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:

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.

In addition, the Sn statistic is supported for the following plots and commands
DIFFERENCE OF SN PLOT Y1 Y2 X
CROSS TABULATE DIFFERENCE OF SN PLOT Y1 Y2 X1 X2
BOOTSTRAP DIFFERENCE OF SN PLOT Y1 Y2
JACKNIFE DIFFERENCE OF SN PLOT Y1 Y2


TABULATE DIFFERENCE OF SN Y X
CROSS TABULATE SN Y X1 X2
LET Z = CROSS TABULATE DIFFERENCE OF SN Y X1 X2

None

None

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.
STATISTIC PLOT	= Generate a statistic versus subset plot.
CROSS TABULATE PLOT	= Generate a statistic versus subset plot (two subset variables).
BOOTSTRAP PLOT	= Generate a bootstrap plot for a statistic.

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

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

Data Analysis

2003/5

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