 0.2 5 O.OI4 ppm. 

The simplest as well as the most complex measurements are invariably accompanied by these fortuitous errors. Absolute agreement is itself an accidental coincidence. Stanley Jevons says, it is one of the most embarrassing things we can meet when experimental results agree too closely . Such agreement should at once excite a feeling of distrust. 

Relative % Variation coefficient in % of error Absolute denaturation capability Variation coefficient in % of error... 

Period Actual Demand Forecast Forecast Error Absolute Error ... 

Absolute error Absolute rmcertainty Bayesian statistics Bell curve... 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

After selection of descriptors/NN training, the best networks were applied to the prediction of 259 chemical shifts from 31 molecules (prediction set), which were not used for training. The mean absolute error obtained for the whole prediction set was 0.25 ppm, and for 90% of the cases the mean absolute error was 0.19 ppm. Some stereochemical effects could be correctly predicted. In terms of speed, the neural network method is very fast - the whole process to predict the NMR shifts of 30 protons in a molecule with 56 atoms, starting from an MDL Molfile, took less than 2 s on a common workstation. 

But decision making in the real world isn t that simple. Statistical decisions are not absolute. No matter which choice we make, there is a probability of being wrong. The converse probability, that we are right, is called the confidence level. If the probability for error is expressed as a percentage, 100 — (% probability for error) = % confidence level. 

The accuracy of these methods is tested by finding the mean absolute error between the computed and experimental free energies of solvation. The SM4 method does well for neutral molecules in alkane solvents with a mean absolute error of 0.3 kcal/mol. For neutral molecules, the SM5 methods do very well with mean absolute errors in the 0.3 to 0.6 kcal/mol range, depending on the method and solvent. For ions, the SMI method seems to be most accurate with... 

Accuracy is a measure of how close a measure of central tendency is to the true, or expected value, Accuracy is usually expressed as either an absolute error... 

The smallest concentration or absolute amount of analyte such that the probability of type 1 and type 2 errors are equal (LOI). 

Determine the density at least five times, (a) Report the mean, the standard deviation, and the 95% confidence interval for your results, (b) Eind the accepted value for the density of your metal, and determine the absolute and relative error for your experimentally determined density, (c) Use the propagation of uncertainty to determine the uncertainty for your chosen method. Are the results of this calculation consistent with your experimental results ff not, suggest some possible reasons for this disagreement. 

Osmotic pressure experiments provide absolute values for Neither a model nor independent calibration is required to use this method. Experimental errors can arise, of course, and we note particularly the effect of impurities. Polymers which dissociate into ions can also be confusing. We shall return to this topic in Sec. 8.13 for now we assume that the polymers under consideration are nonelectrolytes. 

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