WINSORIZED STANDARD DEVIATION

WINSORIZED STANDARD DEVIATION (LET)

Let Subcommand

Compute the Winsorized standard deviation of a variable.

The standard variance estimate can be heavily influenced by extreme values. The Winsorized standard deviation compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized standard deviation, the bottom 5% of the values are set equal to the value corresponding to the 5th percentile while the upper 5% of the values are set equal to the value corresponding to the 95th percentile. Then the regular standard deviation formula (HELP STANDARD DEVIATION for details) is applied.

LET <par> = WINSORIZED STANDARD DEVIATION <y1>
                            <SUBSET/EXCEPT/FOR qualification>
where <y1> is the response variable;
              <par> is a parameter where the computed Winsorized standard deviation is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = WINSORIZED STANDARD DEVIATION Y1
LET A = WINSORIZED STANDARD DEVIATION Y1 SUBSET TAG > 2

The analyst must specify the percentages to Winsorize in each tail. This is done by defining the internal variables P1 (the lower tail) and P2 (the upper tail). For example, to Winsorize 10% of each tail, do the following:
LET P1 = 10
LET P2 = 10
LET A = WINSORIZED STANDARD DEVIATION Y

Support for the Winsorized standard deviation has been added to the following plots and commands:
WINSORIZED STANDARD DEVIATION PLOT
BOOTSTRAP WINSORIZED STANDARD DEVIATION PLOT
JACKNIFE WINSORIZED STANDARD DEVIATION PLOT
CROSS TABULATE WINSORIZED STANDARD DEVIATION PLOT
DEX WINSORIZED STANDARD DEVIATION PLOT
WINSORIZED STANDARD DEVIATION INTERACTION STATISTIC PLOT
WINSORIZED STANDARD DEVIATION INFLUENCE CURVE
TABULATE WINSORIZED STANDARD DEVIATION
CROSS TABULATE WINSORIZED STANDARD DEVIATION
LET ... = CROSS TABULATE WINSORIZED STANDARD DEVIATION

None

None

WINSORIZE	= Winsorize a variable.
WINSORIZED VARIANCE	= Compute a Winsorized variance.
WINSORIZED MEAN	= Compute a Winsorized mean.
WINSORIZED COVARIANCE	= Compute a Winsorized covariance.
WINSORIZED CORRELATION	= Compute a Winsorized correlation.
VARIANCE	= Compute the variance.
BIWEIGHT MIDVARIANCE	= Compute the biweight midvariance.

Robust Data Analysis

7/2002

 
LET Y1 = CAUCHY RANDOM NUMBERS FOR I = 1 1 100
LET A1 = STANDARD DEVIATION Y1
LET P1 = 10
LET P2 = 10
LET A2 = WINSORIZED STANDARD DEVIATION Y1
    

 
SKIP 25
READ SPLETT2.DAT Y MACHINE
XTIC OFFSET 0.5 0.5
LABEL CASE ASIS
X1LABEL Machine Manfufacturer
Y1LABEL Absorbed Energy (10% Winsorized SD)
LET P1 = 10
LET P2 = 10
WINSORIZED STANDARD DEVIATION PLOT Y MACHINE