DIFFERENCE OF SN

DIFFERENCE OF SN (LET)

Let Subcommand

Compute the difference the S_n scale estimates for two response variables.

The S_n scale estimate is a robust estimate of scale that is defined as:
\( S_{n} = c \mbox{Median}_{i} \{\mbox{Median}_{j} |x_{i} - x_{j}| \} \)

That is, for each i we compute the median of {|x_i - x_j| j = 1, ..., n}. The median of these n numbers is then the estimate of S_n. The constant c is determined to make S_n a consistent estimator. The value used is 1.1926 (this is the value needed to make S_n a consistent estimator for data from a normal distribution).

The S_n statistic measures typical distances between values (in contrast to the median absolute deviation and the standard deviation which measure the distance from a central location).

Enter HELP SN SCALE for a more detailed discussion of the S_n scale estimate.

For the difference of S_n scale estimates, the S_n scale estimate is computed for each of the two samples then their difference is taken.

LET <par> = DIFFERENCE OF SN <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed difference of S_n scale statistics is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF SN Y1 Y2
LET A = DIFFERENCE OF SN Y1 Y2 SUBSET TAG > 2

Dataplot uses code provided by Rousseeuw and Croux to compute the S_n estimate. This algorithm uses an efficient computational method for computing S_n.

The Rousseeuw and Croux article (see the Reference section below) also proposes the Q_n scale estimate. The article discusses the properties of both estimators in detail.

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

SN SCALE	= Compute the Sn scale estimate of a variable.
QN SCALE	= Compute the Qn scale estimate of a variable.
DIFFERENCE OF MAD	= Compute the difference of the median absolute deviations between two variables.
DIFFERENCE OF IQ RANGE	= Compute the difference of iq ranges between two variables.
DIFFERENCE OF SD	= Compute the difference of standard deviations between two variables.
DIFFERENCE OF QN	= Compute the difference of the Qn scale estimates between two variables.
STATISTICS PLOT	= Generate a statistic versus subset plot.
BOOTSTRAP PLOT	= Generate a bootstrap plot.
TABULATE	= Perform a tabulation for a specified statistic.

Peter J. Rousseuw and Christophe Croux (1993), "Alternatives to the Median Absolute Deviation," Journal of the American Statistical Association, Vol. 88, No. 424, pp. 1273-1283.

Mosteller and Tukey (1977), "Data Analysis and Regression: A Second Course in Statistics," Addison-Wesley, pp. 203-209.

Data Analysis

2003/05

SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET A = DIFFERENCE OF SN Y1 Y2
TABULATE DIFFERENCE OF SN Y1 Y2 X
.
XTIC OFFSET 0.2 0.2
MAJOR XTIC MARK NUMBER 3
MINOR XTIC MARK NUMBER 0
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF SN
CHARACTER X
LINE BLANK
DIFFERENCE OF SN PLOT Y1 Y2 X
CHARACTER X ALL
LINE BLANK ALL
BOOTSTRAP DIFFERENCE OF SN PLOT Y1 Y2 X
    

Dataplot generated the following output.

       **************************************
       **  LET A = DIFFERENCE OF SN Y1 Y2  **
       **************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.47704038E+00
  
  
       *****************************************
       **  TABULATE DIFFERENCE OF SN Y1 Y2 X  **
       *****************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF SN
 **********************************************
     1.00000     *   -0.298023E-06
     2.00000     *    0.238520
     3.00000     *    0.357780