 Dataplot Vol 2 Vol 1

# AVERAGE ABSOLUTE DEVIATION

Name:
AVERAGE ABSOLUTE DEVIATION (LET)
Type:
Let Subcommand
Purpose:
Compute the average absolute deviation for a variable.
Description:
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.

Syntax:
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.
Examples:
LET A = AVERAGE ABSOLUTE DEVIATION Y1
LET A = AVERAGE ABSOLUTE DEVIATION Y1 SUBSET TAG > 2
Note:
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.

Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
AAD is a synonym for AVERAGE ABSOLUTE DEVIATION
Related Commands:
 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.
References:
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.

Applications:
Data Analysis
Implementation Date:
Pre-1987 1989/01: Fixed computational bug 2014/07: Compute difference from mean rather than the median
Program:

.  Step 1: Data from Rosner paper (this data contains outliers)
.
-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 from the median:   ^aad2"
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


NIST is an agency of the U.S. Commerce Department.

Date created: 01/31/2015
Last updated: 11/02/2015