AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN

AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN (LET)

Let Subcommand

Compute the average absolute deviation from the median for a variable.

The average absolute deviation from the median is defined as

\[ \mbox{AAD} = \frac{\sum_{i=1}^{n}{|X_{i}-\tilde{X}|}}{N} \]

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.

LET <par> = AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN <y>
                        <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
LET A = AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN Y1 ...             SUBSET TAG > 2

Prior to the 2014/07 version, the AVERAGE ABSOLUTE DEVIATION command computed the average absolute deviation from the median. In the 2014/07 version, the AVERAGE ABSOLUTE DEVIATION command was modified to compute differences from the mean and the AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN command was added to compute differences from the median.

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

AVERAGE ABSOLUTE DEVIATION	=	Compute the average absolute deviation from the mean of a variable.
DIFFERENCE OF AVERAGE ABSOSOLUTE DEVIATION FROM MEDIAN	=	Compute the difference in absolute average deviation from the median of two variables.
DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION	=	Compute the difference in absolute average deviation of two variables.
MEDIAN ABSOLUTE DEVIATION	=	Compute the median absolute deviation of a variable.
STANDARD DEVIATION	=	= Compute the standard deviation of a variable.
VARIANCE	=	Compute the variance of a variable.
RANGE	=	Compute the range of a variable.

Dixon and Massey (1957), "Introduction to Statistical Analysis," Second Edition, McGraw-Hill, pp. 75-76.

Rosner, Bernard (May 1983), "Percentage Points for a Generalized ESD Many-Outlier Procedure", Technometrics, Vol. 25, No. 2, pp. 165-172.

Data Analysis

2014/07: Added as distinct command from AVERAGE ABSOLUTE DEVIATION

.  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