DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN

DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN (LET)

Let Subcommand

Compute the difference between the average absolute deviations from the median for two response variables.

The average absolute deviation from the median is defined as

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

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.

For the difference of average absolute deviations from the median, the average absolute deviation from the median is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the first response variable;
            <par> is a parameter where the computed difference of the average absolute deviations from the median is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN Y1 Y2

Prior to the 2014/07 version, the AVERAGE ABSOLUTE DEVIATION 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 commands
AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN
DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN


to compute differences from the median.

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

None

None

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

Data Analysis

2014/07: Original implementation

 
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET A = DIFFERENCE OF AAD Y1 Y2
SET WRITE DECIMALS 4
TABULATE DIFFERENCE OF AAD Y1 Y2 X
    

The following output is generated

 
            Cross Tabulate DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION
 
(Response Variables: Y1       Y2      )
---------------------------------------------
       X          |   DIFFERENCE OF A
---------------------------------------------
  0.1000000E+01   |    -0.1664000E-01
  0.2000000E+01   |     0.1666400E+00
  0.3000000E+01   |     0.2604000E+00
    

 
.
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF AAD
CHAR X
LINE BLANK
DIFFERENCE OF AAD PLOT Y1 Y2 X
CHAR X ALL
LINE BLANK ALL
BOOTSTRAP DIFFERENCE OF AAD PLOT Y1 Y2 X