Unexplained Error

As just mentioned, the T-test tests the significance of a particular parameter estimate. What is really needed is also a test of the overall significance of a model. To start, the total sum of squares of the observed data, SStotai, is partitioned into a component due to regression, SSregression, and a component due to residual, unexplained error, SSE,... 

A statistical relationship, unlike a mathematical one, does not provide an exact or perfect data fit in the way that a functional one does. Even in the best of conditions, y is composed of the estimate of x, as well as some amount of unexplained error or disturbance called statistical error, e. That is,... 

Comments Bias-corrected standard error measurements allow the characterization of the variance attributable to random unexplained error. The bias value is calculated as the mean difference between two columns of data, most commonly actual minus NIR predicted values. 

The goal of standardization is to have the total error (bias and unexplained error) among instruments of the same magnitude as the variation of predicting subsamples from a container of the product. 

In the situation where more that two instruments are to be compared, an analysis of variance can be used to remove sample and instrument differences and compare bias and unexplained error for the... 

As shown by the above formulas, SED can be partitioned into two errors (a) a systematic difference (bias) between the two sets of analysis values calculated as the difference between the means of the two sets of values, and (b) SED corrected for bias (SED(C)) or unexplained error, caused by using an equation not designed specifically for the samples being tested. The slope of reference values regressed on predicted values usually differs from 1, and is included in unexplained error. 

Having defined the errors, two control limits are needed one to determine if a meaningful bias is occurring and one to determine if a meaningful increase in unexplained error is occurring. Details of... 

Assuming that (a) a difference between the NIRS analytical values and reference values in either bias or unexplained error is to be detected with 90% confidence, (b) at least 100 samples are present in the calibration set, and (c) a bias greater than the SEC and an unexplained error greater than two times the SEC are unacceptable, the following procedure is recommended ... 

Compute the bias and unexplained error of the analytical values in the test set. 

If bias or unexplained error control limits are exceed, steps should be taken to either add these samples to the existing calibration set and reealibrate, or develop a new calibration for this specific group of samples. Adjusting the bias only fixes the problem on a temporary basis another set of nine samples would probably suggest a different bias correction. The problem is in the calibration... 

Because of the previously mentioned inadequacy of the function a —l/a, a different value for the parameter %i is required for the set of points (Fig. 135) at each elongation a. These values are —0.90, — 0.73, and —0.56 for a = 1.4, 2.0, and 3.0, respectively. If the function a — l/a were replaced by an empirical representation of the shape of the stress-strain curve, a single value of xi would suffice to represent all of the data within experimental error. This limitation of Eq. (41) relates to an unexplained feature of the stress-strain curve and is... 

Output errors can be especially insidious since the natural tendency of most model users is to accept the observed data values as the "truth" upon which the adequacy and ability of the model will be judged. Model users should develop a healthy, informed scepticism of the observed data, especially when major, unexplained differences between observed and simulated values exist. The FAT workshop described earlier concluded that rt is clearly inappropriate to allocate all differences between predicted and observed values as model errors measurement errors in field data collection programs can be substantial and must be considered. 

The more sophisticated treatment of Ingle and Crouch [7] comes very close but also misses the mark for an unexplained reason they insert the condition ... it is assumed there is no uncertainty in measuring Ert and Eot... . Now in fact this could happen (or at least there could be no variation in AEr) for example, if one reference spectrum was used in conjunction with multiple sample spectra using an FTIR spectrometer. However, that would not be a true indication of the total error of the measurement, since the effect of the noise in the reference reading would have been removed from the calculated SD, whereas the true total error of the reading would in... 

The statistical submodel characterizes the pharmacokinetic variability of the mAb and includes the influence of random - that is, not quantifiable or uncontrollable factors. If multiple doses of the antibody are administered, then three hierarchical components of random variability can be defined inter-individual variability inter-occasional variability and residual variability. Inter-individual variability quantifies the unexplained difference of the pharmacokinetic parameters between individuals. If data are available from different administrations to one patient, inter-occasional variability can be estimated as random variation of a pharmacokinetic parameter (for example, CL) between the different administration periods. For mAbs, this was first introduced in sibrotuzumab data analysis. In order to individualize therapy based on concentration measurements, it is a prerequisite that inter-occasional variability (variability within one patient at multiple administrations) is lower than inter-individual variability (variability between patients). Residual variability accounts for model misspecification, errors in documentation of the dosage regimen or blood sampling time points, assay variability, and other sources of error. 

Processes that are random or statistically independent of each other, such as imperfections in measurement techniques that lead to unexplainable but characterizable variations in repeated measurements of a fixed true value. Some random errors could be reduced by developing improved techniques. 

In Equation 4.1, C is the n x k matrix of pure chromatograms (k independently varying components), P is the m x k matrix of pure-component spectra, and the matrix e contains unexplained variance, e.g., measurement error. Figure 4.1 shows an example of such a data matrix having two overlapped peaks. 

Parametric population methods also obtain estimates of the standard error of the coefficients, providing consistent significance tests for all proposed models. A hierarchy of successive joint runs, improving an objective criterion, leads to a final covariate model for the pharmacokinetic parameters. The latter step reduces the unexplained interindividual randomness in the parameters, achieving an extension of the deterministic component of the pharmacokinetic model at the expense of the random effects. Recently used individual empirical Bayes estimations exhibit more success in targeting a specific individual concentration after the same dose. 

However, the correlation coefficient of 0.7854 for the final curve fitting effort indicates the presence of many unexplained outlier points. One of the possible concerns was an inherent error in measuring the height of the powder bed from the wet mass density. 

Soft errors occur once and disappear after the computer is rebooted. They are usually caused by power fluctuations or single bit errors. The symptoms are typically unexplained problems with software and are not reproducible. Soft errors are like gnats annoying little things you wish you could kill, but they don t stay in one place long enough for you to do so. However, if these errors increase in frequency, it usually indicates a hard memory error is about to occur. 

For each equation, two statistics that describe the adequacy of the equations were calculated—the adjusted coefficient of de-termination(3)(adjusted R ) and the standard error of estimate (SEE). The adjusted R denotes the proportion of the variability observed in the property that was explained in the terms of the equation. The SEE is a measure of the unexplained variability that still existed after the significant effects were taken into account, Table III. 

In several instances the student made multiple errors on a situation and then responded correctly to one final instance of that situation. Although it is very plausible that learning also occurred in these cases, I am uncomfortable in making this conclusion based only on one response. Thus, these errors remain unexplained. 

The second reason for unexpected, unexplained abnormal results is laboratory error. There are two types the random error and the systematic error. 

Unexplained human error is a category that describes human actions that were wrong for no reason recorded in the investigation reports or for which there is no apparent explanation. One example is the operator who assembled a piece of equipment incorrectly. The committee suspected that a more complete investigation would reveal causes for such errors. 

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