Subtraction absolute error

Rule 1. When adding or subtracting measurements with their associated errors, the absolute errors are summed (never subtracted). For instance, in "17.0 0.5 °C", the "0.5 °C" is the absolute error. 

Subtracting a series of numbers leads to a loss in accmacy. Compared to the preceding example, the calculated absolute error is the same but the relative error increases substantially ... 

In addition and subtraction the absolute error in the result can be no less than the absolute error in the least precisely known quantity In the summation at the right, the absolute error in one quantity is 0.1 g in another, 0.01 g and in the third, 0.001 g. 

All the algebraic and geometric methods for optimization presented so far work when either there is no experimental error or it is smaller than the usual absolute differences obtained when the objective functions for two neighboring points are subtracted. When this is not the case, the direct search and gradient methods can cause one to go in circles, and the geometric method may cause the region containing the maximum to be eliminated from further consideration. 

The B score (Brideau et al., 2003) is a robust analog of the Z score after median polish it is more resistant to outliers and also more robust to row- and column-position related systematic errors (Table 14.1). The iterative median polish procedure followed by a smoothing algorithm over nearby plates is used to compute estimates for row and column (in addition to plate) effects that are subtracted from the measured value and then divided by the median absolute deviation (MAD) of the corrected measures to robustly standardize for the plate-to-plate variability of random noise. A similar approach uses a robust linear model to obtain robust estimates of row and column effects. After adjustment, the corrected measures are standardized by the scale estimate of the robust linear model fit to generate a Z statistic referred to as the R score (Wu, Liu, and Sui, 2008). In a related approach to detect and eliminate systematic position-dependent errors, the distribution of Z score-normalized data for each well position over a screening run or subset is fitted to a statistical model as a function of the plate the resulting trend is used to correct the data (Makarenkov et al., 2007). 

In quality control of colored objects, production requires more consistency than absolute accuracy. After all, there will generally be a product standard having the correct color to which we may reference the color of parts from the current production run. Since the production part and the product standard will be free from the small errors in accuracy, because any small inaccuracies will be the same in measurements of the batch and the standard and thus will subtract out in the different components. What is needed is an instrument with higher day-to-day objectivity than our visual system, and for such an increase in consistency, one must be willing to give up some of the absolute accuracy. This requires an analog simulation of visual colorimetry. 

The estimation of the error of a computed result R from the errors of the component terms or factors A, B, and C depends on whether the errors are determinate or random. The propagation of errors in computations is summarized in Table 26-2. The absolute determinate error e or the variance V = s for a random error is transmitted in addition or subtraction. (Note that the variance is additive for both a sum and a difference.) On the other hand, the relative determinate error ejx or square of the relative standard deviation (sJxY is additive in multiplication. The general case R = f A,. ) is valid only if A, B,C,... are independently variable it is... 

An alternative method is to determine changes in total CO2 content of the sea water by monitoring pH, chlorinity, temperature and alkalinity (Park, 1969 Smith and Key, 1975 Smith and Kinsey, 1978) and to derive values for the flux of CO2 through the organic cycle, by subtracting from the total flux that component attributable to the inorganic carbonate flux as determined by alkalinity measurements. These estimates are relatively free from errors caused by diffusion, as CO2 exchange with the atmosphere is much slower than that of O2. However, the absolute precision of the measurement... 

From a knowledge of the uncertainties in each number, it is possible to estimate the actual uncertainty in the answer. The errors in the individual numbers will propagate throughout a series of calculations, in either a relative or an absolute fashion, depending on whether the operation is a multiplication or division or whether it is an addition or a subtraction. 

In computations requiring addition and/or subtraction, the maximum error in the sum or difference is obtained by adding absolute values of the... 

It is however unrealistic to employ this instrument in the high momentum transfer region for absolute studies on anything heavier than Sulphur, mainly because of the core electron contribution. The above spectrometer can be used in comparative studies (difference experiments) where are subtracted out all systematic errors and the core contribution. 

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