Root-mean-square uncertainty

The sum in Equation (5) is calculated over all of the measured data points, N, and the deviation at each point is weighted by 1/e , where e, is the root-mean-square uncertainty in Xobs- The jv weighting introduces a penalty for adding additional, unnecessary, shells of scatterers. 

For CWI to be meaningful, error estimates on the relative travel time change given in Eq. 4 must be provided. Following Brenguier et al. (2008a), the standard deviation of the time lag (i.e., the root-mean-square uncertainty of the linear fit) is given by... 

The BC and K0 models, on the other hand, show much smaller root mean square errors, typically in the 1 % range, over an amazingly substantial range x of intensities fitted, Fig. 5.8, lower set of data points. Maximal deviations from the exact profiles amount to no more than twice the root mean square errors shown, that is well within the experimental uncertainties of the best measurements. The BC model is especially well suited to approximate quadrupole-induced profiles. The K0 model, on the other... 

Root mean square error (uncertainty of calibration)... 

Similarly, the root mean square [RMS) of errors gives an insight into the errors of the prediction. In Catalyst-HypoGen, the RMS is scaled according to the uncertainty of each activity measure (Unc) ... 

All non-negligible uncertainties are combined by root-mean-square summations. That sum establishes the quality of the traceability link. A traceable measurement may fail as an appropriate measurement if its uncertainty is too large. Its quality will then be too low for the purpose. Conversely, it should be recognized that there are highly reproducible chemical measurements which are useful, but are not traceable to any standard. 

Whereas type A and B uncertainty components [6] are almost always added by root-mean-square additions, there are circumstances under which direct additions of uncertainties from dependent error sources are preferable. When protocols use such direct additions of uncertainties, these conditions should be clearly explained in the protocol. That information is needed for a fair inter-laboratory comparison of values and uncertainties of measurements on the same material. 

We used p instead of = in Equation 5.37 because the exact numerical value depends on the definition of the uncertainties—you will see different values in different books. If we define At in Figure 5.13 as the full width at half maximum or the root-mean-squared deviation from the mean, the numerical value in Equation 5.37 changes. It also changes a little if the distribution of frequencies is not Gaussian. Equation 5.37 represents the best possible case more generally we write... 

The standard errors reported for the constants in the two equations above were calculated as the root mean square of the component standard errors and this propagation of uncertainty in the combined equations causes the slopes to barely overlap, whereas there is no overlap of the slopes calculated from eq. 3. We cannot hope to use these equations to calculate accurate enthalpies of formation for alkanes or alcohols with nc > 6 for the same reason we cannot use eq. 3 and the same restricted data range the calculated results do not reproduce the experimental results due to the sensitivity of the calculation to the slope/intercept. 

The statistical parameters and the occupation numbers allow a rough estimate of the reliability of the data. However, the range of variation is partially caused by strong slopes of the sea bed, especially in the northern Baltic Sea. In order to estimate the uncertainty in the data, some of the original data sets were resampled to the target grids and cross correlated. For the Belt Sea, which is densely covered by input data, root mean square deviations (rms) of... 

The assignment of an uncertainty to a selected value that is based on only one experimental source is a highly subjective procedure. In some cases, the number of data points the selected value is based on allows the use of the root mean square [82TAY] deviation of the data points Jf, to describe the standard deviation associated with the average X ... 

We can give precision to the meaning of uncertainty in an observable by defining it as the root-mean-square deviation from the expectation value. Thus, if Ap is the uncertainty... 

Root mean square. Subsequent signal values are squared, the mean of the squares is calculated, and the square root of that mean is taken. Used to describe the uncertainty of a signal, the timing accuracy of a detector or of an electronic system, or the deviation of an optical surface from the ideal shape. 

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