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Robust summaries
Published in Rafael A. Irizarry, Introduction to Data Science, 2019
Another way to robustly estimate the standard deviation in the presence of outliers is to use the median absolute deviation (MAD). To compute the MAD, we first compute the median, and then for each value we compute the distance between that value and the median. The MAD is defined as the median of these distances. For technical reasons not discussed here, this quantity needs to be multiplied by 1.4826 to assure it approximates the actual standard deviation. The mad function already incorporates this correction. For the height data, we get a MAD of: mad(outlier_example) #> [1] 0.237
Statistics
Published in Dušan Teodorović, Miloš Nikolić, Quantitative Methods in Transportation, 2020
Dušan Teodorović, Miloš Nikolić
The Mean Absolute Deviation (MAD) represents the average absolute error in the observations. The MAD equals: MAD=∑i=1n|Ai−Fi|n
Forecasting in the air transport industry
Published in Bijan Vasigh, Ken Fleming, Thomas Tacker, Introduction to Air Transport Economics, 2018
Bijan Vasigh, Ken Fleming, Thomas Tacker
Another measure of forecasting accuracy is Mean Absolute Deviation (MAD). MAD finds the average of the absolute value of the deviations. Since the deviations are not squared, large deviations are not given extra weight. The general formula for MAD is:
Improving the Morrell C-model's accuracy in predicting the ball mills’ power draw based on calculating the dynamic voidage of grinding media
Published in Mineral Processing and Extractive Metallurgy, 2023
Mohammad Hasan Golpayegani, Bahram Rezai
As mentioned above, the static voidage of Bond’s proposed BSDs was also measured. Figure 7 illustrates a comparison of the static voidage of BSDs. As depicted, the minimum and maximum grinding media’s static voidage occur for BSD1 and BSD7, respectively. Moreover, according to Table 3, for all values of Cs and Jt, the grinding media’s dynamic voidage is maximum in BSD7 (in the range of 41.22%–48.98%) and minimum in BSD1 (in the range of 35.61%–40.92%). Since the variation range of spherical particles’ diameter significantly affects bed voidage, a statistical index representing the balls’ dimensional dispersion can contribute to analysing these results. To this end, the mean absolute deviation (MAD) of balls’ diameter as a suitable measure of dispersion was selected. The MAD, a dimensionless statistical index, measures how much the values in a data set are likely to differ from their mean (Christine et al. 2007). Therefore, the following equation, which calculates the MAD of the balls’ diameter, was utilised: where Di is the balls’ diameter values in a given BSD (in millimetres), Dm is the balls’ mean diameter (in millimetres), and n is the number of balls.
A visual–textual fused approach to automated tagging of flood-related tweets during a flood event
Published in International Journal of Digital Earth, 2019
Xiao Huang, Cuizhen Wang, Zhenlong Li, Huan Ning
Due to the short acquisition period of the test dataset (15th August to 15th September) and the ubiquitous existence of extreme values, we apply a modified Z score to statistically evaluate the sensitiveness for each word. The modified Z score measures the outlier strength or how much a score differs from its median instead of mean, hence less influenced by extreme values. It is computed using the Median Absolute Deviation (MAD), modified from Iglewicz and Hoaglin (1993):where is a constant of 0.6745, denotes the occurrence of a certain word on day . denotes the sample median and is the modified Z score on day . MAD is calculated by taking the median of the absolute deviations from the median:
Method for automated detection of outliers in crash simulations
Published in International Journal of Crashworthiness, 2023
David Kracker, Revan Kumar Dhanasekaran, Axel Schumacher, Jochen Garcke
Similar to the standard deviation, the MAD is a measure of the dispersion of the data, but now with respect to the median. To calculate the threshold for outlier detection, the MAD is multiplied by the value a and added to the median. Typical values for a from the literature are 3, 2.5 and 2 [22]. All data exceeding the resulting threshold are marked as outliers. In the following, this procedure is called the MAD method.