AVERAGE ABSOLUTE DEVIATION

AVERAGE ABSOLUTE DEVIATION (LET)

Let Subcommand

Compute the average absolute deviation for a variable.

The average absolute deviation is defined as

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

with \( \bar{X} \) and N denoting the mean of the variable and the number of observations, respectively. This statistic is sometimes used as an alternative to the standard deviation.

LET <par> = AVERAGE ABSOLUTE DEVIATION <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 Y1
LET A = AVERAGE ABSOLUTE DEVIATION Y1 SUBSET TAG > 2

Prior to the 2014/07 version, this command computed the difference from the median rather than the mean. The 2014/07 version corrected this command to compute differences from the mean and added the command
AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN

to compute differences from the median.

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

None

AAD is a synonym for AVERAGE ABSOLUTE DEVIATION

AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN	=	Compute the average absolute deviation from the median of a variable.
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

Pre-1987 1989/01: Fixed computational bug 2014/07: Compute difference from mean rather than the median

 
.  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 aad  = average absolute deviation y
let aad2 = average absolute deviation from the median y
let mad  = average absolute deviation y
let sd   = standard deviation y
.
print "Average Absolute Deviation:                   ^aad"
print "Average Absolute Deviation from the median:   ^aad2"
print "Median Absolute Deviation:                    ^mad"
print "Standard Deviation:                           ^sd"
    

The following output is generated

Average Absolute Deviation:                   0.8546090535
Average Absolute Deviation from the median:   0.8248148148
Median Absolute Deviation:                    0.8546090535
Standard Deviation:                           1.1828696348