Median absolute deviation

A wholly different approach is that of Huber, who orders the values according to size, and determines the median (cf. Section 1.1.1) then the absolute deviations jx, - x l are calculated and also ordered, the median absolute deviation (MAD) being found. MAD is then used as is Sx earlier, the coefficient k being chosen to be between 3 and 5. This algorithm is much more robust than the ones described before. 

MAD median absolute deviation, Huber s outlier test... 

For this type of estimation the results of the measurements have to be arranged in numerical order. Together with the median also robust measures of dispersion, such as median absolute deviation, mad yj = med y, — med yi, and interquantile ranges (Sachs [1992]) should be used. 

Together with a median it has to be said which type of median has been computed (see the footnote in Sect. 4.1.2) and also which kind of uncertainty (derived from median absolute deviation, mad Xi, or quantiles see Danzer [1989] Huber [1981] Hampel et al. [1986] Rousseeuw and Leroy [1987]). 

To calculate the robust standard deviation for this data set, you first have to calculate the absolute difference between each result and the median, x, — median, and then find the median of these values. The median absolute deviation (MAD) is 0.02 %abv. This is converted to a standard deviation equivalent (MADe) by multiplying by 1.483 ... 

A robust counterpart to the standard deviation s is the median absolute deviation (MAD, x mad). 

If the data include outliers, it is advisable to use robust versions of centering and scaling. The simplest possibility is to replace the arithmetic means of the columns by the column medians, and the standard deviations of the columns by the median absolute deviations (MAD), see Sections 1.6.3 and 1.6.4, as shown in the following M-code for a matrix X. 

Finally, a median-based exclusion algorithm has been applied to data obtained with a fully implanted array of four microelectrochemical sensors.38,39 The Z-score was calculated from the values of individual sensors and the median absolute deviation, as shown in equation (8.11), and sensor readings were removed from the data set if the value was greater than one. 

Robust statistics are a set of methods that are largely unaffected by the presence of extreme values. Commonly used statistics of this type are the median and the median absolute deviation (MAD). The median is a measure of the central tendency of the data and can be used to replace the mean value. If the data are normally... 

The median absolute deviation, MAD, is a robust estimate for gauging the spread of the data and similar to the standard deviation. To calculate the MAD value, we use Equation 2.26,... 

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). 

The robust variance estimate can be derived from a statistic related to the unfortunately abbreviated median absolute deviation (MAD ), which is calculated from... 

A method to avoid the sensitivity of the standard deviation to extreme values is to compute the median absolute deviation (MAD), denoted by which replaces the mean by the robust median. It can be computed as follows ... 

Fig. 8 Median absolute deviations for different methods shown only when smaller than 0.4 eV.

It may be worth to notice that PBE, PBEsol and LDA are the methods having the largest median absolute deviation from the median, being 2-3 times worse than the winner, PBEO. Furthermore, Hartree-Fock is the method yielding the worst mean absolute error (6.1 eV, 1 eV larger than the worst method containing a density functional approximation). 

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