
AVERAGE ABSOLUTE DEVIATION FROM THE MEDIANName:
\[ \mbox{AAD} = \frac{\sum_{i=1}^{n}{X_{i}\tilde{X}}}{N} \] where \( \tilde{X} \) is the median of the variable and N is the number of observations. This statistic is sometimes used as an alternative to the standard deviation.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed average absolute deviation is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN Y1 ... SUBSET TAG > 2
Rosner, Bernard (May 1983), "Percentage Points for a Generalized ESD ManyOutlier Procedure", Technometrics, Vol. 25, No. 2, pp. 165172.
. Step 1: Data from Rosner paper (this data contains outliers) . serial read y 0.25 0.68 0.94 1.15 1.20 1.26 1.26 1.34 1.38 1.43 1.49 1.49 1.55 1.56 1.58 1.65 1.69 1.70 1.76 1.77 1.81 1.91 1.94 1.96 1.99 2.06 2.09 2.10 2.14 2.15 2.23 2.24 2.26 2.35 2.37 2.40 2.47 2.54 2.62 2.64 2.90 2.92 2.92 2.93 3.21 3.26 3.30 3.59 3.68 4.30 4.64 5.34 5.42 6.01 end of data . let aad2 = average absolute deviation from the median y let aad = average absolute deviation y let mad = average absolute deviation y let sd = standard deviation y . print "Average Absolute Deviation from the median: ^aad2" print "Average Absolute Deviation: ^aad" print "Median Absolute Deviation: ^mad" print "Standard Deviation: ^sd"The following output is generated Average Absolute Deviation from the median: 0.8248148148 Average Absolute Deviation: 0.8546090535 Median Absolute Deviation: 0.8546090535 Standard Deviation: 1.1828696348  
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Date created: 01/31/2015 