Errors, standard

B. Standard Error-Back-Propagation Training Routine 

SEM = standard error of the means. IGF-I = insulin-like growth factor I. 

This gives the standard errors in the fitted parameters a. 

In Eq. (12), SE is the standard error, c is the number of selected variables, p is the total number of variables (which can differ from c), and d is a smoothing parameter to be set by the user. As was mentioned above, there is a certain threshold beyond which an increase in the number of variables results in some decrease in the quality of modeling. In fact, the smoothing parameter reflects the user s guess of how much detail is to be modeled in the training set. 

Standard-abweichung, /. standard deviation, -einheit, /. standard unit, -fehler, m. standard error, -losung, /. standard solution, -wert, m. standard value. 

Another reason for investing in error reduction is to conform with regulatory standards. Error reduction yields regulatory relief. 

The estimate of variability for a sample mean is the standard error of the mean  

The standard deviation gives the accuracy of prediction. If Y is related to one or more predictor variables, the error of prediction is reduced to the standard error of estimate S, (the standard deviation of the errors), where 

There are instances where deviations, as measured by the standard error, are scaled to the magnitude of the mean to yield the coefficient of variation. This is calculated by 

The classification as a carcinogen need not apply to fibres with a length weighted geometric mean diameter less two standard errors greater than 6 pm Sodium dichromate Sodium dichromate dihydrate 

The same results were gained for Cr analysis in high alloyed steels. The error of linear calibration in this case is 0.28%. The application of theoretical corrections decreases this error to 0.07%. The standard error of the linear calibration on the base of the analytical pai ameter Ici.j,yipj,j,p is 0.23% and the application of the theoretical corrections in this case gives error 0.04%. 

The diagonal elements of this matrix approximate the variances of the corresponding parameters. The square roots of these variances are estimates of the standard errors in the parameters and, in effect, are a measure of the uncertainties of those parameters. 

Confidence intervals also can be reported using the mean for a sample of size n, drawn from a population of known O. The standard deviation for the mean value. Ox, which also is known as the standard error of the mean, is 

Example 3 Calculating Sample Weight for Screen-Size Measurement Weight W of bulk sample for screen analysis is calculated by the Gayle model for percent retained on a specified screen with relative standard error s.e. in percent 

In Eq. (14) "est stands for the calculated (estimated) response, exp" for the experimental one, and n and m are the numbers of objects in the training set and the test set respectively. CoSE stands for Compound Standard Error. As an option, one can employ several test sets, if needed. 

This sum, when divided by the number of data points minus the number of degrees of freedom, approximates the overall variance of errors. It is a measure of the overall fit of the equation to the data. Thus, two different models with the same number of adjustable parameters yield different values for this variance when fit to the same data with the same estimated standard errors in the measured variables. Similarly, the same model, fit to different sets of data, yields different values for the overall variance. The differences in these variances are the basis for many standard statistical tests for model and data comparison. Such statistical tests are discussed in detail by Crow et al. (1960) and Brownlee (1965). 

Example 1 Sample Quantity for Composition Quality Control Testing An example is sampling for quality control of a 1,000 metric ton (VFg) trainload of-Ks in (9.4 mm) nominal top-size bentonite. The specification requires silica to be determined with an accuracy of plus or minus three percent for two standard errors (s.e.). With one s.e. of 1.5 percent, V is 0.000225 (one s.e. weight fraction of 0.015 squared). The problem to be solved is thus calculating weight of sample to determine sihca with the specified error variance. 

So how does one infer that two samples come from different populations when only small samples are available The key is the discovery of the t-distribution by Gosset in 1908 (publishing under the pseudonym of Student) and development of the concept by Fisher in 1926. This revolutionary concept enables the estimation of ct ( standard deviation of the population) from values of standard errors of the mean and thus to estimate 

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